%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SCT171+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n015.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 21:39:02 EDT 2022
% Result : Theorem 2.51s 2.61s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1176
% Syntax : Number of formulae : 12068 (1762 unt; 0 def)
% Number of atoms : 39392 (9797 equ)
% Maximal formula atoms : 152 ( 3 avg)
% Number of connectives : 46566 (19242 ~;23030 |; 868 &)
% ( 412 <=>;3014 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of predicates : 58 ( 56 usr; 1 prp; 0-2 aty)
% Number of functors : 446 ( 446 usr; 45 con; 0-11 aty)
% Number of variables : 40695 (1410 sgn11290 !; 90 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X2,X1,X39,X63,X76,X57,X103,X41,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
=> ( ! [X46] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),X103))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X2,X2,X57,X46)),X41))
& hAPP(X2,X2,X76,hAPP(X2,X2,X57,X46)) = ti(X2,X46) ) )
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X2,X2,X76,X26)),X103))
& hAPP(X2,X2,X57,hAPP(X2,X2,X76,X26)) = ti(X2,X26)
& hAPP(X2,X1,X39,hAPP(X2,X2,X76,X26)) = hAPP(X2,X1,X63,X26) ) )
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X63),X41) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X103) ) ) ) ),
file('<stdin>',fact_757_folding__image_Oeq__general__inverses) ).
fof(c_0_1,axiom,
! [X2,X1,X3] :
( comm_monoid_mult(X3)
=> ! [X99,X39,X38,X76,X57,X103,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ! [X46] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),X103))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X57,X46)),X41))
& hAPP(X1,X2,X76,hAPP(X2,X1,X57,X46)) = ti(X2,X46) ) )
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X41))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X76,X26)),X103))
& hAPP(X2,X1,X57,hAPP(X1,X2,X76,X26)) = ti(X1,X26)
& hAPP(X2,X3,X39,hAPP(X1,X2,X76,X26)) = hAPP(X1,X3,X38,X26) ) )
=> hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X38),X99),X41) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X39),X99),X103) ) ) ) ),
file('<stdin>',fact_710_fold__image__eq__general__inverses) ).
fof(c_0_2,axiom,
! [X2,X1,X76,X39,X41,X42,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X9),X9))
=> ( ! [X18,X100,X101,X102] :
( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X18),X101))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X100),X102)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X18),X100)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X101),X102))) )
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X2,X1,X76,X26)),hAPP(X2,X1,X39,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X41)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X41))) ) ) ) ) ),
file('<stdin>',fact_758_folding__image_Orelated) ).
fof(c_0_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_83__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(c_0_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
file('<stdin>',fact_14_PW) ).
fof(c_0_6,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_7,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_8,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_9,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_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_10,axiom,
! [X2,X1,X42,X41,X26,X27] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X42)),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)))),X41)),X26),X27))
<=> 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),X26),X27)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X42),X41))) ),
file('<stdin>',fact_969_inf__Int__eq2) ).
fof(c_0_11,axiom,
! [X2,X1,X42,X41,X26,X27] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X42)),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)))),X41)),X26),X27))
<=> 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),X26),X27)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X42),X41))) ),
file('<stdin>',fact_818_sup__Un__eq2) ).
fof(c_0_12,axiom,
! [X2,X1] :
( comm_monoid_mult(X1)
=> ! [X76,X39,X41,X42,X99] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X99),X99))
=> ( ! [X18,X100,X101,X102] :
( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X18),X101))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X100),X102)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X18),X100)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X101),X102))) )
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X2,X1,X76,X26)),hAPP(X2,X1,X39,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X76),X99),X41)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X39),X99),X41))) ) ) ) ) ),
file('<stdin>',fact_709_fold__image__related) ).
fof(c_0_13,axiom,
~ ! [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
=> ( ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
=> ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_94__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_14,axiom,
? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
& ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
& hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_93__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_) ).
fof(c_0_15,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_82_n_I3_J) ).
fof(c_0_16,axiom,
! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) ),
file('<stdin>',fact_46_n_I2_J) ).
fof(c_0_17,axiom,
! [X30] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X30))),lab)),lba)),arrow_301600364e_Prof)),
file('<stdin>',fact_42_PiProf) ).
fof(c_0_18,axiom,
! [X1,X2,X42,X41] :
( 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)))),X42)),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)))),X41)))
<=> 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)),X42),X41)) ),
file('<stdin>',fact_161_pred__subset__eq2) ).
fof(c_0_19,axiom,
! [X2,X1,X3] :
( comm_monoid_add(X3)
=> ! [X38,X42,X103,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X103))
=> hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),hAPP(fun(X1,fun(X2,bool)),fun(X1,X3),hAPP(fun(X1,fun(fun(X2,bool),X3)),fun(fun(X1,fun(X2,bool)),fun(X1,X3)),combs(X1,fun(X2,bool),X3),hAPP(fun(X1,fun(X2,X3)),fun(X1,fun(fun(X2,bool),X3)),hAPP(fun(fun(X2,X3),fun(fun(X2,bool),X3)),fun(fun(X1,fun(X2,X3)),fun(X1,fun(fun(X2,bool),X3))),combb(fun(X2,X3),fun(fun(X2,bool),X3),X1),big_co1399186613setsum(X2,X3)),X38)),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X1),collect(X2)),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X1),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X103)))),X42)))),X41) = hAPP(fun(X2,bool),X3,hAPP(fun(X2,X3),fun(fun(X2,bool),X3),big_co1399186613setsum(X2,X3),hAPP(fun(X2,fun(X1,bool)),fun(X2,X3),hAPP(fun(X2,fun(fun(X1,bool),X3)),fun(fun(X2,fun(X1,bool)),fun(X2,X3)),combs(X2,fun(X1,bool),X3),hAPP(fun(X2,fun(X1,X3)),fun(X2,fun(fun(X1,bool),X3)),hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),fun(fun(X2,fun(X1,X3)),fun(X2,fun(fun(X1,bool),X3))),combb(fun(X1,X3),fun(fun(X1,bool),X3),X2),big_co1399186613setsum(X1,X3)),hAPP(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)),combc(X1,X2,X3),X38))),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X2),collect(X1)),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X2),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),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)),X41)))),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),X42))))),X103) ) ) ),
file('<stdin>',fact_892_setsum__setsum__restrict) ).
fof(c_0_20,axiom,
! [X2,X1,X39,X76,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40))
=> hAPP(X2,X1,X39,X26) = hAPP(X2,X1,X76,X26) )
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X40) ) ) ),
file('<stdin>',fact_745_folding__image_Ocong) ).
fof(c_0_21,axiom,
! [X2,X3,X1] :
( semiring_0(X1)
=> ! [X38,X40,X39,X43] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X39),X43)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),hAPP(fun(X3,X1),fun(X2,fun(X3,X1)),hAPP(fun(X2,fun(fun(X3,X1),fun(X3,X1))),fun(fun(X3,X1),fun(X2,fun(X3,X1))),combc(X2,fun(X3,X1),fun(X3,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X3,X1),fun(X3,X1))),hAPP(fun(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X3,X1),fun(X3,X1)))),combb(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),X2),combb(X1,X1,X3)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X38))),X39))),X43)),X40) ),
file('<stdin>',fact_983_setsum__product) ).
fof(c_0_22,axiom,
! [X29,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)),X29))))) = 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,X29))))) ),
file('<stdin>',fact_426_card__less__Suc) ).
fof(c_0_23,axiom,
! [X3,X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X38,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X41) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combb(fun(X1,bool),X2,X3),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X41)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X38)))))),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),X41)) ) ),
file('<stdin>',fact_891_setsum__image__gen) ).
fof(c_0_24,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),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),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)),X40))),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)),X43)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X43))),X38)),zero_zero(X2))),X40) ) ),
file('<stdin>',fact_917_setsum__restrict__set_H) ).
fof(c_0_25,axiom,
! [X2,X1,X38,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( 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),X38),X40)))
=> ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& ~ 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),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)),X40))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X38)),hAPP(X1,X2,X38,X26)))))) ) ) ),
file('<stdin>',fact_521_pigeonhole__infinite) ).
fof(c_0_26,axiom,
! [X29,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)),X29)))) = 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,X29))))) ),
file('<stdin>',fact_428_card__less__Suc2) ).
fof(c_0_27,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X43))),X38)),zero_zero(X2))),X40) ) ),
file('<stdin>',fact_994_setsum__restrict__set) ).
fof(c_0_28,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X15,X14,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
file('<stdin>',fact_988_setsum__delta) ).
fof(c_0_29,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X11,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),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),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)),X40))),X11))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X11)),X38)),zero_zero(X2))),X40) ) ),
file('<stdin>',fact_916_setsum__restrict__set_H_H) ).
fof(c_0_30,axiom,
! [X2,X1,X11,X38,X39,X41] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),X11)),X38)),X39)),X41) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X41),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),X11)))),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X41),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),fNot),X11))))),
file('<stdin>',fact_887_if__image__distrib) ).
fof(c_0_31,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X15,X14,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
file('<stdin>',fact_987_setsum__delta_H) ).
fof(c_0_32,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X38,X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X15)),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X46))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X38,X46))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X14)),X17)) ) ) ) ),
file('<stdin>',fact_192_order__less__le__subst2) ).
fof(c_0_33,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X38,X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X15)),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X46))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X38,X46))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X14)),X17)) ) ) ) ),
file('<stdin>',fact_191_order__le__less__subst2) ).
fof(c_0_34,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X15)),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X17),X15))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X46),X26))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X46)),hAPP(X2,X1,X38,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X17)),X14)) ) ) ) ),
file('<stdin>',fact_188_xt4) ).
fof(c_0_35,axiom,
! [X2,X1] :
( ( order(X1)
& ord(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X15)),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),X15))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X46),X26))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X46)),hAPP(X2,X1,X38,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X17)),X14)) ) ) ) ),
file('<stdin>',fact_187_xt6) ).
fof(c_0_36,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X17,X14,X38,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X15)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X15),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X26),X46))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X26)),hAPP(X2,X1,X38,X46))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X17))) ) ) ) ),
file('<stdin>',fact_190_order__less__le__subst1) ).
fof(c_0_37,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X17,X14,X38,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),hAPP(X2,X1,X38,X15)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X15),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X26),X46))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X26)),hAPP(X2,X1,X38,X46))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X17))) ) ) ) ),
file('<stdin>',fact_189_order__le__less__subst1) ).
fof(c_0_38,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X15)))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X46),X26))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X46)),hAPP(X1,X2,X38,X26))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X14))) ) ) ) ),
file('<stdin>',fact_158_xt7) ).
fof(c_0_39,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X17),hAPP(X1,X2,X38,X15)))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),X26))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X46)),hAPP(X1,X2,X38,X26))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X14))) ) ) ) ),
file('<stdin>',fact_157_xt5) ).
fof(c_0_40,axiom,
! [X10,X11,X12,X13,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X12)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
file('<stdin>',fact_7__C1_C) ).
fof(c_0_41,axiom,
! [X10,X11,X12,X13,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X12)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
file('<stdin>',fact_6__C2_C) ).
fof(c_0_42,axiom,
! [X10,X11,X12,X13,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ),
file('<stdin>',fact_9_pairwise__neutrality) ).
fof(c_0_43,axiom,
! [X29,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,X29))))) != zero_zero(nat) ),
file('<stdin>',fact_427_card__less) ).
fof(c_0_44,axiom,
! [X16] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ) ) ),
file('<stdin>',fact_84__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(c_0_45,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X39)),X76)),one_one(X2)),X40) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X40)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X76),one_one(X2)),X40)) ) ),
file('<stdin>',fact_697_fold__image__distrib) ).
fof(c_0_46,axiom,
! [X2,X3,X1] :
( comm_monoid_add(X1)
=> ! [X38,X43,X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),X38)),X43)),X40) = hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X2,bool),fun(X3,X1),hAPP(fun(X3,fun(fun(X2,bool),X1)),fun(fun(X2,bool),fun(X3,X1)),combc(X3,fun(X2,bool),X1),hAPP(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1)),hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),fun(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1))),combb(fun(X2,X1),fun(fun(X2,bool),X1),X3),big_co1399186613setsum(X2,X1)),hAPP(fun(X2,fun(X3,X1)),fun(X3,fun(X2,X1)),combc(X2,X3,X1),X38))),X40)),X43) ),
file('<stdin>',fact_978_setsum__commute) ).
fof(c_0_47,axiom,
! [X29,X25] :
( hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X25),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
=> ( ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> ! [X19,X20] :
( ti(arrow_2142409994le_alt,X19) != ti(arrow_2142409994le_alt,X20)
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X29)))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26))) ) ) )
=> hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X25),X29)) ) ),
file('<stdin>',fact_81_dictatorI) ).
fof(c_0_48,axiom,
! [X16] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ) ) ),
file('<stdin>',fact_45__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(c_0_49,axiom,
! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_50,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X39,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X40)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X43)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ) ),
file('<stdin>',fact_866_fold__image__Un__Int) ).
fof(c_0_51,axiom,
! [X25] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X25))
<=> ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> ! [X27] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X27),arrow_301600364e_Prof))
=> ! [X19,X20] :
( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X27,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X27))) ) ) ) ) ),
file('<stdin>',fact_23_IIA__def) ).
fof(c_0_52,axiom,
! [X10,X11,X17,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X17)
=> ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X17)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X17)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X17)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ),
file('<stdin>',fact_8__C4_C) ).
fof(c_0_53,axiom,
! [X1,X11,X53] :
( 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),X11)),X53))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) ) ),
file('<stdin>',fact_290_finite__Collect__disjI) ).
fof(c_0_54,axiom,
! [X10,X11,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ),
file('<stdin>',fact_10__C3_C) ).
fof(c_0_55,axiom,
! [X87,X3,X1,X2,X76,X88,X39,X52,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X39),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X43),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X52))))
=> ( hBOOL(hAPP(fun(fun(X3,X87),bool),bool,hAPP(fun(X3,X87),fun(fun(fun(X3,X87),bool),bool),member(fun(X3,X87)),X76),hAPP(fun(X3,fun(X87,bool)),fun(fun(X3,X87),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X87,bool)),fun(fun(X3,X87),bool)),pi(X3,X87),X52),hAPP(fun(X87,bool),fun(X3,fun(X87,bool)),combk(fun(X87,bool),X3),X88))))
=> hAPP(fun(X1,X3),fun(X1,X87),hAPP(fun(X3,X87),fun(fun(X1,X3),fun(X1,X87)),hAPP(fun(X1,bool),fun(fun(X3,X87),fun(fun(X1,X3),fun(X1,X87))),compose(X1,X3,X87),X40),X76),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X40),X39),X38)) = hAPP(fun(X1,X2),fun(X1,X87),hAPP(fun(X2,X87),fun(fun(X1,X2),fun(X1,X87)),hAPP(fun(X1,bool),fun(fun(X2,X87),fun(fun(X1,X2),fun(X1,X87))),compose(X1,X2,X87),X40),hAPP(fun(X2,X3),fun(X2,X87),hAPP(fun(X3,X87),fun(fun(X2,X3),fun(X2,X87)),hAPP(fun(X2,bool),fun(fun(X3,X87),fun(fun(X2,X3),fun(X2,X87))),compose(X2,X3,X87),X43),X76),X39)),X38) ) ) ),
file('<stdin>',fact_565_compose__assoc) ).
fof(c_0_56,axiom,
! [X3,X1,X2,X39,X52,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X39),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X43),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X52))))
=> hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X40),X39),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),X40),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X52)))) ) ),
file('<stdin>',fact_566_funcset__compose) ).
fof(c_0_57,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X38,X103,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X103))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X41),X103)))
=> hAPP(X1,X2,X38,X26) = one_one(X2) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X41),X103)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X41)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X103)) ) ) ) ),
file('<stdin>',fact_968_fold__image__Un__one) ).
fof(c_0_58,axiom,
! [X11,X29] : 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)),X29))))),
file('<stdin>',fact_301_finite__M__bounded__by__nat) ).
fof(c_0_59,axiom,
! [X1,X2,X3,X6,X38,X39,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)))
=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40))))
=> hAPP(X2,X3,hAPP(fun(X3,X2),fun(X2,X3),hAPP(fun(X3,bool),fun(fun(X3,X2),fun(X2,X3)),the_inv_into(X3,X2),X40),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),X6) = hAPP(X2,X3,hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),the_inv_into(X3,X1),X40),X39)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)),X38)),X6) ) ) ),
file('<stdin>',fact_738_the__inv__into__comp) ).
fof(c_0_60,axiom,
! [X1,X2,X3,X6,X38,X39,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)))
=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40))))
=> hAPP(X2,X3,hAPP(fun(X3,X2),fun(X2,X3),hAPP(fun(X3,bool),fun(fun(X3,X2),fun(X2,X3)),hilbert_inv_into(X3,X2),X40),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),X6) = hAPP(X2,X3,hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X40),X39)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)),X38)),X6) ) ) ),
file('<stdin>',fact_737_inv__into__comp) ).
fof(c_0_61,axiom,
! [X1,X42,X41,X26] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X42)),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)),X41)),X26))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X42),X41))) ),
file('<stdin>',fact_897_inf__Int__eq) ).
fof(c_0_62,axiom,
! [X1,X42,X41,X26] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X42)),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)),X41)),X26))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X42),X41))) ),
file('<stdin>',fact_804_sup__Un__eq) ).
fof(c_0_63,axiom,
! [X6,X7,X8,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X8),X14),X15)))
<=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
& ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X14)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X15)),X8)) )
& ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X14)
=> ( ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X14)
=> ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X15)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X7)),X8)) ) )
& ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X14)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
file('<stdin>',fact_91_in__below) ).
fof(c_0_64,axiom,
! [X6,X7,X8,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X8),X14),X15)))
<=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
& ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X15)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X7)),X8)) )
& ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X15)
=> ( ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X14)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X14)),X8)) ) )
& ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X15)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
file('<stdin>',fact_79_in__above) ).
fof(c_0_65,axiom,
! [X2,X1,X43,X52,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> 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),X43,X26)),hAPP(X1,fun(X2,bool),X52,X26))) )
=> 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),X40),X43)),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),X40),X52))) ),
file('<stdin>',fact_258_Pi__mono) ).
fof(c_0_66,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7))),zero_zero(X1)))
<=> ( ti(X1,X6) = zero_zero(X1)
& ti(X1,X7) = zero_zero(X1) ) ) ),
file('<stdin>',fact_686_sum__squares__le__zero__iff) ).
fof(c_0_67,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X34,X35] : ~ 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),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35))),zero_zero(X1))) ),
file('<stdin>',fact_688_not__sum__squares__lt__zero) ).
fof(c_0_68,axiom,
! [X2,X1,X43,X38,X39,X40] :
( ! [X47] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X47),X40))
=> hAPP(X1,X2,X38,X47) = hAPP(X1,X2,X39,X47) )
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
<=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),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),X40),X43))) ) ),
file('<stdin>',fact_272_Pi__cong) ).
fof(c_0_69,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X40)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X40)),
file('<stdin>',fact_886_Un__Int__crazy) ).
fof(c_0_70,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),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),X40),X43))) ),
file('<stdin>',fact_559_restrictI) ).
fof(c_0_71,axiom,
! [X1,X2,X41,X42] :
( ! [X26,X27] :
( 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),X26),X27)),X42))
<=> 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),X26),X27)),X41)) )
<=> ti(fun(product_prod(X1,X2),bool),X42) = ti(fun(product_prod(X1,X2),bool),X41) ),
file('<stdin>',fact_80_pred__equals__eq2) ).
fof(c_0_72,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
file('<stdin>',fact_32_assms_I1_J) ).
fof(c_0_73,axiom,
! [X1,X2] :
( ab_semigroup_mult(X2)
=> ! [X9,X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X1,X2,X39,X26) = hAPP(X1,X2,X76,X26) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),X9),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X76),X9),X40) ) ) ),
file('<stdin>',fact_701_fold__image__cong) ).
fof(c_0_74,axiom,
! [X1,X53,X11] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) )
=> 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),X11)),X53)))) ),
file('<stdin>',fact_284_finite__Collect__conjI) ).
fof(c_0_75,axiom,
! [X66,X38] :
( ! [X44] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),hAPP(nat,nat,X38,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)),X38)),X66)))) ),
file('<stdin>',fact_314_finite__less__ub) ).
fof(c_0_76,axiom,
! [X2,X1,X39,X76,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),X38),X39)),X76)),X40) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X40)) ) ),
file('<stdin>',fact_742_folding__image_Odistrib) ).
fof(c_0_77,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43))) ),
file('<stdin>',fact_273_Pi__I_H) ).
fof(c_0_78,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43))) ),
file('<stdin>',fact_149_Pi__I) ).
fof(c_0_79,axiom,
! [X1,X2,X38,X40,X43] : 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),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X40),X43))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X43)))),
file('<stdin>',fact_918_image__Int__subset) ).
fof(c_0_80,axiom,
! [X2,X1,X38,X40,X43] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X40),X38)),X43)),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),X43),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X40)))) ),
file('<stdin>',fact_546_inv__into__funcset) ).
fof(c_0_81,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),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)),X14)),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ) ),
file('<stdin>',fact_532_Ints__odd__less__0) ).
fof(c_0_82,axiom,
! [X1] :
( linord1278240602ring_1(X1)
=> ! [X89,X90,X35,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X90))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X89))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X90),X89) = one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X90),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X89),X35))),X21)) ) ) ) ) ) ),
file('<stdin>',fact_698_convex__bound__le) ).
fof(c_0_83,axiom,
! [X1] :
( linord626643107strict(X1)
=> ! [X89,X90,X35,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X90))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X89))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X90),X89) = one_one(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),times_times(X1),X90),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X89),X35))),X21)) ) ) ) ) ) ),
file('<stdin>',fact_570_convex__bound__lt) ).
fof(c_0_84,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43)))) ),
file('<stdin>',fact_560_restrict__in__funcset) ).
fof(c_0_85,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)))) ),
file('<stdin>',fact_873_distrib__inf__le) ).
fof(c_0_86,axiom,
! [X2,X1,X38,X39,X71,X60] :
( ti(fun(X1,bool),X71) = ti(fun(X1,bool),X60)
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X60))
=> hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X71) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X39),X60) ) ),
file('<stdin>',fact_713_image__cong) ).
fof(c_0_87,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = 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),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)),X40))),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)),X43))),
file('<stdin>',fact_907_Int__def) ).
fof(c_0_88,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = 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),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)),X40))),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)),X43))),
file('<stdin>',fact_792_Un__def) ).
fof(c_0_89,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X113,X54,X30] :
( 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),X30),one_one(nat))))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X113))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X113)))) ) ),
file('<stdin>',fact_867_setsum__ub__add__nat) ).
fof(c_0_90,axiom,
! [X2,X1,X43,X40,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X43),X40))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,X25,X43)),hAPP(fun(X2,bool),X1,X25,X40)) = hAPP(fun(X2,bool),X1,X25,X40) ) ) ),
file('<stdin>',fact_306_folding__image__simple__idem_Osubset__idem) ).
fof(c_0_91,axiom,
! [X2,X1,X43,X40,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hAPP(fun(X2,bool),X1,X25,hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X40),X43)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,X25,X40)),hAPP(fun(X2,bool),X1,X25,X43)) ) ) ),
file('<stdin>',fact_808_folding__image__simple__idem_Ounion__idem) ).
fof(c_0_92,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43)))) ),
file('<stdin>',fact_270_funcsetI) ).
fof(c_0_93,axiom,
! [X2,X1,X6,X40,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X40))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(X2,X1,X39,X6)),hAPP(fun(X2,bool),X1,X25,X40)) = hAPP(fun(X2,bool),X1,X25,X40) ) ) ),
file('<stdin>',fact_312_folding__image__simple__idem_Oin__idem) ).
fof(c_0_94,axiom,
! [X1,X2,X39,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X39),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),X43),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X40))))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X39),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X2,bool),nat,finite_card(X2),X43) ) ) ) ) ) ),
file('<stdin>',fact_277_card__bij) ).
fof(c_0_95,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
=> 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),X38),X40)),X43)) ),
file('<stdin>',fact_530_image__subsetI) ).
fof(c_0_96,axiom,
! [X25] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X25))
<=> ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> ! [X19,X20] :
( ! [X16] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X16)))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26))) ) ) ),
file('<stdin>',fact_24_unanimity__def) ).
fof(c_0_97,axiom,
! [X1,X2,X39,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( 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),X38),X40)),X43))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),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(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),X43)),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X2,bool),nat,finite_card(X2),X43) ) ) ) ) ) ),
file('<stdin>',fact_508_card__bij__eq) ).
fof(c_0_98,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)))) ),
file('<stdin>',fact_874_distrib__sup__le) ).
fof(c_0_99,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X39)),X76)),X40) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X76),X40)) ) ),
file('<stdin>',fact_989_setsum_Odistrib) ).
fof(c_0_100,axiom,
! [X2,X1,X6,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X6),X6) = ti(X1,X6) ),
file('<stdin>',fact_307_folding__image__simple__idem_Oidem) ).
fof(c_0_101,axiom,
! [X2,X1] :
( comm_monoid_add(X1)
=> ! [X38,X39,X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),plus_plus(X1)),X38)),X39)),X40) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X39),X40)) ),
file('<stdin>',fact_980_setsum__addf) ).
fof(c_0_102,axiom,
! [X2,X1,X39,X38,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( hAPP(X1,X2,X39,hAPP(X1,X1,X38,X26)) = hAPP(X1,X2,X39,hAPP(X1,X1,X38,X27))
<=> hAPP(X1,X2,X39,X26) = hAPP(X1,X2,X39,X27) ) ) )
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),X40)) ) ) ),
file('<stdin>',fact_525_inj__on__image__iff) ).
fof(c_0_103,axiom,
! [X1,X42,X38,X6,X7] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7)))
=> ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),X42))
=> hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X38),X42))) ) ),
file('<stdin>',fact_753_mlex__leq) ).
fof(c_0_104,axiom,
! [X2,X1] :
( semiring_0(X1)
=> ! [X38,X40,X106] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),X106) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X38)),X106)),X40) ),
file('<stdin>',fact_982_setsum__left__distrib) ).
fof(c_0_105,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),X38),X40))),hAPP(fun(X2,bool),nat,finite_card(X2),X40)))
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40)) ),
file('<stdin>',fact_501_pigeonhole) ).
fof(c_0_106,axiom,
! [X8,X6,X7] :
( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X8),X6),X7)),arrow_1568854078le_Lin)) ) ),
file('<stdin>',fact_140_below__Lin) ).
fof(c_0_107,axiom,
! [X8,X6,X7] :
( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X8),X6),X7)),arrow_1568854078le_Lin)) ) ),
file('<stdin>',fact_51_above__Lin) ).
fof(c_0_108,axiom,
! [X1,X2,X43,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> 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)),the_inv_into(X1,X2),X40),X38),X6)),X43)) ) ) ),
file('<stdin>',fact_547_the__inv__into__into) ).
fof(c_0_109,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X7] :
( 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7))))
<=> ( ti(X1,X6) != zero_zero(X1)
| ti(X1,X7) != zero_zero(X1) ) ) ),
file('<stdin>',fact_687_sum__squares__gt__zero__iff) ).
fof(c_0_110,axiom,
! [X1,X2,X6,X11,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( ! [X46] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),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)))))
=> hBOOL(hAPP(X1,bool,X11,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),top_top(fun(X1,bool))),X38),X46))) )
=> hBOOL(hAPP(X1,bool,X11,X6)) ) ),
file('<stdin>',fact_511_inj__transfer) ).
fof(c_0_111,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
file('<stdin>',fact_668_Suc__mult__le__cancel1) ).
fof(c_0_112,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
file('<stdin>',fact_665_Suc__mult__less__cancel1) ).
fof(c_0_113,axiom,
! [X6,X7,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
=> ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X7),X6)),X8)) ) ) ),
file('<stdin>',fact_47_notin__Lin__iff) ).
fof(c_0_114,axiom,
! [X14,X15,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X8))
=> ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),X8)) ) ),
file('<stdin>',fact_48_Lin__irrefl) ).
fof(c_0_115,axiom,
! [X1,X42,X41] :
( 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)),X42)),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)),X41)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X42),X41)) ),
file('<stdin>',fact_214_pred__subset__eq) ).
fof(c_0_116,axiom,
! [X2,X1,X39,X76,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X2),fun(fun(X2,bool),bool),inj_on(X2,X2),X76),X40))
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,bool)),image(X2,X2),X76),X40)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,hAPP(fun(X2,X2),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X2),fun(X2,X1)),comp(X2,X1,X2),X39),X76)),X40) ) ) ),
file('<stdin>',fact_739_folding__image_Oreindex) ).
fof(c_0_117,axiom,
! [X1,X2,X3,X40,X38,X39] : hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X38),X39)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40))),
file('<stdin>',fact_672_compose__extensional) ).
fof(c_0_118,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X40),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X43)),X38) = ti(fun(X1,X2),X38) ) ),
file('<stdin>',fact_569_Id__compose) ).
fof(c_0_119,axiom,
! [X3,X1,X2,X38,X39] :
( 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),X39),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),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),combb(X1,X3,X2),X38),X39)),top_top(fun(X2,bool))))) ),
file('<stdin>',fact_490_finite__range__imageI) ).
fof(c_0_120,axiom,
! [X2,X1,X3] :
( ab_semigroup_mult(X3)
=> ! [X39,X9,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X76),X40))
=> hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X39),X9),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X76),X40)) = hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X39),X76)),X9),X40) ) ) ),
file('<stdin>',fact_718_fold__image__reindex) ).
fof(c_0_121,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X40),X43)),finite_psubset(X1)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ) ),
file('<stdin>',fact_746_in__finite__psubset) ).
fof(c_0_122,axiom,
! [X2,X1,X39,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),X38),X39),X9),X40) ) ),
file('<stdin>',fact_744_folding__image_Oeq__fold) ).
fof(c_0_123,axiom,
! [X6,X7,X8,X9] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X8),X9)))
<=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X9)
& ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X9)
=> ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7) )
& ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X9)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ),
file('<stdin>',fact_5_in__mktop) ).
fof(c_0_124,axiom,
! [X6,X7,X8,X9] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X8),X9)))
<=> ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X9)
& ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X9)
=> ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7) )
& ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X9)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ),
file('<stdin>',fact_4_in__mkbot) ).
fof(c_0_125,axiom,
! [X1,X2,X39,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X40),X39),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X40)) = ti(fun(X1,X2),X39) ) ),
file('<stdin>',fact_568_compose__Id) ).
fof(c_0_126,axiom,
! [X1,X2,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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),X40),X38),X6)),X40)) ),
file('<stdin>',fact_475_inv__into__into) ).
fof(c_0_127,axiom,
! [X54,X57,X38] :
( ! [X33,X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X44))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X38,X33)),hAPP(nat,nat,X38,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,X38,X54)),X57)),hAPP(nat,nat,X38,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)))) ),
file('<stdin>',fact_260_mono__nat__linear__lb) ).
fof(c_0_128,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_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_129,axiom,
! [X1] :
( order(X1)
=> ! [X30,X54,X38] :
( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X54)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54)) ) ) ),
file('<stdin>',fact_434_lift__Suc__mono__less__iff) ).
fof(c_0_130,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> 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),X38),X40)),X43)) ),
file('<stdin>',fact_492_funcset__image) ).
fof(c_0_131,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
file('<stdin>',fact_856_sup2E) ).
fof(c_0_132,axiom,
! [X1,X2,X40,X43,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ) ),
file('<stdin>',fact_497_inj__image__subset__iff) ).
fof(c_0_133,axiom,
! [X1] :
( order(X1)
=> ! [X30,X72,X38] :
( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X72))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X72))) ) ) ),
file('<stdin>',fact_435_lift__Suc__mono__less) ).
fof(c_0_134,axiom,
! [X1] :
( order(X1)
=> ! [X30,X72,X38] :
( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X72))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X72))) ) ) ),
file('<stdin>',fact_433_lift__Suc__mono__le) ).
fof(c_0_135,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X57,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) ),
file('<stdin>',fact_890_setsum__shift__bounds__nat__ivl) ).
fof(c_0_136,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X57,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) ),
file('<stdin>',fact_888_setsum__shift__bounds__cl__nat__ivl) ).
fof(c_0_137,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X43)) ) ) ),
file('<stdin>',fact_995_setsum__Un__Int) ).
fof(c_0_138,axiom,
! [X3,X1,X2,X105,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X105),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X105),X38)),X40)) ) ),
file('<stdin>',fact_724_comp__inj__on__iff) ).
fof(c_0_139,axiom,
! [X1] :
( semiring(X1)
=> ! [X21,X96,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X96)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X96)),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X96)),X37) ),
file('<stdin>',fact_617_combine__common__factor) ).
fof(c_0_140,axiom,
! [X40,X57] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X40),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),X40)))))
=> X40 = 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),X40))) ),
file('<stdin>',fact_489_subset__card__intvl__is__intvl) ).
fof(c_0_141,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) ),
file('<stdin>',fact_975_inf2D1) ).
fof(c_0_142,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ),
file('<stdin>',fact_974_inf2D2) ).
fof(c_0_143,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> ~ ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
file('<stdin>',fact_972_inf2E) ).
fof(c_0_144,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
file('<stdin>',fact_274_card__inj) ).
fof(c_0_145,axiom,
! [X2,X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> ( ? [X84] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X84),X40))
& 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),X84),X40)),X43)) )
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
file('<stdin>',fact_510_inj__on__iff__card__le) ).
fof(c_0_146,axiom,
! [X58,X90,X59,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X90)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X90)),X50)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X90)),X50),
file('<stdin>',fact_708_left__add__mult__distrib) ).
fof(c_0_147,axiom,
! [X2,X1,X40,X38,X6,X7] :
( 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),X40),X38),X6) = 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),X40),X38),X7)
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> ti(X2,X6) = ti(X2,X7) ) ) ),
file('<stdin>',fact_476_inv__into__injective) ).
fof(c_0_148,axiom,
! [X1] :
( order(X1)
=> ! [X14,X15,X17,X81] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81))
& ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X14))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) )
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X81)) ) ) ),
file('<stdin>',fact_769_atLeastatMost__psubset__iff) ).
fof(c_0_149,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( 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),X38),X40)),X43))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
file('<stdin>',fact_509_card__inj__on__le) ).
fof(c_0_150,axiom,
! [X1,X2,X6,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),X43)) ) ),
file('<stdin>',fact_143_funcset__mem) ).
fof(c_0_151,axiom,
! [X1,X2,X3,X39,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X39),X38)),X40))
=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X39),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),X40))) ),
file('<stdin>',fact_722_inj__on__imageI) ).
fof(c_0_152,axiom,
! [X2,X1,X43,X48,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X48),X40))
=> 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),X40),X43)),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),X48),X43))) ),
file('<stdin>',fact_160_Pi__anti__mono) ).
fof(c_0_153,axiom,
! [X3,X1,X2,X39,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X39),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X39),X38)),X40)) ) ),
file('<stdin>',fact_723_comp__inj__on) ).
fof(c_0_154,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X113,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X113))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X30),X113))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X113)) ) ) ),
file('<stdin>',fact_955_setsum__add__nat__ivl) ).
fof(c_0_155,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff) ).
fof(c_0_156,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff) ).
fof(c_0_157,axiom,
! [X1] :
( order(X1)
=> ! [X14,X15,X17,X81] :
( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_762_atLeastatMost__subset__iff) ).
fof(c_0_158,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr1471790799AtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff) ).
fof(c_0_159,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr676655987ssThan(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff) ).
fof(c_0_160,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr676655987ssThan(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff) ).
fof(c_0_161,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr1471790799AtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff) ).
fof(c_0_162,axiom,
! [X1,X2,X39,X38,X40] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
=> ti(fun(X1,X2),X38) = ti(fun(X1,X2),X39) ) ) ),
file('<stdin>',fact_711_extensionalityI) ).
fof(c_0_163,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X34,X35] : 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35)))) ),
file('<stdin>',fact_685_sum__squares__ge__zero) ).
fof(c_0_164,axiom,
! [X1,X42,X38,X6,X7] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7)))
=> hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X38),X42))) ),
file('<stdin>',fact_754_mlex__less) ).
fof(c_0_165,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14))
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
file('<stdin>',fact_491_atLeastLessThan__subset__iff) ).
fof(c_0_166,axiom,
! [X2,X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),X38),X40))),hAPP(fun(X1,bool),nat,finite_card(X1),X40))) ),
file('<stdin>',fact_498_card__image__le) ).
fof(c_0_167,axiom,
! [X1,X6,X7,X38] :
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X38)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7))) ),
file('<stdin>',fact_748_in__measure) ).
fof(c_0_168,axiom,
! [X2,X1,X38,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> ? [X85] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X85),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X85))
& ti(fun(X1,bool),X43) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X85) ) ) ),
file('<stdin>',fact_514_finite__subset__image) ).
fof(c_0_169,axiom,
! [X1,X43,X88,X40,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X88))
=> 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X88))) ) ),
file('<stdin>',fact_909_Int__mono) ).
fof(c_0_170,axiom,
! [X1,X43,X88,X40,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X88))
=> 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X88))) ) ),
file('<stdin>',fact_788_Un__mono) ).
fof(c_0_171,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( 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),X38),X40)),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40) = ti(fun(X1,bool),X40) ) ) ),
file('<stdin>',fact_494_endo__inj__surj) ).
fof(c_0_172,axiom,
! [X2,X1,X43,X40,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ) ),
file('<stdin>',fact_973_inf2I) ).
fof(c_0_173,axiom,
! [X1,X2,X6,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6))) ) ),
file('<stdin>',fact_139_Pi__mem) ).
fof(c_0_174,axiom,
! [X1,X2,X6,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
=> ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6)))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40)) ) ),
file('<stdin>',fact_87_PiE) ).
fof(c_0_175,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
<=> ? [X79] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X79),X40))
& ti(fun(X1,bool),X43) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X79) ) ),
file('<stdin>',fact_463_subset__image__iff) ).
fof(c_0_176,axiom,
! [X1,X2,X40,X38,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43))) ) ),
file('<stdin>',fact_488_inj__on__strict__subset) ).
fof(c_0_177,axiom,
! [X1,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
=> ( 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),X11))))
<=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ) ),
file('<stdin>',fact_298_finite__Collect__not) ).
fof(c_0_178,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ) ),
file('<stdin>',fact_684_mult__left__le__imp__le) ).
fof(c_0_179,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ) ),
file('<stdin>',fact_683_mult__right__le__imp__le) ).
fof(c_0_180,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
file('<stdin>',fact_682_mult__less__imp__less__left) ).
fof(c_0_181,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
file('<stdin>',fact_681_mult__left__less__imp__less) ).
fof(c_0_182,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
file('<stdin>',fact_680_mult__less__imp__less__right) ).
fof(c_0_183,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
file('<stdin>',fact_679_mult__right__less__imp__less) ).
fof(c_0_184,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ) ),
file('<stdin>',fact_673_mult__le__cancel__left__pos) ).
fof(c_0_185,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ) ),
file('<stdin>',fact_639_mult__less__cancel__left__pos) ).
fof(c_0_186,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14)) ) ) ),
file('<stdin>',fact_674_mult__le__cancel__left__neg) ).
fof(c_0_187,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ),
file('<stdin>',fact_645_mult__less__cancel__left__neg) ).
fof(c_0_188,axiom,
! [X1,X2,X3,X105,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X105),X38)),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X38),X40)) ),
file('<stdin>',fact_726_inj__on__imageI2) ).
fof(c_0_189,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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),X40),X38)),X43)) ),
file('<stdin>',fact_503_inj__on__inv__into) ).
fof(c_0_190,axiom,
! [X1,X2,X15,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> ~ ! [X26] :
( ti(X1,X15) = hAPP(X2,X1,X38,X26)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40)) ) ),
file('<stdin>',fact_512_imageE) ).
fof(c_0_191,axiom,
! [X1,X2,X9,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X9),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
<=> ? [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40))
& ti(X1,X9) = hAPP(X2,X1,X38,X26) ) ),
file('<stdin>',fact_468_image__iff) ).
fof(c_0_192,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
file('<stdin>',fact_678_mult__le__less__imp__less) ).
fof(c_0_193,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
file('<stdin>',fact_677_mult__less__le__imp__less) ).
fof(c_0_194,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
file('<stdin>',fact_676_mult__strict__mono_H) ).
fof(c_0_195,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
file('<stdin>',fact_675_mult__strict__mono) ).
fof(c_0_196,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
file('<stdin>',fact_633_mult__mono) ).
fof(c_0_197,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
file('<stdin>',fact_632_mult__mono_H) ).
fof(c_0_198,axiom,
! [X2,X1,X42,X6,X7] :
( 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),X42),X6),X7))
<=> 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),X6),X7)),X42)) ),
file('<stdin>',fact_269_in__rel__def) ).
fof(c_0_199,axiom,
! [X54,X30,X57] :
( 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ) ),
file('<stdin>',fact_705_nat__mult__less__cancel1) ).
fof(c_0_200,axiom,
! [X54,X30,X57] :
( 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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ) ),
file('<stdin>',fact_704_nat__mult__le__cancel1) ).
fof(c_0_201,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> ( 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_eq(nat),X54),X30)) ) ),
file('<stdin>',fact_696_mult__le__cancel1) ).
fof(c_0_202,axiom,
! [X54,X57,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)))
<=> ( 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_eq(nat),X54),X30)) ) ),
file('<stdin>',fact_695_mult__le__cancel2) ).
fof(c_0_203,axiom,
! [X1,X2,X43,X40,X38,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) ) ) ),
file('<stdin>',fact_957_inj__on__image__Int) ).
fof(c_0_204,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ) ),
file('<stdin>',fact_638_mult__less__cancel__left__disj) ).
fof(c_0_205,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X17,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X17)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ) ),
file('<stdin>',fact_637_mult__less__cancel__right__disj) ).
fof(c_0_206,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> 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))),X40)))) ),
file('<stdin>',fact_278_finite__Collect__subsets) ).
fof(c_0_207,axiom,
! [X3,X2,X1,X39,X52,X38,X40,X43] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
=> ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X39),X43) = ti(fun(X3,bool),X52)
=> 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)),hAPP(fun(X2,bool),fun(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3))),compose(X2,X1,X3),X40),X39),X38)),X40) = ti(fun(X3,bool),X52) ) ),
file('<stdin>',fact_564_surj__compose) ).
fof(c_0_208,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ),
file('<stdin>',fact_963_card_Ounion__inter) ).
fof(c_0_209,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
file('<stdin>',fact_962_card__Un__Int) ).
fof(c_0_210,axiom,
! [X3,X1,X2,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,bool),bool),inj_on(X1,fun(X3,X2)),hAPP(fun(X1,X2),fun(X1,fun(X3,X2)),hAPP(fun(X2,fun(X3,X2)),fun(fun(X1,X2),fun(X1,fun(X3,X2))),combb(X2,fun(X3,X2),X1),combk(X2,X3)),X38)),top_top(fun(X1,bool)))) ),
file('<stdin>',fact_90_inj__fun) ).
fof(c_0_211,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X30,X54] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X30))) ) ) ),
file('<stdin>',fact_965_setsum__cl__ivl__Suc) ).
fof(c_0_212,axiom,
! [X3,X1,X2,X39,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X39),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))),X38))),X38) = ti(fun(X1,X3),X39) ),
file('<stdin>',fact_736_o__inv__o__cancel) ).
fof(c_0_213,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
file('<stdin>',fact_859_sup2I2) ).
fof(c_0_214,axiom,
! [X2,X1,X43,X40,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
file('<stdin>',fact_858_sup2I1) ).
fof(c_0_215,axiom,
! [X2,X1,X40,X43,X6,X7] :
( ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) )
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
file('<stdin>',fact_857_sup2CI) ).
fof(c_0_216,axiom,
! [X6,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X8),X6)),arrow_1568854078le_Lin)) ),
file('<stdin>',fact_50_mkbot__Lin) ).
fof(c_0_217,axiom,
! [X6,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X8),X6)),arrow_1568854078le_Lin)) ),
file('<stdin>',fact_49_mktop__Lin) ).
fof(c_0_218,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),X40))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
file('<stdin>',fact_551_inj__on__restrict__eq) ).
fof(c_0_219,axiom,
! [X3,X1,X2,X39,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),top_top(fun(X3,bool))))
=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),top_top(fun(X3,bool)))) ) ),
file('<stdin>',fact_721_inj__comp) ).
fof(c_0_220,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X14,X17,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X17)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ),
file('<stdin>',fact_185_add__less__cancel__right) ).
fof(c_0_221,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ),
file('<stdin>',fact_184_add__less__cancel__left) ).
fof(c_0_222,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
file('<stdin>',fact_180_add__less__imp__less__right) ).
fof(c_0_223,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
file('<stdin>',fact_179_add__less__imp__less__left) ).
fof(c_0_224,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X14,X17,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X17)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ),
file('<stdin>',fact_178_add__le__cancel__right) ).
fof(c_0_225,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ),
file('<stdin>',fact_177_add__le__cancel__left) ).
fof(c_0_226,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ),
file('<stdin>',fact_173_add__le__imp__le__right) ).
fof(c_0_227,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ),
file('<stdin>',fact_172_add__le__imp__le__left) ).
fof(c_0_228,axiom,
! [X1,X11,X53] : 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),X11)),X53)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53)),
file('<stdin>',fact_895_Collect__conj__eq) ).
fof(c_0_229,axiom,
! [X1,X11,X53] : 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),X11)),X53)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53)),
file('<stdin>',fact_805_Collect__disj__eq) ).
fof(c_0_230,axiom,
! [X2,X1,X38,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> 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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43))) ),
file('<stdin>',fact_462_image__mono) ).
fof(c_0_231,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ),
file('<stdin>',fact_556_inj__on__the__inv__into) ).
fof(c_0_232,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> ( 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),X54),X30)) ) ),
file('<stdin>',fact_663_mult__less__cancel1) ).
fof(c_0_233,axiom,
! [X54,X57,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)))
<=> ( 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),X54),X30)) ) ),
file('<stdin>',fact_662_mult__less__cancel2) ).
fof(c_0_234,axiom,
! [X57,X54,X30] :
( 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),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
file('<stdin>',fact_250_nat__add__left__cancel__le) ).
fof(c_0_235,axiom,
! [X57,X54,X30] :
( 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),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
file('<stdin>',fact_235_nat__add__left__cancel__less) ).
fof(c_0_236,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X38,X39] :
( ! [X26] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)))
=> hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39)) ) ),
file('<stdin>',fact_186_le__funI) ).
fof(c_0_237,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
<=> ! [X26] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26))) ) ),
file('<stdin>',fact_110_le__fun__def) ).
fof(c_0_238,axiom,
! [X1,X11,X40,X43] :
( ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
& hBOOL(hAPP(X1,bool,X11,X26)) )
<=> ( ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& hBOOL(hAPP(X1,bool,X11,X26)) )
| ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43))
& hBOOL(hAPP(X1,bool,X11,X26)) ) ) ),
file('<stdin>',fact_798_bex__Un) ).
fof(c_0_239,axiom,
! [X1,X2,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> hAPP(X1,X2,X38,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X7)) = ti(X2,X7) ) ),
file('<stdin>',fact_558_f__the__inv__into__f) ).
fof(c_0_240,axiom,
! [X2,X1,X38,X40,X43] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
=> hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X43),X38),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X40),X38)),X43)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X43) ),
file('<stdin>',fact_562_compose__id__inv__into) ).
fof(c_0_241,axiom,
! [X1,X11,X40,X43] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
=> hBOOL(hAPP(X1,bool,X11,X26)) )
<=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(X1,bool,X11,X26)) )
& ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43))
=> hBOOL(hAPP(X1,bool,X11,X26)) ) ) ),
file('<stdin>',fact_799_ball__Un) ).
fof(c_0_242,axiom,
! [X1,X2,X14,X40,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X40)) ) ),
file('<stdin>',fact_481_inj__image__mem__iff) ).
fof(c_0_243,axiom,
! [X1,X43,X40,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),X52)) ) ),
file('<stdin>',fact_787_Un__least) ).
fof(c_0_244,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X17,X81,X14,X15] :
( ( ti(X1,X14) != ti(X1,X15)
& ti(X1,X17) != ti(X1,X81) )
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X81)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X81)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X17)) ) ),
file('<stdin>',fact_580_crossproduct__noteq) ).
fof(c_0_245,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X91,X7,X6,X9] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X91),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X9)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X91),X9)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X7))
<=> ( ti(X1,X91) = ti(X1,X6)
| ti(X1,X7) = ti(X1,X9) ) ) ),
file('<stdin>',fact_577_crossproduct__eq) ).
fof(c_0_246,axiom,
! [X2,X1,X82,X38,X40,X48] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X48)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X82),X48))
=> hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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),X40),X38)),X82)) = ti(fun(X1,bool),X82) ) ),
file('<stdin>',fact_484_image__inv__into__cancel) ).
fof(c_0_247,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X54))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X30)) ) ),
file('<stdin>',fact_694_one__le__mult__iff) ).
fof(c_0_248,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51))) ) ),
file('<stdin>',fact_693_one__less__mult) ).
fof(c_0_249,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X30,X54] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(nat,X1,X38,X30)) ) ) ),
file('<stdin>',fact_964_setsum__op__ivl__Suc) ).
fof(c_0_250,axiom,
! [X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X8)),arrow_301600364e_Prof)) ),
file('<stdin>',fact_52_const__Lin__Prof) ).
fof(c_0_251,axiom,
! [X1] :
( linord1117847801e_zero(X1)
=> ! [X34,X35] :
( ! [X98] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X98))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X98),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X98),X34)),X35)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
file('<stdin>',fact_699_field__le__mult__one__interval) ).
fof(c_0_252,axiom,
! [X1,X40,X43,X52] :
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X40)) ),
file('<stdin>',fact_875_Un__Int__assoc__eq) ).
fof(c_0_253,axiom,
! [X2,X1,X38,X39,X40] :
( ! [X19] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40))
=> hAPP(X1,X2,X38,X19) = hAPP(X1,X2,X39,X19) )
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),X40)) ) ),
file('<stdin>',fact_318_inj__on__cong) ).
fof(c_0_254,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X38,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X54)),X30))) ) ),
file('<stdin>',fact_961_setsum__head__Suc) ).
fof(c_0_255,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X38,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X54)),X30))) ) ),
file('<stdin>',fact_960_setsum__head__upt__Suc) ).
fof(c_0_256,axiom,
! [X25,X29] :
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X25),X29))
<=> ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X29) ) ),
file('<stdin>',fact_34_dictator__def) ).
fof(c_0_257,axiom,
! [X1] :
( linord893533164strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
file('<stdin>',fact_650_comm__mult__strict__left__mono) ).
fof(c_0_258,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
file('<stdin>',fact_649_mult__strict__left__mono) ).
fof(c_0_259,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
file('<stdin>',fact_648_mult__strict__right__mono) ).
fof(c_0_260,axiom,
! [X1] :
( ordere1490568538miring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
file('<stdin>',fact_629_comm__mult__left__mono) ).
fof(c_0_261,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
file('<stdin>',fact_628_mult__left__mono) ).
fof(c_0_262,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
file('<stdin>',fact_627_mult__right__mono) ).
fof(c_0_263,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
file('<stdin>',fact_652_mult__strict__left__mono__neg) ).
fof(c_0_264,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
file('<stdin>',fact_651_mult__strict__right__mono__neg) ).
fof(c_0_265,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
file('<stdin>',fact_631_mult__left__mono__neg) ).
fof(c_0_266,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
file('<stdin>',fact_630_mult__right__mono__neg) ).
fof(c_0_267,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X45,X21,X37] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X37),X45))) ) ) ),
file('<stdin>',fact_921_inf__mono) ).
fof(c_0_268,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X45,X21,X37] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X37),X45))) ) ) ),
file('<stdin>',fact_848_sup__mono) ).
fof(c_0_269,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
file('<stdin>',fact_181_add__strict__mono) ).
fof(c_0_270,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
file('<stdin>',fact_174_add__mono) ).
fof(c_0_271,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
file('<stdin>',fact_153_add__le__less__mono) ).
fof(c_0_272,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
file('<stdin>',fact_152_add__less__le__mono) ).
fof(c_0_273,axiom,
! [X29,X63,X38] :
( ! [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,X38,X16)),hAPP(nat,nat,X38,X64))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X63))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X38,X29)),hAPP(nat,nat,X38,X63))) ) ),
file('<stdin>',fact_261_less__mono__imp__le__mono) ).
fof(c_0_274,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)),zero_zero(X1)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X15)) ) ) ) ),
file('<stdin>',fact_621_mult__le__0__iff) ).
fof(c_0_275,axiom,
! [X50,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),zero_zero(nat)),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X50))) ) ),
file('<stdin>',fact_661_mult__less__mono1) ).
fof(c_0_276,axiom,
! [X50,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),zero_zero(nat)),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X59))) ) ),
file('<stdin>',fact_660_mult__less__mono2) ).
fof(c_0_277,axiom,
! [X50,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),X50),X61))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X61))) ) ),
file('<stdin>',fact_576_mult__le__mono) ).
fof(c_0_278,axiom,
! [X50,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),X50),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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
file('<stdin>',fact_254_add__le__mono) ).
fof(c_0_279,axiom,
! [X50,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),X50),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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
file('<stdin>',fact_239_add__less__mono) ).
fof(c_0_280,axiom,
! [X1,X6,X40,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
& hBOOL(hAPP(X1,bool,X11,X6)) ) ),
file('<stdin>',fact_896_Int__Collect) ).
fof(c_0_281,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X49))) ) ),
file('<stdin>',fact_692_n__less__n__mult__m) ).
fof(c_0_282,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51))) ) ),
file('<stdin>',fact_691_n__less__m__mult__n) ).
fof(c_0_283,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)),X34)) ) ) ) ),
file('<stdin>',fact_690_mult__right__le__one__le) ).
fof(c_0_284,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)),X34)) ) ) ) ),
file('<stdin>',fact_689_mult__left__le__one__le) ).
fof(c_0_285,axiom,
! [X38] :
( ! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X38,hAPP(nat,nat,suc,X16))),hAPP(nat,nat,X38,X16)))
=> ? [X16] :
! [X62] : hAPP(nat,nat,X38,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X62)) = hAPP(nat,nat,X38,X16) ),
file('<stdin>',fact_752_weak__decr__stable) ).
fof(c_0_286,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
file('<stdin>',fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
fof(c_0_287,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
file('<stdin>',fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(c_0_288,axiom,
! [X2,X1,X40,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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))),X38)),X40)) = ti(fun(X1,bool),X40) ),
file('<stdin>',fact_485_image__surj__f__inv__f) ).
fof(c_0_289,axiom,
! [X1,X2,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> hAPP(X2,X1,X38,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),X40),X38),X7)) = ti(X1,X7) ),
file('<stdin>',fact_474_f__inv__into__f) ).
fof(c_0_290,axiom,
! [X1,X2,X40,X43,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) ),
file('<stdin>',fact_958_image__Int) ).
fof(c_0_291,axiom,
! [X3,X1,X2,X6,X39,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),X39)) = hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),X39) ),
file('<stdin>',fact_749_folding__idem_Oidem__left__comp) ).
fof(c_0_292,axiom,
! [X2,X1,X39,X38,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X2,X1,X39,hAPP(X1,X2,X38,X26)) = ti(X1,X26) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
file('<stdin>',fact_275_inj__on__inverseI) ).
fof(c_0_293,axiom,
! [X1,X2,X15,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X15),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)))))
<=> ? [X26] :
( ti(X2,X15) = hAPP(X1,X2,X38,X26)
& ! [X46] :
( ti(X2,X15) = hAPP(X1,X2,X38,X46)
=> ti(X1,X46) = ti(X1,X26) ) ) ) ),
file('<stdin>',fact_480_range__ex1__eq) ).
fof(c_0_294,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X94)) ),
file('<stdin>',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(c_0_295,axiom,
! [X1,X2,X41,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X41),X40))
=> 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),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X41)) = ti(fun(X1,bool),X41) ) ),
file('<stdin>',fact_502_inv__into__image__cancel) ).
fof(c_0_296,axiom,
! [X57,X29,X63] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X63))
=> hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X63),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57))) ),
file('<stdin>',fact_810_atLeastLessThan__add__Un) ).
fof(c_0_297,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ),
file('<stdin>',fact_371_even__less__0__iff) ).
fof(c_0_298,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ),
file('<stdin>',fact_350_double__add__less__zero__iff__single__add__less__zero) ).
fof(c_0_299,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1))) ) ),
file('<stdin>',fact_345_double__add__le__zero__iff__single__add__le__zero) ).
fof(c_0_300,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34))
=> ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34)) ) ) ),
file('<stdin>',fact_849_le__supE) ).
fof(c_0_301,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X6,X7,X9] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X6),X7)),X9))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X9))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X9)) ) ) ),
file('<stdin>',fact_841_le__sup__iff) ).
fof(c_0_302,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
=> ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)
<=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
file('<stdin>',fact_780_inj__on__Un__image__eq__iff) ).
fof(c_0_303,axiom,
! [X1] :
( ring_1(X1)
=> ! [X15,X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),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),times_times(X1),X14),X15)),ring_1_Ints(X1))) ) ) ),
file('<stdin>',fact_571_Ints__mult) ).
fof(c_0_304,axiom,
! [X1] :
( ring_1(X1)
=> ! [X15,X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),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),X14),X15)),ring_1_Ints(X1))) ) ) ),
file('<stdin>',fact_536_Ints__add) ).
fof(c_0_305,axiom,
! [X1,X43,X52,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)),X40) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X40)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X40)),
file('<stdin>',fact_885_Un__Int__distrib2) ).
fof(c_0_306,axiom,
! [X1,X43,X52,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)),X40) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X40)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X40)),
file('<stdin>',fact_884_Int__Un__distrib2) ).
fof(c_0_307,axiom,
! [X2,X1,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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))),X38)),top_top(fun(X1,bool)))) ),
file('<stdin>',fact_504_surj__imp__inj__inv) ).
fof(c_0_308,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ? [X44,X84] :
( ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X84),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)),X44)))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),X84),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)),X44)))) ) ),
file('<stdin>',fact_523_finite__imp__nat__seg__image__inj__on) ).
fof(c_0_309,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X43))) ) ),
file('<stdin>',fact_618_extensional__subset) ).
fof(c_0_310,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43)) ) ) ),
file('<stdin>',fact_279_card__psubset) ).
fof(c_0_311,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
file('<stdin>',fact_796_Un__iff) ).
fof(c_0_312,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
file('<stdin>',fact_774_UnE) ).
fof(c_0_313,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54)),X30)) ),
file('<stdin>',fact_533_less__eq__nat_Osimps_I2_J) ).
fof(c_0_314,axiom,
! [X49,X50,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
file('<stdin>',fact_256_add__leD1) ).
fof(c_0_315,axiom,
! [X49,X50,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ),
file('<stdin>',fact_255_add__leD2) ).
fof(c_0_316,axiom,
! [X58,X59,X50] :
( 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)),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X50)) ),
file('<stdin>',fact_241_add__lessD1) ).
fof(c_0_317,axiom,
! [X49,X50,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
=> ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ) ),
file('<stdin>',fact_193_add__leE) ).
fof(c_0_318,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37))) ) ),
file('<stdin>',fact_183_add__strict__right__mono) ).
fof(c_0_319,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22))) ) ),
file('<stdin>',fact_182_add__strict__left__mono) ).
fof(c_0_320,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37))) ) ),
file('<stdin>',fact_176_add__right__mono) ).
fof(c_0_321,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22))) ) ),
file('<stdin>',fact_175_add__left__mono) ).
fof(c_0_322,axiom,
! [X2,X1,X38,X39,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
=> hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X39),X40) ),
file('<stdin>',fact_561_restrict__ext) ).
fof(c_0_323,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( ( ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> one_one(nat) = zero_zero(nat) )
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ) ),
file('<stdin>',fact_967_card_Ounion__inter__neutral) ).
fof(c_0_324,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X76),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X76),X40)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X39),X76)),X40) ) ) ),
file('<stdin>',fact_996_setsum_Oreindex) ).
fof(c_0_325,axiom,
! [X2,X1] :
( semiring_0(X1)
=> ! [X106,X38,X40] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X106),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X1,X1),fun(fun(X2,X1),fun(X2,X1)),combb(X1,X1,X2),hAPP(X1,fun(X1,X1),times_times(X1),X106)),X38)),X40) ),
file('<stdin>',fact_981_setsum__right__distrib) ).
fof(c_0_326,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X38,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X41))
=> hAPP(X1,X2,X38,X26) = one_one(X2) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X41) = one_one(X2) ) ) ),
file('<stdin>',fact_700_fold__image__1) ).
fof(c_0_327,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) ),
file('<stdin>',fact_919_setsum__shift__bounds__Suc__ivl) ).
fof(c_0_328,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) ),
file('<stdin>',fact_889_setsum__shift__bounds__cl__Suc__ivl) ).
fof(c_0_329,axiom,
! [X1,X43,X52,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
file('<stdin>',fact_910_Int__greatest) ).
fof(c_0_330,axiom,
! [X50,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),times_times(nat),X50),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X59))) ),
file('<stdin>',fact_575_mult__le__mono2) ).
fof(c_0_331,axiom,
! [X50,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),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X50))) ),
file('<stdin>',fact_574_mult__le__mono1) ).
fof(c_0_332,axiom,
! [X50,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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X50))) ),
file('<stdin>',fact_253_add__le__mono1) ).
fof(c_0_333,axiom,
! [X50,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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X50))) ),
file('<stdin>',fact_238_add__less__mono1) ).
fof(c_0_334,axiom,
! [X1,X2,X38,X40] : hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40))),
file('<stdin>',fact_670_restrict__extensional) ).
fof(c_0_335,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40)) ) ),
file('<stdin>',fact_493_finite__surj__inj) ).
fof(c_0_336,axiom,
! [X57,X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)),
file('<stdin>',fact_768_image__add__atLeastAtMost) ).
fof(c_0_337,axiom,
! [X57,X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)),
file('<stdin>',fact_517_image__add__atLeastLessThan) ).
fof(c_0_338,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_646_mult__neg__pos) ).
fof(c_0_339,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_642_mult__pos__neg2) ).
fof(c_0_340,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_641_mult__pos__neg) ).
fof(c_0_341,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ),
file('<stdin>',fact_635_split__mult__neg__le) ).
fof(c_0_342,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_625_mult__nonpos__nonneg) ).
fof(c_0_343,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_624_mult__nonneg__nonpos2) ).
fof(c_0_344,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_623_mult__nonneg__nonpos) ).
fof(c_0_345,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_359_add__neg__nonpos) ).
fof(c_0_346,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_358_add__nonpos__neg) ).
fof(c_0_347,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_347_add__neg__neg) ).
fof(c_0_348,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_340_add__nonpos__nonpos) ).
fof(c_0_349,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)),X34)) ) ) ),
file('<stdin>',fact_847_sup__least) ).
fof(c_0_350,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X21,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34)) ) ) ),
file('<stdin>',fact_846_le__supI) ).
fof(c_0_351,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
file('<stdin>',fact_915_inj__on__Int) ).
fof(c_0_352,axiom,
! [X1,X2,X3] :
( comm_monoid_add(X3)
=> ! [X76,X38,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> hAPP(fun(X2,bool),X3,hAPP(fun(X2,X3),fun(fun(X2,bool),X3),big_co1399186613setsum(X2,X3),X76),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X76),X38)),X43) ) ),
file('<stdin>',fact_991_setsum__reindex) ).
fof(c_0_353,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21)),zero_zero(X1))) ),
file('<stdin>',fact_636_not__square__less__zero) ).
fof(c_0_354,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66) ) ) ),
file('<stdin>',fact_815_ivl__disj__un_I16_J) ).
fof(c_0_355,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66) ) ) ),
file('<stdin>',fact_814_ivl__disj__un_I15_J) ).
fof(c_0_356,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66) ) ) ),
file('<stdin>',fact_811_ivl__disj__un_I22_J) ).
fof(c_0_357,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66) ) ) ),
file('<stdin>',fact_809_ivl__disj__un_I21_J) ).
fof(c_0_358,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66) ) ) ),
file('<stdin>',fact_779_ivl__disj__un_I17_J) ).
fof(c_0_359,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66) ) ) ),
file('<stdin>',fact_778_ivl__disj__un_I20_J) ).
fof(c_0_360,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66) ) ) ),
file('<stdin>',fact_773_ivl__disj__un_I18_J) ).
fof(c_0_361,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66) ) ) ),
file('<stdin>',fact_772_ivl__disj__un_I19_J) ).
fof(c_0_362,axiom,
! [X1,X2,X43,X40,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(fun(X1,bool),fun(X2,X2),X25,X43)) = hAPP(fun(X1,bool),fun(X2,X2),X25,X40) ) ) ),
file('<stdin>',fact_747_folding__idem_Osubset__comp__idem) ).
fof(c_0_363,axiom,
! [X1,X2,X43,X40,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(fun(X1,bool),fun(X2,X2),X25,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(fun(X1,bool),fun(X2,X2),X25,X43)) ) ) ),
file('<stdin>',fact_813_folding__idem_Ounion__idem) ).
fof(c_0_364,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X11,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X11),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X11,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X11),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X54),X30))) ) ),
file('<stdin>',fact_966_setsum__head) ).
fof(c_0_365,axiom,
! [X1,X40] : 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),X40),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X40)))),
file('<stdin>',fact_144_funcset__id) ).
fof(c_0_366,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_234_not__add__less2) ).
fof(c_0_367,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_233_not__add__less1) ).
fof(c_0_368,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
file('<stdin>',fact_903_Int__iff) ).
fof(c_0_369,axiom,
! [X1,X43,X17,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
file('<stdin>',fact_870_IntI) ).
fof(c_0_370,axiom,
! [X1,X2,X6,X40,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(X1,fun(X2,X2),X38,X6)) = hAPP(fun(X1,bool),fun(X2,X2),X25,X40) ) ) ),
file('<stdin>',fact_751_folding__idem_Oin__comp__idem) ).
fof(c_0_371,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) ),
file('<stdin>',fact_901_IntD1) ).
fof(c_0_372,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ),
file('<stdin>',fact_900_IntD2) ).
fof(c_0_373,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
file('<stdin>',fact_869_IntE) ).
fof(c_0_374,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) ),
file('<stdin>',fact_456_card_Oeq__fold__g) ).
fof(c_0_375,axiom,
! [X1,X40] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
file('<stdin>',fact_455_card__def) ).
fof(c_0_376,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X43)),hAPP(fun(X1,bool),nat,finite_card(X1),X40)))
=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ) ),
file('<stdin>',fact_281_card__seteq) ).
fof(c_0_377,axiom,
! [X2,X1,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X43),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ) ),
file('<stdin>',fact_478_finite__surj) ).
fof(c_0_378,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22)) ) ) ),
file('<stdin>',fact_644_zero__less__mult__pos2) ).
fof(c_0_379,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22)) ) ) ),
file('<stdin>',fact_643_zero__less__mult__pos) ).
fof(c_0_380,axiom,
! [X2,X3,X1,X39,X38,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X39),X38),X6) = hAPP(X3,X2,X39,hAPP(X1,X3,X38,X6)) ),
file('<stdin>',fact_563_compose__eq) ).
fof(c_0_381,axiom,
! [X1,X2,X40,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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))),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)) = ti(fun(X1,bool),X40) ),
file('<stdin>',fact_506_image__inv__f__f) ).
fof(c_0_382,axiom,
! [X1,X2,X83,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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))),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X83)) = ti(fun(X1,bool),X83) ),
file('<stdin>',fact_505_inv__image__comp) ).
fof(c_0_383,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X52)),
file('<stdin>',fact_883_Un__Int__distrib) ).
fof(c_0_384,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X52)),
file('<stdin>',fact_882_Int__Un__distrib) ).
fof(c_0_385,axiom,
! [X1,X2,X38,X40] :
( 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),X38),X40)))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40)) ) ),
file('<stdin>',fact_479_finite__imageD) ).
fof(c_0_386,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_232_inj__on__add__nat) ).
fof(c_0_387,axiom,
! [X1,X40,X43] : 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X40)),
file('<stdin>',fact_914_Int__lower1) ).
fof(c_0_388,axiom,
! [X1,X40,X43] : 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X43)),
file('<stdin>',fact_913_Int__lower2) ).
fof(c_0_389,axiom,
! [X2,X1,X38,X40,X43] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X43)),
file('<stdin>',fact_781_image__Un) ).
fof(c_0_390,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_285_finite__Collect__less__nat) ).
fof(c_0_391,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_283_finite__Collect__le__nat) ).
fof(c_0_392,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),X94)) ),
file('<stdin>',fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(c_0_393,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94))) ),
file('<stdin>',fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(c_0_394,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45)) ),
file('<stdin>',fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_395,axiom,
! [X2,X1,X38,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ),
file('<stdin>',fact_469_imageI) ).
fof(c_0_396,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> 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)),the_inv_into(X1,X2),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)) = ti(fun(X1,bool),X40) ),
file('<stdin>',fact_557_the__inv__into__onto) ).
fof(c_0_397,axiom,
! [X1,X2,X15,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool)))))
=> ~ ! [X26] : ti(X1,X15) != hAPP(X2,X1,X38,X26) ),
file('<stdin>',fact_520_rangeE) ).
fof(c_0_398,axiom,
! [X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X49)))),
file('<stdin>',fact_573_le__cube) ).
fof(c_0_399,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
<=> ? [X44,X84] : ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X84),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)),X44))) ),
file('<stdin>',fact_522_finite__conv__nat__seg__image) ).
fof(c_0_400,axiom,
! [X1,X40,X38,X30] :
( ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X38),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)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
file('<stdin>',fact_516_nat__seg__image__imp__finite) ).
fof(c_0_401,axiom,
! [X11,X30] :
( ? [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X30))
& hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ? [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X30)))
& hBOOL(hAPP(nat,bool,X11,X26)) ) ),
file('<stdin>',fact_764_ex__nat__less) ).
fof(c_0_402,axiom,
! [X11,X30] :
( ? [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X30))
& hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ? [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X30)))
& hBOOL(hAPP(nat,bool,X11,X26)) ) ),
file('<stdin>',fact_519_ex__nat__less__eq) ).
fof(c_0_403,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X15)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),zero_zero(X1))) ) ) ) ),
file('<stdin>',fact_620_zero__le__mult__iff) ).
fof(c_0_404,axiom,
! [X2,X1,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
<=> ! [X26] : hAPP(X2,X1,X38,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))),X38),X26)) = ti(X1,X26) ),
file('<stdin>',fact_487_surj__iff__all) ).
fof(c_0_405,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) ) ),
file('<stdin>',fact_971_setsum_Oeq__fold) ).
fof(c_0_406,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X40] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ) ),
file('<stdin>',fact_970_setsum_OF__eq) ).
fof(c_0_407,axiom,
! [X11,X30] :
( ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X30))
=> hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ! [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X30)))
=> hBOOL(hAPP(nat,bool,X11,X26)) ) ),
file('<stdin>',fact_765_all__nat__less) ).
fof(c_0_408,axiom,
! [X11,X30] :
( ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X30))
=> hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ! [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X30)))
=> hBOOL(hAPP(nat,bool,X11,X26)) ) ),
file('<stdin>',fact_518_all__nat__less__eq) ).
fof(c_0_409,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
file('<stdin>',fact_954_less__infI2) ).
fof(c_0_410,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X21,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
file('<stdin>',fact_953_less__infI1) ).
fof(c_0_411,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X21,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
file('<stdin>',fact_927_le__infI1) ).
fof(c_0_412,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
file('<stdin>',fact_926_le__infI2) ).
fof(c_0_413,axiom,
! [X1,X3,X2,X87,X38,X39,X76] : hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X38),hAPP(fun(X1,X87),fun(X1,X3),hAPP(fun(X87,X3),fun(fun(X1,X87),fun(X1,X3)),comp(X87,X3,X1),X39),X76)) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),hAPP(fun(X87,X3),fun(X87,X2),hAPP(fun(X3,X2),fun(fun(X87,X3),fun(X87,X2)),comp(X3,X2,X87),X38),X39)),X76),
file('<stdin>',fact_729_o__assoc) ).
fof(c_0_414,axiom,
! [X54,X30] :
( 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),X30)))
<=> ( 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)),X30)) ) ),
file('<stdin>',fact_356_add__gr__0) ).
fof(c_0_415,axiom,
! [X1,X2,X40,X43] :
( 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),X40),X43)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ) ),
file('<stdin>',fact_311_finite__Plus__iff) ).
fof(c_0_416,axiom,
! [X1,X2,X40,X43] :
( 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),X40),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
file('<stdin>',fact_309_finite__PlusD_I1_J) ).
fof(c_0_417,axiom,
! [X1,X2,X40,X43] :
( 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),X40),X43)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ),
file('<stdin>',fact_308_finite__PlusD_I2_J) ).
fof(c_0_418,axiom,
! [X1,X3,X2,X40,X39,X38] : hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X39),X38) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X39),X38)),X40),
file('<stdin>',fact_567_compose__def) ).
fof(c_0_419,axiom,
! [X2,X1,X53,X11] :
( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X26),X46))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X26),X46)) )
=> 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))),X11),X53)) ),
file('<stdin>',fact_257_predicate2I) ).
fof(c_0_420,axiom,
! [X3,X2,X1,X39,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X39),top_top(fun(X1,bool))) = top_top(fun(X3,bool))
=> 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)),comp(X1,X3,X2),X39),X38)),top_top(fun(X2,bool))) = top_top(fun(X3,bool)) ) ),
file('<stdin>',fact_720_comp__surj) ).
fof(c_0_421,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( 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),ord_atLeast(X1),X6)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
file('<stdin>',fact_862_atLeast__subset__iff) ).
fof(c_0_422,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( 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),ord_greaterThan(X1),X6)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
file('<stdin>',fact_542_greaterThan__subset__iff) ).
fof(c_0_423,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X51,X49] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X49))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X51))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X49),X51))) ) ) ),
file('<stdin>',fact_655_less__1__mult) ).
fof(c_0_424,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
file('<stdin>',fact_640_mult__pos__pos) ).
fof(c_0_425,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X22,X21] :
( ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(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),times_times(X1),X21),X22))) ) ),
file('<stdin>',fact_634_split__mult__pos__le) ).
fof(c_0_426,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
file('<stdin>',fact_622_mult__nonneg__nonneg) ).
fof(c_0_427,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
file('<stdin>',fact_363_add__pos__nonneg) ).
fof(c_0_428,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
file('<stdin>',fact_362_add__nonneg__pos) ).
fof(c_0_429,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
file('<stdin>',fact_349_add__pos__pos) ).
fof(c_0_430,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
file('<stdin>',fact_344_add__nonneg__nonneg) ).
fof(c_0_431,axiom,
! [X2,X1,X3,X38,X39] : 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),X38),X39)),top_top(fun(X2,bool))) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X38),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X39),top_top(fun(X2,bool)))),
file('<stdin>',fact_477_range__composition) ).
fof(c_0_432,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
file('<stdin>',fact_647_mult__neg__neg) ).
fof(c_0_433,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(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),times_times(X1),X21),X22))) ) ) ),
file('<stdin>',fact_626_mult__nonpos__nonpos) ).
fof(c_0_434,axiom,
! [X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ? [X26] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X26),arrow_1568854078le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X26)) ) ),
file('<stdin>',fact_88_complete__Lin) ).
fof(c_0_435,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
file('<stdin>',fact_361_add__strict__increasing) ).
fof(c_0_436,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
file('<stdin>',fact_360_add__strict__increasing2) ).
fof(c_0_437,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
file('<stdin>',fact_348_pos__add__strict) ).
fof(c_0_438,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
file('<stdin>',fact_342_add__increasing) ).
fof(c_0_439,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21,X37] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
file('<stdin>',fact_341_add__increasing2) ).
fof(c_0_440,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X6,X7,X9] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X7),X9)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X9)) ) ) ),
file('<stdin>',fact_928_le__inf__iff) ).
fof(c_0_441,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22))) ) ) ),
file('<stdin>',fact_923_le__infI) ).
fof(c_0_442,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36))) ) ) ),
file('<stdin>',fact_922_inf__greatest) ).
fof(c_0_443,axiom,
! [X1] :
( linordered_field(X1)
=> ! [X34,X35] :
( ! [X75] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X75))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X75))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
file('<stdin>',fact_454_field__le__epsilon) ).
fof(c_0_444,axiom,
~ ! [X32] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),X32))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X32),arrow_1568854078le_Lin)) ),
file('<stdin>',fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).
fof(c_0_445,axiom,
~ ! [X31] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),X31))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X31),arrow_1568854078le_Lin)) ),
file('<stdin>',fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).
fof(c_0_446,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
file('<stdin>',fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(c_0_447,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
file('<stdin>',fact_38__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(c_0_448,axiom,
! [X2,X1,X3,X38,X39,X106] : 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)),comp(X3,X1,X2),X38),X39)),X106) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X38),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X39),X106)),
file('<stdin>',fact_725_image__compose) ).
fof(c_0_449,axiom,
! [X2,X1,X3,X38,X39,X40] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X39),X40)) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),combb(X2,X1,X3),X38),X39)),X40),
file('<stdin>',fact_467_image__image) ).
fof(c_0_450,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( ! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X47))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X36)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36)) ) ) ),
file('<stdin>',fact_156_dense__le__bounded) ).
fof(c_0_451,axiom,
! [X1,X2,X6,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
=> ti(X1,X6) = ti(X1,X7) ) ) ) ),
file('<stdin>',fact_138_inj__onD) ).
fof(c_0_452,axiom,
! [X1,X2,X7,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
<=> ti(X1,X6) = ti(X1,X7) ) ) ) ),
file('<stdin>',fact_137_inj__on__iff) ).
fof(c_0_453,axiom,
! [X1,X2,X6,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( ti(X1,X6) != ti(X1,X7)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
=> hAPP(X1,X2,X38,X6) != hAPP(X1,X2,X38,X7) ) ) ) ),
file('<stdin>',fact_136_inj__on__contraD) ).
fof(c_0_454,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
<=> ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X27)
=> ti(X1,X26) = ti(X1,X27) ) ) ) ),
file('<stdin>',fact_135_inj__on__def) ).
fof(c_0_455,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X35,X36,X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X36),X34)) ),
file('<stdin>',fact_877_inf__sup__distrib2) ).
fof(c_0_456,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X35,X36,X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X36),X34)) ),
file('<stdin>',fact_876_sup__inf__distrib2) ).
fof(c_0_457,axiom,
! [X1] :
( comm_semiring(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
file('<stdin>',fact_616_comm__semiring__class_Odistrib) ).
fof(c_0_458,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
file('<stdin>',fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(c_0_459,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X49,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X49)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X49) ),
file('<stdin>',fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(c_0_460,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)))
<=> ( 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)),X30)) ) ),
file('<stdin>',fact_664_nat__0__less__mult__iff) ).
fof(c_0_461,axiom,
! [X2,X1,X15,X38,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( ti(X2,X15) = hAPP(X1,X2,X38,X6)
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X15),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ) ),
file('<stdin>',fact_470_rev__image__eqI) ).
fof(c_0_462,axiom,
! [X1,X2,X40,X15,X38,X6] :
( ti(X1,X15) = hAPP(X2,X1,X38,X6)
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40))) ) ),
file('<stdin>',fact_458_image__eqI) ).
fof(c_0_463,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X40) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& hAPP(X1,nat,X38,X26) = hAPP(nat,nat,suc,zero_zero(nat))
& ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( ti(X1,X26) != ti(X1,X27)
=> hAPP(X1,nat,X38,X27) = zero_zero(nat) ) ) ) ) ),
file('<stdin>',fact_992_setsum__eq__Suc0__iff) ).
fof(c_0_464,axiom,
! [X1,X2,X11] :
( ! [X18] : hBOOL(hAPP(product_prod(X1,X2),bool,X11,X18))
<=> ! [X19,X20] : hBOOL(hAPP(product_prod(X1,X2),bool,X11,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X19),X20))) ),
file('<stdin>',fact_15_split__paired__All) ).
fof(c_0_465,axiom,
! [X1,X2,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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))),X38)),top_top(fun(X2,bool))) = top_top(fun(X1,bool)) ),
file('<stdin>',fact_507_inj__imp__surj__inv) ).
fof(c_0_466,axiom,
! [X1,X40,X17,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
file('<stdin>',fact_803_UnI2) ).
fof(c_0_467,axiom,
! [X1,X43,X17,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
file('<stdin>',fact_802_UnI1) ).
fof(c_0_468,axiom,
! [X1,X40,X17,X43] :
( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
file('<stdin>',fact_777_UnCI) ).
fof(c_0_469,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)),
file('<stdin>',fact_902_Int__assoc) ).
fof(c_0_470,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)),
file('<stdin>',fact_797_Un__assoc) ).
fof(c_0_471,axiom,
! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X50)),
file('<stdin>',fact_604_add__mult__distrib) ).
fof(c_0_472,axiom,
! [X1] :
( ring_char_0(X1)
=> ! [X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(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)),X14)),X14) != zero_zero(X1) ) ),
file('<stdin>',fact_543_Ints__odd__nonzero) ).
fof(c_0_473,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( 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),X14),X14)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X14)) ) ),
file('<stdin>',fact_351_zero__less__double__add__iff__zero__less__single__add) ).
fof(c_0_474,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( 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),X14),X14)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14)) ) ),
file('<stdin>',fact_346_zero__le__double__add__iff__zero__le__single__add) ).
fof(c_0_475,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)))
=> ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22)) ) ) ),
file('<stdin>',fact_920_le__infE) ).
fof(c_0_476,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6))
=> ( ~ hBOOL(hAPP(X1,bool,X40,X6))
=> hBOOL(hAPP(X1,bool,X43,X6)) ) ),
file('<stdin>',fact_775_sup1E) ).
fof(c_0_477,axiom,
! [X1,X2,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ) ),
file('<stdin>',fact_553_the__inv__into__f__f) ).
fof(c_0_478,axiom,
! [X1,X2,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> 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),X40),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ) ),
file('<stdin>',fact_147_inv__into__f__f) ).
fof(c_0_479,axiom,
! [X1,X2,X6,X7,X11,X53] :
( 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))),X11),X53))
=> ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X6),X7)) ) ),
file('<stdin>',fact_203_predicate2D) ).
fof(c_0_480,axiom,
! [X2,X1,X53,X11,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X6),X7))
=> ( 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))),X11),X53))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X6),X7)) ) ),
file('<stdin>',fact_201_rev__predicate2D) ).
fof(c_0_481,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ),
file('<stdin>',fact_282_card__mono) ).
fof(c_0_482,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ),
file('<stdin>',fact_280_psubset__card__mono) ).
fof(c_0_483,axiom,
! [X1,X2,X6,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X7) = ti(X1,X6) ) ) ),
file('<stdin>',fact_552_the__inv__into__f__eq) ).
fof(c_0_484,axiom,
! [X1,X2,X7,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
=> 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),X40),X38),X7) = ti(X1,X6) ) ) ),
file('<stdin>',fact_148_inv__into__f__eq) ).
fof(c_0_485,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X40) = one_one(nat)
<=> ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& hAPP(X1,nat,X38,X26) = one_one(nat)
& ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( ti(X1,X26) != ti(X1,X27)
=> hAPP(X1,nat,X38,X27) = zero_zero(nat) ) ) ) ) ),
file('<stdin>',fact_993_setsum__eq__1__iff) ).
fof(c_0_486,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7)) = zero_zero(X1)
<=> ( ti(X1,X6) = zero_zero(X1)
& ti(X1,X7) = zero_zero(X1) ) ) ),
file('<stdin>',fact_653_sum__squares__eq__zero__iff) ).
fof(c_0_487,axiom,
! [X11,X54,X30] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
=> ( ( X54 = X30
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) ) ) ),
file('<stdin>',fact_221_nat__less__cases) ).
fof(c_0_488,axiom,
! [X1,X25,X112] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X25),X112)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112)) ) ),
file('<stdin>',fact_790_finite__Un) ).
fof(c_0_489,axiom,
! [X58,X49] : 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),X49),X58)))),
file('<stdin>',fact_414_less__add__Suc2) ).
fof(c_0_490,axiom,
! [X58,X49] : 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),X49)))),
file('<stdin>',fact_413_less__add__Suc1) ).
fof(c_0_491,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
file('<stdin>',fact_266_psubset__trans) ).
fof(c_0_492,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52)) ) ),
file('<stdin>',fact_204_subset__trans) ).
fof(c_0_493,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
file('<stdin>',fact_200_subset__psubset__trans) ).
fof(c_0_494,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
file('<stdin>',fact_199_psubset__subset__trans) ).
fof(c_0_495,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
=> hBOOL(hAPP(X1,bool,X40,X6)) ),
file('<stdin>',fact_899_inf1D1) ).
fof(c_0_496,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
=> hBOOL(hAPP(X1,bool,X43,X6)) ),
file('<stdin>',fact_898_inf1D2) ).
fof(c_0_497,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
=> ~ ( hBOOL(hAPP(X1,bool,X40,X6))
=> ~ hBOOL(hAPP(X1,bool,X43,X6)) ) ),
file('<stdin>',fact_868_inf1E) ).
fof(c_0_498,axiom,
! [X30,X54] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),hAPP(nat,nat,suc,X54)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X54)) ),
file('<stdin>',fact_403_Suc__le__mono) ).
fof(c_0_499,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
file('<stdin>',fact_394_Suc__less__eq) ).
fof(c_0_500,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),hAPP(nat,nat,suc,X51)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
file('<stdin>',fact_386_Suc__less__SucD) ).
fof(c_0_501,axiom,
! [X1,X2,X38,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X38,X6)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))))),
file('<stdin>',fact_464_rangeI) ).
fof(c_0_502,axiom,
! [X1,X2,X40,X38,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ) ),
file('<stdin>',fact_163_subset__inj__on) ).
fof(c_0_503,axiom,
! [X50,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),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X50)) ) ),
file('<stdin>',fact_389_less__trans__Suc) ).
fof(c_0_504,axiom,
! [X1,X2,X6,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(X1,fun(X2,X2),X38,X6)),hAPP(X1,fun(X2,X2),X38,X6)) = hAPP(X1,fun(X2,X2),X38,X6) ),
file('<stdin>',fact_750_folding__idem_Oidem__comp) ).
fof(c_0_505,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X66)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X77) ) ),
file('<stdin>',fact_865_ivl__disj__un_I14_J) ).
fof(c_0_506,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X66)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X77) ) ),
file('<stdin>',fact_855_ivl__disj__un_I13_J) ).
fof(c_0_507,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X66)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X77) ) ),
file('<stdin>',fact_854_ivl__disj__un_I12_J) ).
fof(c_0_508,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X66)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X77) ) ),
file('<stdin>',fact_812_ivl__disj__un_I11_J) ).
fof(c_0_509,axiom,
! [X1,X2,X39,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( ! [X26] : hAPP(X1,X2,X38,hAPP(X2,X1,X39,X26)) = ti(X2,X26)
=> 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))),X38) = ti(fun(X2,X1),X39) ) ),
file('<stdin>',fact_150_inj__imp__inv__eq) ).
fof(c_0_510,axiom,
! [X2,X1,X3,X87,X109,X38,X39,X6,X105,X110,X111] :
( hAPP(X2,X1,X38,hAPP(X3,X2,X39,X6)) = hAPP(X87,X1,X105,hAPP(X109,X87,X110,X111))
=> hAPP(X3,X1,hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),comp(X2,X1,X3),X38),X39),X6) = hAPP(X109,X1,hAPP(fun(X109,X87),fun(X109,X1),hAPP(fun(X87,X1),fun(fun(X109,X87),fun(X109,X1)),comp(X87,X1,X109),X105),X110),X111) ),
file('<stdin>',fact_735_comp__cong) ).
fof(c_0_511,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X49] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)),X49) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1))),X49) ),
file('<stdin>',fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(c_0_512,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
file('<stdin>',fact_879_inf__sup__distrib1) ).
fof(c_0_513,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
file('<stdin>',fact_878_sup__inf__distrib1) ).
fof(c_0_514,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X93) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),X95) ),
file('<stdin>',fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(c_0_515,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X36)) ),
file('<stdin>',fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(c_0_516,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),X22) ),
file('<stdin>',fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_517,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X34)) ),
file('<stdin>',fact_933_inf__sup__ord_I1_J) ).
fof(c_0_518,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X34)) ),
file('<stdin>',fact_932_inf__le1) ).
fof(c_0_519,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X35)) ),
file('<stdin>',fact_931_inf__sup__ord_I2_J) ).
fof(c_0_520,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X35)) ),
file('<stdin>',fact_930_inf__le2) ).
fof(c_0_521,axiom,
! [X2,X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> 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),X40),X43))) ) ),
file('<stdin>',fact_310_finite__Plus) ).
fof(c_0_522,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
file('<stdin>',fact_265_psubsetD) ).
fof(c_0_523,axiom,
! [X1,X6,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
file('<stdin>',fact_208_in__mono) ).
fof(c_0_524,axiom,
! [X1,X43,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
file('<stdin>',fact_206_set__rev__mp) ).
fof(c_0_525,axiom,
! [X1,X6,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
file('<stdin>',fact_205_set__mp) ).
fof(c_0_526,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
file('<stdin>',fact_195_subsetD) ).
fof(c_0_527,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X6,X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,X2,X39,X6))) ) ),
file('<stdin>',fact_106_le__funD) ).
fof(c_0_528,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X6,X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,X2,X39,X6))) ) ),
file('<stdin>',fact_96_le__funE) ).
fof(c_0_529,axiom,
! [X54,X30] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
file('<stdin>',fact_405_not__less__eq__eq) ).
fof(c_0_530,axiom,
! [X1] :
( linorder(X1)
=> ! [X17,X81,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
=> ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
<=> ( ti(X1,X14) = ti(X1,X17)
& ti(X1,X15) = ti(X1,X81) ) ) ) ) ),
file('<stdin>',fact_473_atLeastLessThan__eq__iff) ).
fof(c_0_531,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X15,X17,X81] :
( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
=> ti(X1,X14) = ti(X1,X17) ) ) ) ),
file('<stdin>',fact_472_atLeastLessThan__inj_I1_J) ).
fof(c_0_532,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X15,X17,X81] :
( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
=> ti(X1,X15) = ti(X1,X81) ) ) ) ),
file('<stdin>',fact_471_atLeastLessThan__inj_I2_J) ).
fof(c_0_533,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X57,X38] :
( hAPP(nat,X1,X38,zero_zero(nat)) = zero_zero(X1)
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X57)) ) ),
file('<stdin>',fact_959_setsum__shift__lb__Suc0__0__upt) ).
fof(c_0_534,axiom,
! [X57,X38] :
( hAPP(nat,nat,X38,zero_zero(nat)) = zero_zero(nat)
=> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X57)) ),
file('<stdin>',fact_956_setsum__shift__lb__Suc0__0) ).
fof(c_0_535,axiom,
! [X50,X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X49)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X51)),
file('<stdin>',fact_605_add__mult__distrib2) ).
fof(c_0_536,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X38),X39))
<=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
& ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X39),X38)) ) ) ),
file('<stdin>',fact_159_less__fun__def) ).
fof(c_0_537,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40) = ti(fun(X1,X2),X38) ),
file('<stdin>',fact_671_extensional__restrict) ).
fof(c_0_538,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X37,X45,X21,X22,X97] :
( ti(X1,X97) != zero_zero(X1)
=> ( ( ti(X1,X21) = ti(X1,X22)
& ti(X1,X37) != ti(X1,X45) )
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X97),X37)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X97),X45)) ) ) ),
file('<stdin>',fact_654_add__scale__eq__noteq) ).
fof(c_0_539,axiom,
! [X2,X1,X7,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> hAPP(X2,X1,X38,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))),X38),X7)) = ti(X1,X7) ),
file('<stdin>',fact_486_surj__f__inv__f) ).
fof(c_0_540,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
file('<stdin>',fact_851_less__supI1) ).
fof(c_0_541,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X34,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
file('<stdin>',fact_850_less__supI2) ).
fof(c_0_542,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X34,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
file('<stdin>',fact_843_le__supI2) ).
fof(c_0_543,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
file('<stdin>',fact_842_le__supI1) ).
fof(c_0_544,axiom,
! [X2,X1,X43,X40] :
( ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) )
=> 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),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43)) )
& ( ~ ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) )
=> 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),X40),X43)) = zero_zero(nat) ) ),
file('<stdin>',fact_316_card__Plus__conv__if) ).
fof(c_0_545,axiom,
! [X2,X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> 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),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43)) ) ),
file('<stdin>',fact_305_card__Plus) ).
fof(c_0_546,axiom,
! [X2,X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
<=> 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40) ) ),
file('<stdin>',fact_500_inj__on__iff__eq__card) ).
fof(c_0_547,axiom,
! [X2,X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ) ),
file('<stdin>',fact_499_eq__card__imp__inj__on) ).
fof(c_0_548,axiom,
! [X36,X34,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
file('<stdin>',fact_268_termination__basic__simps_I1_J) ).
fof(c_0_549,axiom,
! [X35,X34,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X36))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
file('<stdin>',fact_267_termination__basic__simps_I2_J) ).
fof(c_0_550,axiom,
! [X35,X34,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X36))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
file('<stdin>',fact_263_termination__basic__simps_I4_J) ).
fof(c_0_551,axiom,
! [X36,X34,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
file('<stdin>',fact_262_termination__basic__simps_I3_J) ).
fof(c_0_552,axiom,
! [X49,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),X49),X59))) ),
file('<stdin>',fact_252_trans__le__add2) ).
fof(c_0_553,axiom,
! [X49,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),X49))) ),
file('<stdin>',fact_251_trans__le__add1) ).
fof(c_0_554,axiom,
! [X49,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),X49),X59))) ),
file('<stdin>',fact_237_trans__less__add2) ).
fof(c_0_555,axiom,
! [X49,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),X49))) ),
file('<stdin>',fact_236_trans__less__add1) ).
fof(c_0_556,axiom,
! [X58,X50] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X50))
=> ~ ! [X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
=> X50 != hAPP(nat,nat,suc,X64) ) ),
file('<stdin>',fact_440_Suc__lessE) ).
fof(c_0_557,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
file('<stdin>',fact_422_Suc__le__lessD) ).
fof(c_0_558,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
file('<stdin>',fact_418_Suc__le__eq) ).
fof(c_0_559,axiom,
! [X30,X54] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
file('<stdin>',fact_416_less__eq__Suc__le) ).
fof(c_0_560,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
file('<stdin>',fact_400_Suc__leD) ).
fof(c_0_561,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
file('<stdin>',fact_387_Suc__lessD) ).
fof(c_0_562,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X52)),
file('<stdin>',fact_904_Int__left__commute) ).
fof(c_0_563,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X52)),
file('<stdin>',fact_795_Un__left__commute) ).
fof(c_0_564,axiom,
! [X1,X112,X25] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X25),X112))) ) ),
file('<stdin>',fact_789_finite__UnI) ).
fof(c_0_565,axiom,
! [X1,X2,X15,X38,X6] :
( ti(X1,X15) = hAPP(X2,X1,X38,X6)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))))) ),
file('<stdin>',fact_465_range__eqI) ).
fof(c_0_566,axiom,
! [X1,X2,X40,X43,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)
<=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
file('<stdin>',fact_482_inj__image__eq__iff) ).
fof(c_0_567,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),hAPP(nat,nat,suc,X51))) ),
file('<stdin>',fact_374_Suc__mono) ).
fof(c_0_568,axiom,
! [X1,X54,X11,X57] :
( hBOOL(hAPP(X1,bool,X11,X57))
=> ? [X26] :
( hBOOL(hAPP(X1,bool,X11,X26))
& ! [X46] :
( hBOOL(hAPP(X1,bool,X11,X46))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X54,X26)),hAPP(X1,nat,X54,X46))) ) ) ),
file('<stdin>',fact_712_ex__has__least__nat) ).
fof(c_0_569,axiom,
! [X2,X1,X38,X40] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(X2,X1),X38),X40)),X40) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40),
file('<stdin>',fact_550_image__restrict__eq) ).
fof(c_0_570,axiom,
! [X1,X53,X11] :
( ! [X26] :
( hBOOL(hAPP(X1,bool,X11,X26))
=> hBOOL(hAPP(X1,bool,X53,X26)) )
=> 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),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) ),
file('<stdin>',fact_716_Collect__mono) ).
fof(c_0_571,axiom,
! [X1,X43,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),
file('<stdin>',fact_783_Un__upper2) ).
fof(c_0_572,axiom,
! [X1,X40,X43] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),
file('<stdin>',fact_782_Un__upper1) ).
fof(c_0_573,axiom,
! [X1,X43,X40,X6] :
( hBOOL(hAPP(X1,bool,X40,X6))
=> ( hBOOL(hAPP(X1,bool,X43,X6))
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6)) ) ),
file('<stdin>',fact_871_inf1I) ).
fof(c_0_574,axiom,
! [X2,X1,X39,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ( ! [X26] : hAPP(X1,X2,X39,hAPP(X2,X1,X38,X26)) = ti(X2,X26)
=> 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))),X38) = ti(fun(X1,X2),X39) ) ),
file('<stdin>',fact_513_surj__imp__inv__eq) ).
fof(c_0_575,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
file('<stdin>',fact_212_set__eq__subset) ).
fof(c_0_576,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
file('<stdin>',fact_194_equalityI) ).
fof(c_0_577,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
file('<stdin>',fact_131_xt1_I8_J) ).
fof(c_0_578,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
file('<stdin>',fact_130_order__le__less__trans) ).
fof(c_0_579,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
file('<stdin>',fact_129_xt1_I7_J) ).
fof(c_0_580,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
file('<stdin>',fact_128_order__less__le__trans) ).
fof(c_0_581,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X36)) ) ) ),
file('<stdin>',fact_99_order__trans) ).
fof(c_0_582,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X34)) ) ) ),
file('<stdin>',fact_97_xt1_I6_J) ).
fof(c_0_583,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
file('<stdin>',fact_56_order__less__trans) ).
fof(c_0_584,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
file('<stdin>',fact_55_xt1_I10_J) ).
fof(c_0_585,axiom,
! [X1,X2,X6,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),top_top(fun(X1,bool))),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ),
file('<stdin>',fact_555_the__inv__f__f) ).
fof(c_0_586,axiom,
! [X1,X2,X6,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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),top_top(fun(X1,bool))),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ),
file('<stdin>',fact_86_inv__f__f) ).
fof(c_0_587,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
file('<stdin>',fact_3__096P_A_058_AProf_096) ).
fof(c_0_588,axiom,
! [X1,X2,X6,X7,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
=> 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),top_top(fun(X1,bool))),X38),X7) = ti(X1,X6) ) ),
file('<stdin>',fact_85_inv__f__eq) ).
fof(c_0_589,axiom,
! [X50,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),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X50)) ) ),
file('<stdin>',fact_230_le__trans) ).
fof(c_0_590,axiom,
arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
file('<stdin>',fact_141_Prof__def) ).
fof(c_0_591,axiom,
! [X49,X51,X50,X61] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X50),X61))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X61) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X50),X51)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ) ),
file('<stdin>',fact_240_less__add__eq__less) ).
fof(c_0_592,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49,X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X49),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1))),X49) ),
file('<stdin>',fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(c_0_593,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X37)) ),
file('<stdin>',fact_940_inf_Oassoc) ).
fof(c_0_594,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) ),
file('<stdin>',fact_939_inf__sup__aci_I2_J) ).
fof(c_0_595,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) ),
file('<stdin>',fact_938_inf__assoc) ).
fof(c_0_596,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) ),
file('<stdin>',fact_835_sup__assoc) ).
fof(c_0_597,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) ),
file('<stdin>',fact_834_inf__sup__aci_I6_J) ).
fof(c_0_598,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X37)) ),
file('<stdin>',fact_833_sup_Oassoc) ).
fof(c_0_599,axiom,
! [X1] :
( ab_semigroup_mult(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
file('<stdin>',fact_599_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(c_0_600,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X93) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),X93)) ),
file('<stdin>',fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(c_0_601,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),X94) ),
file('<stdin>',fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(c_0_602,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)) ),
file('<stdin>',fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_603,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),X45) ),
file('<stdin>',fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_604,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)) ),
file('<stdin>',fact_170_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_605,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
<=> X30 = X54 ) ),
file('<stdin>',fact_421_le__less__Suc__eq) ).
fof(c_0_606,axiom,
! [X54,X30] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54))) ),
file('<stdin>',fact_396_not__less__eq) ).
fof(c_0_607,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X7,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X7))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X6),X7) = zero_zero(X1)
<=> ( ti(X1,X6) = zero_zero(X1)
& ti(X1,X7) = zero_zero(X1) ) ) ) ) ),
file('<stdin>',fact_343_add__nonneg__eq__0__iff) ).
fof(c_0_608,axiom,
! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X50)),
file('<stdin>',fact_703_nat__mult__assoc) ).
fof(c_0_609,axiom,
! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X50)),
file('<stdin>',fact_224_nat__add__assoc) ).
fof(c_0_610,axiom,
! [X1] :
( ord(X1)
=> ! [X29,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X29),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X57)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X57),X29)) ) ),
file('<stdin>',fact_860_atLeast__iff) ).
fof(c_0_611,axiom,
! [X1] :
( ord(X1)
=> ! [X29,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X29),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X57)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X57),X29)) ) ),
file('<stdin>',fact_538_greaterThan__iff) ).
fof(c_0_612,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> ( hAPP(nat,nat,suc,X49) != X51
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),X51)) ) ),
file('<stdin>',fact_390_Suc__lessI) ).
fof(c_0_613,axiom,
! [X1,X112,X25] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112)) )
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X25),X112))) ),
file('<stdin>',fact_872_finite__Int) ).
fof(c_0_614,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40) ),
file('<stdin>',fact_483_card__image) ).
fof(c_0_615,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51)) ),
file('<stdin>',fact_420_Suc__leI) ).
fof(c_0_616,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,X43,X6))
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
file('<stdin>',fact_801_sup1I2) ).
fof(c_0_617,axiom,
! [X1,X43,X40,X6] :
( hBOOL(hAPP(X1,bool,X40,X6))
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
file('<stdin>',fact_800_sup1I1) ).
fof(c_0_618,axiom,
! [X1,X40,X43,X6] :
( ( ~ hBOOL(hAPP(X1,bool,X43,X6))
=> hBOOL(hAPP(X1,bool,X40,X6)) )
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
file('<stdin>',fact_776_sup1CI) ).
fof(c_0_619,axiom,
! [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),
file('<stdin>',fact_425_card__Collect__le__nat) ).
fof(c_0_620,axiom,
! [X2,X1,X76,X25] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
=> 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),X76),X25))) ),
file('<stdin>',fact_459_finite__imageI) ).
fof(c_0_621,axiom,
! [X2,X1,X38,X40] :
( ! [X26,X46] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X46),X40))
=> ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X46)
=> ti(X1,X26) = ti(X1,X46) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
file('<stdin>',fact_317_inj__onI) ).
fof(c_0_622,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X30)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
| X54 = hAPP(nat,nat,suc,X30) ) ),
file('<stdin>',fact_404_le__Suc__eq) ).
fof(c_0_623,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> X49 = hAPP(nat,nat,suc,X51) ) ),
file('<stdin>',fact_401_le__SucE) ).
fof(c_0_624,axiom,
! [X51,X73] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X73))
=> ? [X33] : X73 = hAPP(nat,nat,suc,X33) ),
file('<stdin>',fact_438_Suc__le__D) ).
fof(c_0_625,axiom,
! [X11,X29,X63] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),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,X29)) ) ) ),
file('<stdin>',fact_430_inc__induct) ).
fof(c_0_626,axiom,
! [X1] :
( preorder(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
file('<stdin>',fact_115_less__le__not__le) ).
fof(c_0_627,axiom,
! [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,
file('<stdin>',fact_291_card__Collect__less__nat) ).
fof(c_0_628,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
<=> ( X54 = zero_zero(nat)
| ? [X64] :
( X54 = hAPP(nat,nat,suc,X64)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X30)) ) ) ),
file('<stdin>',fact_410_less__Suc__eq__0__disj) ).
fof(c_0_629,axiom,
! [X1,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
file('<stdin>',fact_259_subsetI) ).
fof(c_0_630,axiom,
! [X1,X3,X2,X87,X14,X15,X17,X81] :
( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),X17),X81)
=> ! [X108] : hAPP(X3,X2,X14,hAPP(X1,X3,X15,X108)) = hAPP(X87,X2,X17,hAPP(X1,X87,X81,X108)) ),
file('<stdin>',fact_732_o__eq__elim) ).
fof(c_0_631,axiom,
! [X1,X3,X2,X87,X107,X14,X15,X17,X81] :
( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),X17),X81)
=> hAPP(X3,X2,X14,hAPP(X1,X3,X15,X107)) = hAPP(X87,X2,X17,hAPP(X1,X87,X81,X107)) ),
file('<stdin>',fact_731_o__eq__dest) ).
fof(c_0_632,axiom,
! [X1,X38] :
( 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),X38),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),X38),top_top(fun(X1,bool))) = top_top(fun(X1,bool)) ) ),
file('<stdin>',fact_495_finite__UNIV__inj__surj) ).
fof(c_0_633,axiom,
! [X1,X38,X25] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
=> ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X25) = zero_zero(nat)
<=> ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X25))
=> hAPP(X1,nat,X38,X26) = zero_zero(nat) ) ) ),
file('<stdin>',fact_986_setsum__eq__0__iff) ).
fof(c_0_634,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
| X54 = X30 ) ),
file('<stdin>',fact_395_less__Suc__eq) ).
fof(c_0_635,axiom,
! [X30,X54] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
<=> X30 = X54 ) ),
file('<stdin>',fact_393_not__less__less__Suc__eq) ).
fof(c_0_636,axiom,
! [X51,X49] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X49)))
=> X49 = X51 ) ),
file('<stdin>',fact_392_less__antisym) ).
fof(c_0_637,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> X49 = X51 ) ),
file('<stdin>',fact_388_less__SucE) ).
fof(c_0_638,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
file('<stdin>',fact_417_less__Suc__eq__le) ).
fof(c_0_639,axiom,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X51)),
file('<stdin>',fact_406_Suc__n__not__le__n) ).
fof(c_0_640,axiom,
! [X57,X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)
<=> X54 = X30 ),
file('<stdin>',fact_606_Suc__mult__cancel1) ).
fof(c_0_641,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
| ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
file('<stdin>',fact_197_subset__iff__psubset__eq) ).
fof(c_0_642,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
& ti(fun(X1,bool),X40) != ti(fun(X1,bool),X43) ) ),
file('<stdin>',fact_196_psubset__eq) ).
fof(c_0_643,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
file('<stdin>',fact_198_psubset__imp__subset) ).
fof(c_0_644,axiom,
! [X1,X2,X3,X17,X38,X26] : hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X17)),X38),X26) = ti(X2,X17),
file('<stdin>',fact_733_K__record__comp) ).
fof(c_0_645,axiom,
! [X60] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
<=> ? [X33] :
! [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),X33)) ) ),
file('<stdin>',fact_304_finite__nat__set__iff__bounded) ).
fof(c_0_646,axiom,
! [X60] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
<=> ? [X33] :
! [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),X33)) ) ),
file('<stdin>',fact_303_finite__nat__set__iff__bounded__le) ).
fof(c_0_647,axiom,
! [X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X63)),
file('<stdin>',fact_766_image__Suc__atLeastAtMost) ).
fof(c_0_648,axiom,
! [X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X63)),
file('<stdin>',fact_515_image__Suc__atLeastLessThan) ).
fof(c_0_649,axiom,
! [X30,X11] :
( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X11,X30))
=> ? [X62] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X30))
& ! [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_367_ex__least__nat__less) ).
fof(c_0_650,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
file('<stdin>',fact_124_linorder__antisym__conv2) ).
fof(c_0_651,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( ti(X1,X6) = ti(X1,X7)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
file('<stdin>',fact_108_order__eq__iff) ).
fof(c_0_652,axiom,
! [X1] :
( order(X1)
=> ! [X7,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
file('<stdin>',fact_105_order__antisym__conv) ).
fof(c_0_653,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ti(X1,X34) = ti(X1,X35) ) ) ),
file('<stdin>',fact_100_order__antisym) ).
fof(c_0_654,axiom,
! [X1] :
( order(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ti(X1,X34) = ti(X1,X35) ) ) ),
file('<stdin>',fact_98_xt1_I5_J) ).
fof(c_0_655,axiom,
! [X1,X38] :
( 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),X38),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),X38),top_top(fun(X1,bool)))) ) ),
file('<stdin>',fact_496_finite__UNIV__surj__inj) ).
fof(c_0_656,axiom,
! [X1] :
( preorder(X1)
=> ! [X11,X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
=> hBOOL(X11) ) ) ),
file('<stdin>',fact_63_order__less__imp__triv) ).
fof(c_0_657,axiom,
! [X1] :
( linorder(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
file('<stdin>',fact_122_leD) ).
fof(c_0_658,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ),
file('<stdin>',fact_112_linorder__not__le) ).
fof(c_0_659,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
file('<stdin>',fact_111_linorder__not__less) ).
fof(c_0_660,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
| ti(X1,X6) = ti(X1,X7) ) ) ),
file('<stdin>',fact_72_not__less__iff__gr__or__eq) ).
fof(c_0_661,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
file('<stdin>',fact_67_order__less__not__sym) ).
fof(c_0_662,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
file('<stdin>',fact_66_order__less__imp__not__less) ).
fof(c_0_663,axiom,
! [X1] :
( preorder(X1)
=> ! [X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ),
file('<stdin>',fact_62_order__less__asym_H) ).
fof(c_0_664,axiom,
! [X1] :
( order(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
file('<stdin>',fact_61_xt1_I9_J) ).
fof(c_0_665,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
file('<stdin>',fact_54_order__less__asym) ).
fof(c_0_666,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51))) ),
file('<stdin>',fact_419_le__imp__less__Suc) ).
fof(c_0_667,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51))) ),
file('<stdin>',fact_402_le__SucI) ).
fof(c_0_668,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51))) ),
file('<stdin>',fact_391_less__SucI) ).
fof(c_0_669,axiom,
! [X1,X2] :
( lattice(X2)
=> ! [X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X38),X39),X26) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)) ),
file('<stdin>',fact_950_inf__fun__def) ).
fof(c_0_670,axiom,
! [X2,X1] :
( lattice(X1)
=> ! [X38,X39,X6] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_inf_inf(fun(X2,X1)),X38),X39),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X2,X1,X38,X6)),hAPP(X2,X1,X39,X6)) ),
file('<stdin>',fact_937_inf__apply) ).
fof(c_0_671,axiom,
! [X1,X2] :
( lattice(X2)
=> ! [X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X38),X39),X26) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)) ),
file('<stdin>',fact_817_sup__fun__def) ).
fof(c_0_672,axiom,
! [X2,X1] :
( lattice(X1)
=> ! [X38,X39,X6] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_sup_sup(fun(X2,X1)),X38),X39),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X2,X1,X38,X6)),hAPP(X2,X1,X39,X6)) ),
file('<stdin>',fact_816_sup__apply) ).
fof(c_0_673,axiom,
! [X54,X30,X57] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
<=> X54 = X30 ) ),
file('<stdin>',fact_706_nat__mult__eq__cancel1) ).
fof(c_0_674,axiom,
! [X1] :
( 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)))) ),
file('<stdin>',fact_364_zero__less__two) ).
fof(c_0_675,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X49))
=> X49 = X51 ) ),
file('<stdin>',fact_231_le__antisym) ).
fof(c_0_676,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X49),X49) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X49) ),
file('<stdin>',fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(c_0_677,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21))) ),
file('<stdin>',fact_619_zero__le__square) ).
fof(c_0_678,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1)))) ),
file('<stdin>',fact_151_less__add__one) ).
fof(c_0_679,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X37)) ),
file('<stdin>',fact_943_inf_Oleft__commute) ).
fof(c_0_680,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
file('<stdin>',fact_942_inf__sup__aci_I3_J) ).
fof(c_0_681,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
file('<stdin>',fact_941_inf__left__commute) ).
fof(c_0_682,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
file('<stdin>',fact_832_sup__left__commute) ).
fof(c_0_683,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
file('<stdin>',fact_831_inf__sup__aci_I7_J) ).
fof(c_0_684,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X37)) ),
file('<stdin>',fact_830_sup_Oleft__commute) ).
fof(c_0_685,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X94)) ),
file('<stdin>',fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(c_0_686,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X45)) ),
file('<stdin>',fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_687,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X35,X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
file('<stdin>',fact_839_sup__ge2) ).
fof(c_0_688,axiom,
! [X1] :
( lattice(X1)
=> ! [X35,X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
file('<stdin>',fact_838_inf__sup__ord_I4_J) ).
fof(c_0_689,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
file('<stdin>',fact_837_sup__ge1) ).
fof(c_0_690,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
file('<stdin>',fact_836_inf__sup__ord_I3_J) ).
fof(c_0_691,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X36,X35] :
( ! [X26] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X36)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36)) ) ),
file('<stdin>',fact_155_dense__le) ).
fof(c_0_692,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ? [X84,X44] :
( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),X84),X40) = 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)),X44))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),X84),X40)) ) ),
file('<stdin>',fact_524_finite__imp__inj__to__nat__seg) ).
fof(c_0_693,axiom,
! [X1,X40] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
file('<stdin>',fact_365_card__ge__0__finite) ).
fof(c_0_694,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ) ),
file('<stdin>',fact_293_finite__subset) ).
fof(c_0_695,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ) ),
file('<stdin>',fact_292_rev__finite__subset) ).
fof(c_0_696,axiom,
! [X2,X1,X39,X38] :
( ! [X26] : hAPP(X2,X1,X39,hAPP(X1,X2,X38,X26)) = ti(X1,X26)
=> hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),top_top(fun(X2,bool))) = top_top(fun(X1,bool)) ),
file('<stdin>',fact_528_surjI) ).
fof(c_0_697,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),
file('<stdin>',fact_905_Int__left__absorb) ).
fof(c_0_698,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),
file('<stdin>',fact_794_Un__left__absorb) ).
fof(c_0_699,axiom,
! [X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X49))),
file('<stdin>',fact_572_le__square) ).
fof(c_0_700,axiom,
! [X51,X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X49))),
file('<stdin>',fact_248_le__add1) ).
fof(c_0_701,axiom,
! [X51,X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51))),
file('<stdin>',fact_247_le__add2) ).
fof(c_0_702,axiom,
! [X34,X35,X36] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X36)),
file('<stdin>',fact_223_nat__add__left__commute) ).
fof(c_0_703,axiom,
! [X30,X11] :
( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X11,X30))
=> ? [X62] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X30))
& ! [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_369_ex__least__nat__le) ).
fof(c_0_704,axiom,
! [X1,X53,X11,X6] :
( hBOOL(hAPP(X1,bool,X11,X6))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53))
=> hBOOL(hAPP(X1,bool,X53,X6)) ) ),
file('<stdin>',fact_211_rev__predicate1D) ).
fof(c_0_705,axiom,
! [X1,X6,X11,X53] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53))
=> ( hBOOL(hAPP(X1,bool,X11,X6))
=> hBOOL(hAPP(X1,bool,X53,X6)) ) ),
file('<stdin>',fact_207_predicate1D) ).
fof(c_0_706,axiom,
! [X1,X40] :
( ~ 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),X40))
=> ? [X19] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40)) ) ),
file('<stdin>',fact_302_ex__new__if__finite) ).
fof(c_0_707,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X40) ),
file('<stdin>',fact_912_Int__absorb2) ).
fof(c_0_708,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
file('<stdin>',fact_911_Int__absorb1) ).
fof(c_0_709,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X40) ),
file('<stdin>',fact_786_Un__absorb2) ).
fof(c_0_710,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
file('<stdin>',fact_785_Un__absorb1) ).
fof(c_0_711,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
<=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
file('<stdin>',fact_784_subset__Un__eq) ).
fof(c_0_712,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
<=> ? [X62] : X30 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62)) ),
file('<stdin>',fact_415_less__iff__Suc__add) ).
fof(c_0_713,axiom,
! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3)),combs(X1,X2,X3),X118),X119),X120) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X118,X120),hAPP(X1,X2,X119,X120)),
file('<stdin>',help_COMBS_1_1_U) ).
fof(c_0_714,axiom,
! [X58,X50] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X50))
=> ( X50 != hAPP(nat,nat,suc,X58)
=> ~ ! [X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
=> X50 != hAPP(nat,nat,suc,X64) ) ) ),
file('<stdin>',fact_439_lessE) ).
fof(c_0_715,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> ? [X62] : X51 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X62)) ),
file('<stdin>',fact_431_less__imp__Suc__add) ).
fof(c_0_716,axiom,
! [X1] :
( ring_char_0(X1)
=> ! [X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14) = zero_zero(X1)
<=> ti(X1,X14) = zero_zero(X1) ) ) ),
file('<stdin>',fact_541_Ints__double__eq__0__iff) ).
fof(c_0_717,axiom,
! [X1] :
( order(X1)
=> ! [X37,X21,X22] :
( ti(X1,X21) = ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X21)) ) ) ),
file('<stdin>',fact_103_xt1_I3_J) ).
fof(c_0_718,axiom,
! [X1] :
( order(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( ti(X1,X22) = ti(X1,X37)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X21)) ) ) ),
file('<stdin>',fact_101_xt1_I4_J) ).
fof(c_0_719,axiom,
! [X1] :
( linorder(X1)
=> ! [X7,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
file('<stdin>',fact_70_linorder__antisym__conv3) ).
fof(c_0_720,axiom,
! [X1] :
( order(X1)
=> ! [X37,X21,X22] :
( ti(X1,X21) = ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X21)) ) ) ),
file('<stdin>',fact_59_xt1_I1_J) ).
fof(c_0_721,axiom,
! [X1] :
( order(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ( ti(X1,X22) = ti(X1,X37)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X21)) ) ) ),
file('<stdin>',fact_57_xt1_I2_J) ).
fof(c_0_722,axiom,
! [X1] :
( order(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( ti(X1,X21) != ti(X1,X22)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ) ),
file('<stdin>',fact_127_xt1_I11_J) ).
fof(c_0_723,axiom,
! [X1] :
( order(X1)
=> ! [X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( ti(X1,X21) != ti(X1,X22)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
file('<stdin>',fact_126_order__le__neq__trans) ).
fof(c_0_724,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
| ti(X1,X34) = ti(X1,X35) ) ) ),
file('<stdin>',fact_125_order__le__imp__less__or__eq) ).
fof(c_0_725,axiom,
! [X1] :
( order(X1)
=> ! [X21,X22] :
( ti(X1,X21) != ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ) ),
file('<stdin>',fact_121_xt1_I12_J) ).
fof(c_0_726,axiom,
! [X1] :
( order(X1)
=> ! [X21,X22] :
( ti(X1,X21) != ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
file('<stdin>',fact_120_order__neq__le__trans) ).
fof(c_0_727,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
file('<stdin>',fact_119_linorder__antisym__conv1) ).
fof(c_0_728,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
| ti(X1,X6) = ti(X1,X7) ) ) ),
file('<stdin>',fact_116_order__le__less) ).
fof(c_0_729,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& ti(X1,X6) != ti(X1,X7) ) ) ),
file('<stdin>',fact_114_order__less__le) ).
fof(c_0_730,axiom,
! [X1,X2,X6,X7,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
=> ti(X1,X6) = ti(X1,X7) ) ),
file('<stdin>',fact_146_injD) ).
fof(c_0_731,axiom,
! [X1,X2,X6,X7,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
<=> ti(X1,X6) = ti(X1,X7) ) ),
file('<stdin>',fact_145_inj__eq) ).
fof(c_0_732,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( X21 = X22
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37)) ) ) ),
file('<stdin>',fact_104_ord__eq__le__trans) ).
fof(c_0_733,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( X22 = X37
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37)) ) ) ),
file('<stdin>',fact_102_ord__le__eq__trans) ).
fof(c_0_734,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( X21 = X22
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X37)) ) ) ),
file('<stdin>',fact_60_ord__eq__less__trans) ).
fof(c_0_735,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( X22 = X37
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X37)) ) ) ),
file('<stdin>',fact_58_ord__less__eq__trans) ).
fof(c_0_736,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
file('<stdin>',fact_123_order__less__imp__le) ).
fof(c_0_737,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),
file('<stdin>',fact_667_mult__Suc) ).
fof(c_0_738,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_atLeastAtMost(nat),X77),X66))),
file('<stdin>',fact_761_finite__atLeastAtMost) ).
fof(c_0_739,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_gr676655987ssThan(nat),X77),X66))),
file('<stdin>',fact_549_finite__greaterThanLessThan) ).
fof(c_0_740,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_gr1471790799AtMost(nat),X77),X66))),
file('<stdin>',fact_548_finite__greaterThanAtMost) ).
fof(c_0_741,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_742,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_370_less__imp__add__positive) ).
fof(c_0_743,axiom,
! [X2,X3,X1,X28,X14,X15] : hAPP(product_prod(X2,X3),X1,hAPP(fun(X2,fun(X3,X1)),fun(product_prod(X2,X3),X1),product_prod_rec(X2,X3,X1),X28),hAPP(X3,product_prod(X2,X3),hAPP(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X14),X15)) = hAPP(X3,X1,hAPP(X2,fun(X3,X1),X28,X14),X15),
file('<stdin>',fact_28_prod_Orecs) ).
fof(c_0_744,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> ( X49 != X51
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ) ),
file('<stdin>',fact_245_le__neq__implies__less) ).
fof(c_0_745,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
| X54 = X30 ) ),
file('<stdin>',fact_243_le__eq__less__or__eq) ).
fof(c_0_746,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
& X54 != X30 ) ),
file('<stdin>',fact_242_nat__less__le) ).
fof(c_0_747,axiom,
! [X34,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35)) ),
file('<stdin>',fact_264_termination__basic__simps_I5_J) ).
fof(c_0_748,axiom,
! [X49,X51] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
| X49 = X51 )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
file('<stdin>',fact_246_less__or__eq__imp__le) ).
fof(c_0_749,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
file('<stdin>',fact_244_less__imp__le__nat) ).
fof(c_0_750,axiom,
! [X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,zero_zero(nat))))
<=> X30 = zero_zero(nat) ),
file('<stdin>',fact_409_less__Suc0) ).
fof(c_0_751,axiom,
! [X1] :
( 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))))) ),
file('<stdin>',fact_366_finite__UNIV__card__ge__0) ).
fof(c_0_752,axiom,
? [X65] : hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X65),arrow_1568854078le_Lin)),
file('<stdin>',fact_271_linear__alt) ).
fof(c_0_753,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
file('<stdin>',fact_36__096Lba_A_058_ALin_096) ).
fof(c_0_754,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
file('<stdin>',fact_35__096Lab_A_058_ALin_096) ).
fof(c_0_755,axiom,
! [X30,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,X30)) ) ),
file('<stdin>',fact_444_nat__induct) ).
fof(c_0_756,axiom,
! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(X2,fun(X1,X3),hAPP(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)),combc(X1,X2,X3),X118),X119),X120) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X118,X120),X119),
file('<stdin>',help_COMBC_1_1_U) ).
fof(c_0_757,axiom,
! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X118),X119),X120) = hAPP(X2,X3,X118,hAPP(X1,X2,X119,X120)),
file('<stdin>',help_COMBB_1_1_U) ).
fof(c_0_758,axiom,
! [X3,X1,X2,X38,X39,X6] : hAPP(X3,X1,hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),comp(X2,X1,X3),X38),X39),X6) = hAPP(X2,X1,X38,hAPP(X3,X2,X39,X6)),
file('<stdin>',fact_730_o__apply) ).
fof(c_0_759,axiom,
! [X1,X2,X3,X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X38),X39),X26) = hAPP(X3,X2,X38,hAPP(X1,X3,X39,X26)),
file('<stdin>',fact_728_o__def) ).
fof(c_0_760,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,suc,X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),
file('<stdin>',fact_666_mult__Suc__right) ).
fof(c_0_761,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),
file('<stdin>',fact_398_add__Suc) ).
fof(c_0_762,axiom,
! [X1,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
<=> hBOOL(hAPP(X1,bool,X40,X6)) ),
file('<stdin>',fact_76_mem__def) ).
fof(c_0_763,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X6),X7) = ti(X1,X6) ) ),
file('<stdin>',fact_929_le__iff__inf) ).
fof(c_0_764,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = ti(X1,X34) ) ),
file('<stdin>',fact_925_inf__absorb1) ).
fof(c_0_765,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = ti(X1,X35) ) ),
file('<stdin>',fact_924_inf__absorb2) ).
fof(c_0_766,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = ti(X1,X34) ) ),
file('<stdin>',fact_845_sup__absorb1) ).
fof(c_0_767,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = ti(X1,X35) ) ),
file('<stdin>',fact_844_sup__absorb2) ).
fof(c_0_768,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X6),X7) = ti(X1,X7) ) ),
file('<stdin>',fact_840_le__iff__sup) ).
fof(c_0_769,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
<=> ? [X62] : X30 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62) ),
file('<stdin>',fact_249_le__iff__add) ).
fof(c_0_770,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X34,X35] :
( ti(X1,X34) != ti(X1,X35)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
file('<stdin>',fact_164_linorder__neqE__linordered__idom) ).
fof(c_0_771,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ti(X1,X6) != ti(X1,X7)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ) ),
file('<stdin>',fact_73_linorder__neq__iff) ).
fof(c_0_772,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
| ti(X1,X34) = ti(X1,X35)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
file('<stdin>',fact_71_linorder__less__linear) ).
fof(c_0_773,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ti(X1,X34) != ti(X1,X35)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
file('<stdin>',fact_69_linorder__neqE) ).
fof(c_0_774,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( ti(X1,X34) != ti(X1,X35)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
file('<stdin>',fact_53_linorder__cases) ).
fof(c_0_775,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22) ),
file('<stdin>',fact_946_inf_Oleft__idem) ).
fof(c_0_776,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) ),
file('<stdin>',fact_945_inf__sup__aci_I4_J) ).
fof(c_0_777,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) ),
file('<stdin>',fact_944_inf__left__idem) ).
fof(c_0_778,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) ),
file('<stdin>',fact_829_sup__left__idem) ).
fof(c_0_779,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) ),
file('<stdin>',fact_828_inf__sup__aci_I8_J) ).
fof(c_0_780,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22) ),
file('<stdin>',fact_827_sup_Oleft__idem) ).
fof(c_0_781,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) ),
file('<stdin>',fact_821_mult__left__idem) ).
fof(c_0_782,axiom,
! [X1,X53,X11] :
( ! [X26] :
( hBOOL(hAPP(X1,bool,X11,X26))
=> hBOOL(hAPP(X1,bool,X53,X26)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53)) ),
file('<stdin>',fact_717_predicate1I) ).
fof(c_0_783,axiom,
! [X1] :
( linorder(X1)
=> ! [X35,X34] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
file('<stdin>',fact_118_not__leE) ).
fof(c_0_784,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
file('<stdin>',fact_117_leI) ).
fof(c_0_785,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
file('<stdin>',fact_113_linorder__le__less__linear) ).
fof(c_0_786,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
file('<stdin>',fact_109_linorder__linear) ).
fof(c_0_787,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
file('<stdin>',fact_95_linorder__le__cases) ).
fof(c_0_788,axiom,
! [X30,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),X30)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60)) ),
file('<stdin>',fact_315_bounded__nat__set__is__finite) ).
fof(c_0_789,axiom,
! [X2,X1] :
( 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)))) ) ),
file('<stdin>',fact_296_finite__Prod__UNIV) ).
fof(c_0_790,axiom,
! [X1,X2] :
( 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))))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ) ),
file('<stdin>',fact_295_finite__Plus__UNIV__iff) ).
fof(c_0_791,axiom,
! [X34,X35] :
( X34 != X35
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X34)) ) ),
file('<stdin>',fact_217_linorder__neqE__nat) ).
fof(c_0_792,axiom,
! [X54,X30] :
( X54 != X30
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54)) ) ),
file('<stdin>',fact_216_nat__neq__iff) ).
fof(c_0_793,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X49)) ),
file('<stdin>',fact_228_nat__le__linear) ).
fof(c_0_794,axiom,
! [X1,X3,X2,X107,X14,X15,X17] :
( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = ti(fun(X1,X2),X17)
=> hAPP(X3,X2,X14,hAPP(X1,X3,X15,X107)) = hAPP(X1,X2,X17,X107) ),
file('<stdin>',fact_734_o__eq__dest__lhs) ).
fof(c_0_795,axiom,
! [X1,X40] :
( ! [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> top_top(fun(X1,bool)) = ti(fun(X1,bool),X40) ),
file('<stdin>',fact_715_UNIV__eq__I) ).
fof(c_0_796,axiom,
! [X2,X1,X14,X15,X12,X13] :
( hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X14),X15) = hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X12),X13)
<=> ( ti(X1,X14) = ti(X1,X12)
& ti(X2,X15) = ti(X2,X13) ) ),
file('<stdin>',fact_22_Pair__eq) ).
fof(c_0_797,axiom,
! [X2,X1,X21,X22,X23,X24] :
( hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X21),X22) = hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X23),X24)
=> ~ ( ti(X1,X21) = ti(X1,X23)
=> ti(X2,X22) != ti(X2,X24) ) ),
file('<stdin>',fact_21_Pair__inject) ).
fof(c_0_798,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( ( ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> one_one(nat) = zero_zero(nat) )
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
file('<stdin>',fact_368_card_Oneutral) ).
fof(c_0_799,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,suc,X51)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),
file('<stdin>',fact_399_add__Suc__right) ).
fof(c_0_800,axiom,
! [X1,X28,X86,X67] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X28),X86),hAPP(nat,nat,suc,X67)) = hAPP(nat,X1,X86,X67),
file('<stdin>',fact_540_nat__case__Suc) ).
fof(c_0_801,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,suc,X51)),
file('<stdin>',fact_397_add__Suc__shift) ).
fof(c_0_802,axiom,
! [X104] : hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X104)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X104)),hAPP(nat,nat,suc,zero_zero(nat))),
file('<stdin>',fact_740_nat_Osize_I4_J) ).
fof(c_0_803,axiom,
! [X104] : hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X104)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X104)),hAPP(nat,nat,suc,zero_zero(nat))),
file('<stdin>',fact_719_nat_Osize_I2_J) ).
fof(c_0_804,axiom,
! [X1,X2] :
( 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)))) ) ),
file('<stdin>',fact_372_finite__fun__UNIVD1) ).
fof(c_0_805,axiom,
! [X1,X2,X38] :
( ! [X26,X46] :
( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X46)
=> ti(X1,X26) = ti(X1,X46) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool)))) ),
file('<stdin>',fact_154_injI) ).
fof(c_0_806,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
file('<stdin>',fact_19_n_I1_J) ).
fof(c_0_807,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_443_zero__induct) ).
fof(c_0_808,axiom,
! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X77)),X66) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X77),X66),
file('<stdin>',fact_767_atLeastSucAtMost__greaterThanAtMost) ).
fof(c_0_809,axiom,
! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X77)),X66) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X77),X66),
file('<stdin>',fact_554_atLeastSucLessThan__greaterThanLessThan) ).
fof(c_0_810,axiom,
! [X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51))
=> ? [X33] : X51 = hAPP(nat,nat,suc,X33) ),
file('<stdin>',fact_432_gr0__implies__Suc) ).
fof(c_0_811,axiom,
! [X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30))
<=> ? [X33] : X30 = hAPP(nat,nat,suc,X33) ),
file('<stdin>',fact_408_gr0__conv__Suc) ).
fof(c_0_812,axiom,
! [X2,X1,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
<=> ! [X46] :
? [X26] : ti(X1,X46) = hAPP(X2,X1,X38,X26) ),
file('<stdin>',fact_529_surj__def) ).
fof(c_0_813,axiom,
! [X2,X1,X7,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ? [X26] : ti(X1,X7) = hAPP(X2,X1,X38,X26) ),
file('<stdin>',fact_527_surjD) ).
fof(c_0_814,axiom,
! [X2,X1,X7,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ~ ! [X26] : ti(X1,X7) != hAPP(X2,X1,X38,X26) ),
file('<stdin>',fact_526_surjE) ).
fof(c_0_815,axiom,
~ ! [X78] :
( hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),X78),top_top(fun(arrow_1998540521e_indi,bool))))
=> hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),X78),top_top(fun(arrow_1998540521e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_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_816,axiom,
hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
file('<stdin>',fact_457_surjh) ).
fof(c_0_817,axiom,
! [X1,X2,X40] : 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),X40),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)),
file('<stdin>',fact_89_Pi__UNIV) ).
fof(c_0_818,axiom,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
file('<stdin>',fact_355_not__one__less__zero) ).
fof(c_0_819,axiom,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
file('<stdin>',fact_353_not__one__le__zero) ).
fof(c_0_820,axiom,
! [X1] :
( top(X1)
=> ! [X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X21))
=> ti(X1,X21) = top_top(X1) ) ),
file('<stdin>',fact_134_top__le) ).
fof(c_0_821,axiom,
! [X1] :
( top(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X14))
<=> ti(X1,X14) = top_top(X1) ) ),
file('<stdin>',fact_133_top__unique) ).
fof(c_0_822,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X14,X15,X17] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X15) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)
<=> ti(X1,X15) = ti(X1,X17) ) ),
file('<stdin>',fact_169_add__left__cancel) ).
fof(c_0_823,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X15,X14,X17] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X14) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)
<=> ti(X1,X15) = ti(X1,X17) ) ),
file('<stdin>',fact_168_add__right__cancel) ).
fof(c_0_824,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X21,X22,X37] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)
=> ti(X1,X22) = ti(X1,X37) ) ),
file('<stdin>',fact_167_add__left__imp__eq) ).
fof(c_0_825,axiom,
! [X1] :
( cancel146912293up_add(X1)
=> ! [X21,X22,X37] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)
=> ti(X1,X22) = ti(X1,X37) ) ),
file('<stdin>',fact_166_add__imp__eq) ).
fof(c_0_826,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X22,X21,X37] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X21) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)
=> ti(X1,X22) = ti(X1,X37) ) ),
file('<stdin>',fact_165_add__right__imp__eq) ).
fof(c_0_827,axiom,
! [X1] :
( top(X1)
=> ! [X14] :
( ti(X1,X14) != top_top(X1)
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),top_top(X1))) ) ),
file('<stdin>',fact_31_less__top) ).
fof(c_0_828,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ti(X1,X34) != ti(X1,X35) ) ),
file('<stdin>',fact_68_less__imp__neq) ).
fof(c_0_829,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ti(X1,X34) != ti(X1,X35) ) ),
file('<stdin>',fact_65_order__less__imp__not__eq) ).
fof(c_0_830,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ti(X1,X35) != ti(X1,X34) ) ),
file('<stdin>',fact_64_order__less__imp__not__eq2) ).
fof(c_0_831,axiom,
! [X1] :
( top(X1)
=> ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X21)) ),
file('<stdin>',fact_30_not__top__less) ).
fof(c_0_832,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X51))),
file('<stdin>',fact_375_zero__less__Suc) ).
fof(c_0_833,axiom,
! [X1,X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35))
| ti(X1,X34) = ti(X1,X35) ),
file('<stdin>',help_fequal_1_1_T) ).
fof(c_0_834,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X51))),
file('<stdin>',fact_373_lessI) ).
fof(c_0_835,axiom,
! [X1] :
( preorder(X1)
=> ! [X34] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X34)) ),
file('<stdin>',fact_74_order__less__irrefl) ).
fof(c_0_836,axiom,
! [X30] :
( X30 != zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30)) ),
file('<stdin>',fact_330_neq0__conv) ).
fof(c_0_837,axiom,
! [X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),zero_zero(nat)))
<=> X30 = zero_zero(nat) ),
file('<stdin>',fact_338_le__0__eq) ).
fof(c_0_838,axiom,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
file('<stdin>',fact_331_less__nat__zero__code) ).
fof(c_0_839,axiom,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
file('<stdin>',fact_329_not__less0) ).
fof(c_0_840,axiom,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
file('<stdin>',fact_319_less__zeroE) ).
fof(c_0_841,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> X51 != zero_zero(nat) ),
file('<stdin>',fact_332_gr__implies__not0) ).
fof(c_0_842,axiom,
! [X55,X56] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
=> X55 != X56 ),
file('<stdin>',fact_220_less__not__refl3) ).
fof(c_0_843,axiom,
! [X51,X49] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
=> X49 != X51 ),
file('<stdin>',fact_219_less__not__refl2) ).
fof(c_0_844,axiom,
! [X57,X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
<=> ( X57 = zero_zero(nat)
| X54 = X30 ) ),
file('<stdin>',fact_707_nat__mult__eq__cancel__disj) ).
fof(c_0_845,axiom,
! [X57,X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
<=> ( X54 = X30
| X57 = zero_zero(nat) ) ),
file('<stdin>',fact_608_mult__cancel1) ).
fof(c_0_846,axiom,
! [X54,X57,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)
<=> ( X54 = X30
| X57 = zero_zero(nat) ) ),
file('<stdin>',fact_607_mult__cancel2) ).
fof(c_0_847,axiom,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
file('<stdin>',fact_218_less__irrefl__nat) ).
fof(c_0_848,axiom,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
file('<stdin>',fact_215_less__not__refl) ).
fof(c_0_849,axiom,
! [X54,X57,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57)
<=> X54 = X30 ),
file('<stdin>',fact_226_nat__add__right__cancel) ).
fof(c_0_850,axiom,
! [X57,X54,X30] :
( 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),X30)
<=> X54 = X30 ),
file('<stdin>',fact_225_nat__add__left__cancel) ).
fof(c_0_851,axiom,
! [X1,X40] : hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X40),
file('<stdin>',fact_990_card__eq__setsum) ).
fof(c_0_852,axiom,
! [X118,X119] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119))
| hBOOL(X118)
| hBOOL(X119) ),
file('<stdin>',help_fdisj_3_1_U) ).
fof(c_0_853,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = ti(X1,X34) ),
file('<stdin>',fact_881_inf__sup__absorb) ).
fof(c_0_854,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = ti(X1,X34) ),
file('<stdin>',fact_880_sup__inf__absorb) ).
fof(c_0_855,axiom,
! [X118,X119] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
| hBOOL(X119) ),
file('<stdin>',help_fconj_3_1_U) ).
fof(c_0_856,axiom,
! [X118,X119] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
| hBOOL(X118) ),
file('<stdin>',help_fconj_2_1_U) ).
fof(c_0_857,axiom,
! [X1,X2,X38,X39] :
( ! [X26] : hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26)
=> ti(fun(X1,X2),X38) = ti(fun(X1,X2),X39) ),
file('<stdin>',fact_75_ext) ).
fof(c_0_858,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X40),
file('<stdin>',fact_906_Int__commute) ).
fof(c_0_859,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X40),
file('<stdin>',fact_793_Un__commute) ).
fof(c_0_860,axiom,
! [X1,X2] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool))))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
file('<stdin>',fact_300_finite__fun__UNIVD2) ).
fof(c_0_861,axiom,
! [X1,X28,X86] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X28),X86),zero_zero(nat)) = ti(X1,X28),
file('<stdin>',fact_539_nat__case__0) ).
fof(c_0_862,axiom,
! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X77),hAPP(nat,nat,suc,X66)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X77),X66),
file('<stdin>',fact_763_atLeastLessThanSuc__atLeastAtMost) ).
fof(c_0_863,axiom,
! [X2,X1] :
( comm_monoid_add(X1)
=> ! [X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),combk(X1,X2),zero_zero(X1))),X40) = zero_zero(X1) ),
file('<stdin>',fact_979_setsum__0) ).
fof(c_0_864,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
file('<stdin>',fact_210_equalityD1) ).
fof(c_0_865,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ),
file('<stdin>',fact_209_equalityD2) ).
fof(c_0_866,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
file('<stdin>',fact_202_equalityE) ).
fof(c_0_867,axiom,
! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),top_top(fun(X1,bool)))),
file('<stdin>',fact_162_subset__UNIV) ).
fof(c_0_868,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
file('<stdin>',tsy_c_Finite__Set_Ofolding__image_res) ).
fof(c_0_869,axiom,
! [X1,X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X34),X35) = ti(X1,X35),
file('<stdin>',help_If_2_1_T) ).
fof(c_0_870,axiom,
! [X1,X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X34),X35) = ti(X1,X34),
file('<stdin>',help_If_1_1_T) ).
fof(c_0_871,axiom,
! [X54,X30] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30)
<=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
& X30 = zero_zero(nat) )
| ( X54 = zero_zero(nat)
& X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
file('<stdin>',fact_412_one__is__add) ).
fof(c_0_872,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
& X30 = zero_zero(nat) )
| ( X54 = zero_zero(nat)
& X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
file('<stdin>',fact_411_add__is__1) ).
fof(c_0_873,axiom,
! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X40)),
file('<stdin>',fact_213_subset__refl) ).
fof(c_0_874,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
=> ( hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
=> ti(fun(X1,bool),X40) = top_top(fun(X1,bool)) ) ),
file('<stdin>',fact_299_card__eq__UNIV__imp__eq__UNIV) ).
fof(c_0_875,axiom,
! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X40)),
file('<stdin>',fact_142_inj__on__id2) ).
fof(c_0_876,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
file('<stdin>',fact_20_injh) ).
fof(c_0_877,axiom,
! [X1] :
? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),top_top(fun(X1,bool)))),
file('<stdin>',fact_714_UNIV__witness) ).
fof(c_0_878,axiom,
! [X1,X2] : 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),
file('<stdin>',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).
fof(c_0_879,axiom,
! [X1,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),top_top(fun(X1,bool)))),
file('<stdin>',fact_27_iso__tuple__UNIV__I) ).
fof(c_0_880,axiom,
! [X1,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),top_top(fun(X1,bool)))),
file('<stdin>',fact_26_UNIV__I) ).
fof(c_0_881,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_407_inj__Suc) ).
fof(c_0_882,axiom,
! [X1] :
( 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))) ),
file('<stdin>',fact_537_Ints__1) ).
fof(c_0_883,axiom,
! [X1] :
( 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))) ),
file('<stdin>',fact_535_Ints__0) ).
fof(c_0_884,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
& X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
file('<stdin>',fact_659_mult__eq__1__iff) ).
fof(c_0_885,axiom,
! [X1] :
( 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)))) ),
file('<stdin>',fact_294_finite__option__UNIV) ).
fof(c_0_886,axiom,
! [X1,X34,X35] :
( ti(X1,X34) != ti(X1,X35)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35)) ),
file('<stdin>',help_fequal_2_1_T) ).
fof(c_0_887,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
file('<stdin>',fact_354_zero__less__one) ).
fof(c_0_888,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
file('<stdin>',fact_352_zero__le__one) ).
fof(c_0_889,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X21) ),
file('<stdin>',fact_949_inf_Ocommute) ).
fof(c_0_890,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34) ),
file('<stdin>',fact_948_inf__sup__aci_I1_J) ).
fof(c_0_891,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34) ),
file('<stdin>',fact_947_inf__commute) ).
fof(c_0_892,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34) ),
file('<stdin>',fact_826_sup__commute) ).
fof(c_0_893,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34) ),
file('<stdin>',fact_825_inf__sup__aci_I5_J) ).
fof(c_0_894,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X21) ),
file('<stdin>',fact_824_sup_Ocommute) ).
fof(c_0_895,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21) ),
file('<stdin>',fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(c_0_896,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21) ),
file('<stdin>',fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_897,axiom,
! [X1] :
( top(X1)
=> ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),top_top(X1))) ),
file('<stdin>',fact_132_top__greatest) ).
fof(c_0_898,axiom,
! [X2,X1] : 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),top_top(fun(X1,bool))),top_top(fun(X2,bool))) = top_top(fun(sum_sum(X1,X2),bool)),
file('<stdin>',fact_313_UNIV__Plus__UNIV) ).
fof(c_0_899,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( X34 = X35
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
file('<stdin>',fact_107_order__eq__refl) ).
fof(c_0_900,axiom,
! [X1] :
( preorder(X1)
=> ! [X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X34)) ),
file('<stdin>',fact_92_order__refl) ).
fof(c_0_901,axiom,
! [X51] :
( X51 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51)) ),
file('<stdin>',fact_333_gr0I) ).
fof(c_0_902,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X51)),
file('<stdin>',fact_339_less__eq__nat_Osimps_I1_J) ).
fof(c_0_903,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X51)),
file('<stdin>',fact_320_le0) ).
fof(c_0_904,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ),
file('<stdin>',fact_985_setsum_Oinfinite) ).
fof(c_0_905,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),X40) = zero_zero(X2) ) ),
file('<stdin>',fact_984_setsum__infinite) ).
fof(c_0_906,axiom,
! [X49,X51] :
( X49 = X51
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
file('<stdin>',fact_229_eq__imp__le) ).
fof(c_0_907,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X51)),
file('<stdin>',fact_227_le__refl) ).
fof(c_0_908,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X49),
file('<stdin>',fact_702_nat__mult__commute) ).
fof(c_0_909,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X49),
file('<stdin>',fact_222_nat__add__commute) ).
fof(c_0_910,axiom,
! [X119,X118] :
( ~ hBOOL(X118)
| ~ hBOOL(X119)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119)) ),
file('<stdin>',help_fconj_1_1_U) ).
fof(c_0_911,axiom,
! [X118,X119] :
( ~ hBOOL(X119)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
file('<stdin>',help_fdisj_2_1_U) ).
fof(c_0_912,axiom,
! [X119,X118] :
( ~ hBOOL(X118)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
file('<stdin>',help_fdisj_1_1_U) ).
fof(c_0_913,axiom,
hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
file('<stdin>',fact_531_greaterThan__0) ).
fof(c_0_914,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
file('<stdin>',fact_1_u) ).
fof(c_0_915,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
file('<stdin>',fact_0_assms_I3_J) ).
fof(c_0_916,axiom,
! [X1] :
( ring_n68954251visors(X1)
=> ! [X14,X15] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15) = zero_zero(X1)
<=> ( ti(X1,X14) = zero_zero(X1)
| ti(X1,X15) = zero_zero(X1) ) ) ),
file('<stdin>',fact_596_mult__eq__0__iff) ).
fof(c_0_917,axiom,
! [X1] :
( no_zero_divisors(X1)
=> ! [X22,X21] :
( ti(X1,X21) != zero_zero(X1)
=> ( ti(X1,X22) != zero_zero(X1)
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) != zero_zero(X1) ) ) ),
file('<stdin>',fact_595_no__zero__divisors) ).
fof(c_0_918,axiom,
! [X1] :
( no_zero_divisors(X1)
=> ! [X21,X22] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) = zero_zero(X1)
=> ( ti(X1,X21) = zero_zero(X1)
| ti(X1,X22) = zero_zero(X1) ) ) ),
file('<stdin>',fact_594_divisors__zero) ).
fof(c_0_919,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X15,X14] :
( ti(X1,X15) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X14)
<=> ti(X1,X14) = zero_zero(X1) ) ),
file('<stdin>',fact_452_add__0__iff) ).
fof(c_0_920,axiom,
! [X1,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X43) = ti(fun(X1,bool),X43),
file('<stdin>',fact_894_Int__UNIV__left) ).
fof(c_0_921,axiom,
! [X1,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X43) = top_top(fun(X1,bool)),
file('<stdin>',fact_806_Un__UNIV__left) ).
fof(c_0_922,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X6),X7) = top_top(X1)
<=> ( ti(X1,X6) = top_top(X1)
& ti(X1,X7) = top_top(X1) ) ) ),
file('<stdin>',fact_934_inf__eq__top__iff) ).
fof(c_0_923,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14) = zero_zero(X1)
<=> ti(X1,X14) = zero_zero(X1) ) ),
file('<stdin>',fact_429_double__eq__0__iff) ).
fof(c_0_924,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)
<=> ti(X1,X14) = zero_zero(X1) ) ),
file('<stdin>',fact_324_double__zero__sym) ).
fof(c_0_925,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),top_top(fun(X1,bool))) = ti(fun(X1,bool),X40),
file('<stdin>',fact_893_Int__UNIV__right) ).
fof(c_0_926,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
file('<stdin>',fact_807_Un__UNIV__right) ).
fof(c_0_927,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = zero_zero(nat)
<=> ( X54 = zero_zero(nat)
| X30 = zero_zero(nat) ) ),
file('<stdin>',fact_609_mult__is__0) ).
fof(c_0_928,axiom,
! [X49,X51] :
( X49 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)
=> ( X51 = one_one(nat)
| X49 = zero_zero(nat) ) ),
file('<stdin>',fact_669_mult__eq__self__implies__10) ).
fof(c_0_929,axiom,
! [X54,X30] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)
<=> ( X54 = one_one(nat)
& X30 = one_one(nat) ) ),
file('<stdin>',fact_602_nat__1__eq__mult__iff) ).
fof(c_0_930,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = one_one(nat)
<=> ( X54 = one_one(nat)
& X30 = one_one(nat) ) ),
file('<stdin>',fact_600_nat__mult__eq__1__iff) ).
fof(c_0_931,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30) = zero_zero(nat)
<=> ( X54 = zero_zero(nat)
& X30 = zero_zero(nat) ) ),
file('<stdin>',fact_336_add__is__0) ).
fof(c_0_932,axiom,
! [X49,X51] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51) = X49
=> X51 = zero_zero(nat) ),
file('<stdin>',fact_337_add__eq__self__zero) ).
fof(c_0_933,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X40) = ti(fun(X1,bool),X40),
file('<stdin>',fact_908_Int__absorb) ).
fof(c_0_934,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X40) = ti(fun(X1,bool),X40),
file('<stdin>',fact_791_Un__absorb) ).
fof(c_0_935,axiom,
! [X1,X80] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X80) = ti(fun(X1,bool),X80),
file('<stdin>',fact_466_image__ident) ).
fof(c_0_936,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
file('<stdin>',tsy_c_Finite__Set_Ofold__image_res) ).
fof(c_0_937,axiom,
! [X51] : hAPP(nat,nat,suc,X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X51),
file('<stdin>',fact_437_Suc__eq__plus1__left) ).
fof(c_0_938,axiom,
! [X51] : hAPP(nat,nat,suc,X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),one_one(nat)),
file('<stdin>',fact_436_Suc__eq__plus1) ).
fof(c_0_939,axiom,
! [X57] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X57)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X57),
file('<stdin>',fact_864_atLeast__Suc__greaterThan) ).
fof(c_0_940,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_424_less__eq__Suc__le__raw) ).
fof(c_0_941,axiom,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
file('<stdin>',fact_286_infinite__UNIV__nat) ).
fof(c_0_942,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res) ).
fof(c_0_943,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res) ).
fof(c_0_944,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res) ).
fof(c_0_945,axiom,
! [X1,X3,X2] : ti(fun(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)))),compose(X1,X3,X2)) = compose(X1,X3,X2),
file('<stdin>',tsy_c_FuncSet_Ocompose_res) ).
fof(c_0_946,axiom,
! [X1] : top_top(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)),
file('<stdin>',fact_78_UNIV__def) ).
fof(c_0_947,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X6) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X7)
<=> ti(X1,X6) = ti(X1,X7) ) ),
file('<stdin>',fact_861_atLeast__eq__iff) ).
fof(c_0_948,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X6) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X7)
<=> ti(X1,X6) = ti(X1,X7) ) ),
file('<stdin>',fact_534_greaterThan__eq__iff) ).
fof(c_0_949,axiom,
! [X2,X1,X118,X119] : hAPP(X2,X1,hAPP(X1,fun(X2,X1),combk(X1,X2),X118),X119) = ti(X1,X118),
file('<stdin>',help_COMBK_1_1_U) ).
fof(c_0_950,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X34) = ti(X1,X34) ),
file('<stdin>',fact_936_inf__top__left) ).
fof(c_0_951,axiom,
! [X1] :
( comm_monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
file('<stdin>',fact_613_mult__1) ).
fof(c_0_952,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
file('<stdin>',fact_612_mult__1__left) ).
fof(c_0_953,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
file('<stdin>',fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(c_0_954,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
file('<stdin>',fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_955,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
file('<stdin>',fact_326_add__0__left) ).
fof(c_0_956,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
file('<stdin>',fact_325_add__0) ).
fof(c_0_957,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),top_top(X1)) = ti(X1,X34) ),
file('<stdin>',fact_935_inf__top__right) ).
fof(c_0_958,axiom,
! [X1] :
( comm_monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
file('<stdin>',fact_615_mult_Ocomm__neutral) ).
fof(c_0_959,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
file('<stdin>',fact_614_mult__1__right) ).
fof(c_0_960,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
file('<stdin>',fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(c_0_961,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
file('<stdin>',fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_962,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
file('<stdin>',fact_323_add__0__right) ).
fof(c_0_963,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
file('<stdin>',fact_322_add_Ocomm__neutral) ).
fof(c_0_964,axiom,
! [X1,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ),
file('<stdin>',fact_357_card__infinite) ).
fof(c_0_965,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X34) = top_top(X1) ),
file('<stdin>',fact_852_sup__top__left) ).
fof(c_0_966,axiom,
! [X1] :
( mult_zero(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X21) = zero_zero(X1) ),
file('<stdin>',fact_598_mult__zero__left) ).
fof(c_0_967,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X21) = zero_zero(X1) ),
file('<stdin>',fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(c_0_968,axiom,
! [X1] :
( lattice(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X34) = ti(X1,X34) ),
file('<stdin>',fact_977_Inf__fin_Oidem) ).
fof(c_0_969,axiom,
! [X1] :
( lattice(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X34) = ti(X1,X34) ),
file('<stdin>',fact_976_Sup__fin_Oidem) ).
fof(c_0_970,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X21) = ti(X1,X21) ),
file('<stdin>',fact_952_inf_Oidem) ).
fof(c_0_971,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X34) = ti(X1,X34) ),
file('<stdin>',fact_951_inf__idem) ).
fof(c_0_972,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X34) = ti(X1,X34) ),
file('<stdin>',fact_823_sup__idem) ).
fof(c_0_973,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X21) = ti(X1,X21) ),
file('<stdin>',fact_822_sup_Oidem) ).
fof(c_0_974,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X34) = ti(X1,X34) ),
file('<stdin>',fact_820_mult__idem) ).
fof(c_0_975,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21) = ti(X1,X21) ),
file('<stdin>',fact_819_times_Oidem) ).
fof(c_0_976,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),top_top(X1)) = top_top(X1) ),
file('<stdin>',fact_853_sup__top__right) ).
fof(c_0_977,axiom,
! [X1] :
( mult_zero(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),zero_zero(X1)) = zero_zero(X1) ),
file('<stdin>',fact_597_mult__zero__right) ).
fof(c_0_978,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),zero_zero(X1)) = zero_zero(X1) ),
file('<stdin>',fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(c_0_979,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res) ).
fof(c_0_980,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res) ).
fof(c_0_981,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X51) = zero_zero(nat),
file('<stdin>',fact_611_mult__0) ).
fof(c_0_982,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X51) = X51,
file('<stdin>',fact_603_nat__mult__1) ).
fof(c_0_983,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X51) = X51,
file('<stdin>',fact_334_plus__nat_Oadd__0) ).
fof(c_0_984,axiom,
! [X49] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),zero_zero(nat)) = zero_zero(nat),
file('<stdin>',fact_610_mult__0__right) ).
fof(c_0_985,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),one_one(nat)) = X51,
file('<stdin>',fact_601_nat__mult__1__right) ).
fof(c_0_986,axiom,
! [X49] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),zero_zero(nat)) = X49,
file('<stdin>',fact_335_Nat_Oadd__0__right) ).
fof(c_0_987,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
file('<stdin>',tsy_c_Finite__Set_Ofolding__idem_res) ).
fof(c_0_988,axiom,
! [X118] :
( ~ hBOOL(hAPP(bool,bool,fNot,X118))
| ~ hBOOL(X118) ),
file('<stdin>',help_fNot_1_1_U) ).
fof(c_0_989,axiom,
! [X67,X68] :
( hAPP(nat,nat,suc,X67) = hAPP(nat,nat,suc,X68)
<=> X67 = X68 ),
file('<stdin>',fact_377_nat_Oinject) ).
fof(c_0_990,axiom,
! [X34,X35] :
( hAPP(nat,nat,suc,X34) = hAPP(nat,nat,suc,X35)
=> X34 = X35 ),
file('<stdin>',fact_376_Suc__inject) ).
fof(c_0_991,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
file('<stdin>',tsy_c_FuncSet_OPi_res) ).
fof(c_0_992,axiom,
! [X3,X1,X4,X5] : ti(X3,hAPP(X1,X3,X4,X5)) = hAPP(X1,X3,X4,X5),
file('<stdin>',tsy_c_hAPP_res) ).
fof(c_0_993,axiom,
! [X1] : ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
file('<stdin>',tsy_c_Wellfounded_Omlex__prod_res) ).
fof(c_0_994,axiom,
! [X1] :
( finite_finite(X1)
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
file('<stdin>',fact_297_finite__UNIV) ).
fof(c_0_995,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
file('<stdin>',fact_276_finite__indi) ).
fof(c_0_996,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
file('<stdin>',tsy_c_COMBS_res) ).
fof(c_0_997,axiom,
! [X1,X6] : hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X6)),
file('<stdin>',fact_25_top1I) ).
fof(c_0_998,axiom,
! [X1,X3,X4,X5] : hAPP(X1,X3,ti(fun(X1,X3),X4),X5) = hAPP(X1,X3,X4,X5),
file('<stdin>',tsy_c_hAPP_arg1) ).
fof(c_0_999,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
file('<stdin>',tsy_c_Sum__Type_OPlus_res) ).
fof(c_0_1000,axiom,
! [X1] :
( finite_finite(X1)
=> ! [X40] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
file('<stdin>',fact_288_finite) ).
fof(c_0_1001,axiom,
! [X1] :
( finite_finite(X1)
=> ! [X40] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
file('<stdin>',fact_287_finite__code) ).
fof(c_0_1002,axiom,
! [X1,X3,X4,X5] : hAPP(X1,X3,X4,ti(X1,X5)) = hAPP(X1,X3,X4,X5),
file('<stdin>',tsy_c_hAPP_arg2) ).
fof(c_0_1003,axiom,
! [X2,X3,X1] : ti(fun(fun(X2,fun(X3,X1)),fun(product_prod(X2,X3),X1)),product_prod_rec(X2,X3,X1)) = product_prod_rec(X2,X3,X1),
file('<stdin>',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).
fof(c_0_1004,axiom,
! [X1,X3,X2] : ti(fun(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3))),comp(X1,X3,X2)) = comp(X1,X3,X2),
file('<stdin>',tsy_c_Fun_Ocomp_res) ).
fof(c_0_1005,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
file('<stdin>',tsy_c_COMBC_res) ).
fof(c_0_1006,axiom,
! [X2,X3,X1] : ti(fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),combb(X2,X3,X1)) = combb(X2,X3,X1),
file('<stdin>',tsy_c_COMBB_res) ).
fof(c_0_1007,axiom,
! [X118] :
( hBOOL(X118)
| hBOOL(hAPP(bool,bool,fNot,X118)) ),
file('<stdin>',help_fNot_2_1_U) ).
fof(c_0_1008,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res) ).
fof(c_0_1009,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res) ).
fof(c_0_1010,axiom,
! [X49] : zero_zero(nat) != hAPP(nat,nat,suc,X49),
file('<stdin>',fact_385_Zero__not__Suc) ).
fof(c_0_1011,axiom,
! [X70] : zero_zero(nat) != hAPP(nat,nat,suc,X70),
file('<stdin>',fact_384_nat_Osimps_I2_J) ).
fof(c_0_1012,axiom,
! [X49] : hAPP(nat,nat,suc,X49) != zero_zero(nat),
file('<stdin>',fact_383_Suc__not__Zero) ).
fof(c_0_1013,axiom,
! [X69] : hAPP(nat,nat,suc,X69) != zero_zero(nat),
file('<stdin>',fact_382_nat_Osimps_I3_J) ).
fof(c_0_1014,axiom,
! [X49] : zero_zero(nat) != hAPP(nat,nat,suc,X49),
file('<stdin>',fact_381_Zero__neq__Suc) ).
fof(c_0_1015,axiom,
! [X49] : hAPP(nat,nat,suc,X49) != zero_zero(nat),
file('<stdin>',fact_380_Suc__neq__Zero) ).
fof(c_0_1016,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
file('<stdin>',tsy_c_Hilbert__Choice_Oinv__into_res) ).
fof(c_0_1017,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
file('<stdin>',tsy_c_Fun_Othe__inv__into_res) ).
fof(c_0_1018,axiom,
! [X51] : X51 != hAPP(nat,nat,suc,X51),
file('<stdin>',fact_379_n__not__Suc__n) ).
fof(c_0_1019,axiom,
! [X51] : hAPP(nat,nat,suc,X51) != X51,
file('<stdin>',fact_378_Suc__n__not__n) ).
fof(c_0_1020,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
file('<stdin>',tsy_c_FuncSet_Orestrict_res) ).
fof(c_0_1021,axiom,
! [X1,X2] : ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
file('<stdin>',tsy_c_FunDef_Oin__rel_res) ).
fof(c_0_1022,axiom,
! [X2,X1] : ti(fun(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool))),image(X2,X1)) = image(X2,X1),
file('<stdin>',tsy_c_Set_Oimage_res) ).
fof(c_0_1023,axiom,
! [X1,X11] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11) = ti(fun(X1,bool),X11),
file('<stdin>',fact_77_Collect__def) ).
fof(c_0_1024,axiom,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res) ).
fof(c_0_1025,axiom,
hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
file('<stdin>',fact_289_card__UNIV__unit) ).
fof(c_0_1026,axiom,
! [X2,X1] :
( top(X1)
=> ! [X6] : hAPP(X2,X1,top_top(fun(X2,X1)),X6) = top_top(X1) ),
file('<stdin>',fact_29_top__apply) ).
fof(c_0_1027,axiom,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
file('<stdin>',fact_863_atLeast__0) ).
fof(c_0_1028,axiom,
! [X1] : ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
file('<stdin>',tsy_c_Nat_Onat_Onat__case_res) ).
fof(c_0_1029,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2) ),
file('<stdin>',tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) ).
fof(c_0_1030,axiom,
! [X1] : ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
file('<stdin>',tsy_c_Wellfounded_Ofinite__psubset_res) ).
fof(c_0_1031,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
file('<stdin>',tsy_c_FuncSet_Oextensional_res) ).
fof(c_0_1032,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
file('<stdin>',tsy_c_Fun_Oinj__on_res) ).
fof(c_0_1033,axiom,
! [X1,X118] : hAPP(X1,X1,combi(X1),X118) = ti(X1,X118),
file('<stdin>',help_COMBI_1_1_U) ).
fof(c_0_1034,axiom,
! [X35] :
( X35 != zero_zero(nat)
=> ~ ! [X74] : X35 != hAPP(nat,nat,suc,X74) ),
file('<stdin>',fact_442_nat_Oexhaust) ).
fof(c_0_1035,axiom,
! [X51] :
( X51 != zero_zero(nat)
=> ? [X33] : X51 = hAPP(nat,nat,suc,X33) ),
file('<stdin>',fact_441_not0__implies__Suc) ).
fof(c_0_1036,axiom,
hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
file('<stdin>',fact_743_nat_Osize_I3_J) ).
fof(c_0_1037,axiom,
! [X51] : hAPP(nat,nat,size_size(nat),X51) = X51,
file('<stdin>',fact_741_nat__size) ).
fof(c_0_1038,axiom,
hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
file('<stdin>',fact_727_nat_Osize_I1_J) ).
fof(c_0_1039,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('<stdin>',fact_423_One__nat__def) ).
fof(c_0_1040,axiom,
! [X1] : ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
file('<stdin>',tsy_c_Wellfounded_Omeasure_res) ).
fof(c_0_1041,axiom,
hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
file('<stdin>',fact_756_bool_Osize_I2_J) ).
fof(c_0_1042,axiom,
hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
file('<stdin>',fact_755_bool_Osize_I1_J) ).
fof(c_0_1043,axiom,
! [X1,X2] : ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
file('<stdin>',tsy_c_Product__Type_OPair_res) ).
fof(c_0_1044,axiom,
! [X1] : ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
file('<stdin>',tsy_c_If_res) ).
fof(c_0_1045,axiom,
! [X1] :
( linorder(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1) ),
file('<stdin>',tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res) ).
fof(c_0_1046,axiom,
! [X1] :
( linorder(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1) ),
file('<stdin>',tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res) ).
fof(c_0_1047,axiom,
! [X1] :
( linorder(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1) ),
file('<stdin>',tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) ).
fof(c_0_1048,axiom,
! [X1] :
( order(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1) ),
file('<stdin>',tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) ).
fof(c_0_1049,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
file('<stdin>',tsy_c_member_res) ).
fof(c_0_1050,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
file('<stdin>',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res) ).
fof(c_0_1051,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
file('<stdin>',tsy_c_Set_OCollect_res) ).
fof(c_0_1052,axiom,
! [X1,X2] : ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
file('<stdin>',tsy_c_COMBK_res) ).
fof(c_0_1053,axiom,
! [X1] :
( semilattice_sup(X1)
=> ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1) ),
file('<stdin>',tsy_c_Lattices_Osemilattice__sup__class_Osup_res) ).
fof(c_0_1054,axiom,
! [X1] :
( semilattice_inf(X1)
=> ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1) ),
file('<stdin>',tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) ).
fof(c_0_1055,axiom,
! [X1] :
( no_zero_divisors(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
fof(c_0_1056,axiom,
! [X1] :
( mult_zero(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_3_res) ).
fof(c_0_1057,axiom,
! [X1] :
( ab_semigroup_mult(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_2_res) ).
fof(c_0_1058,axiom,
! [X1] :
( monoid_mult(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
fof(c_0_1059,axiom,
! [X1] :
( semiring(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
fof(c_0_1060,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
fof(c_0_1061,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
fof(c_0_1062,axiom,
! [X1] :
( monoid_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
fof(c_0_1063,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1) ),
file('<stdin>',tsy_c_SetInterval_Oord__class_OgreaterThan_res) ).
fof(c_0_1064,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1) ),
file('<stdin>',tsy_c_SetInterval_Oord__class_OatLeast_res) ).
fof(c_0_1065,axiom,
! [X2] :
( ord(X2)
=> ti(fun(X2,fun(X2,bool)),ord_less_eq(X2)) = ord_less_eq(X2) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(c_0_1066,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless_res) ).
fof(c_0_1067,axiom,
! [X1] : ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
file('<stdin>',tsy_c_fequal_res) ).
fof(c_0_1068,axiom,
! [X2] : ti(fun(fun(X2,bool),bool),finite_finite_1(X2)) = finite_finite_1(X2),
file('<stdin>',tsy_c_Finite__Set_Ofinite_res) ).
fof(c_0_1069,axiom,
! [X1] : ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
file('<stdin>',tsy_c_Finite__Set_Ocard_res) ).
fof(c_0_1070,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
file('<stdin>',tsy_v_Lba_____res) ).
fof(c_0_1071,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
file('<stdin>',tsy_v_Lab_____res) ).
fof(c_0_1072,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
file('<stdin>',tsy_c_fdisj_res) ).
fof(c_0_1073,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
file('<stdin>',tsy_c_fconj_res) ).
fof(c_0_1074,axiom,
! [X1] :
( ring_1(X1)
=> ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1) ),
file('<stdin>',tsy_c_Int_Oring__1__class_OInts_res) ).
fof(c_0_1075,axiom,
! [X1] :
( zero(X1)
=> ! [X6] :
( zero_zero(X1) = ti(X1,X6)
<=> ti(X1,X6) = zero_zero(X1) ) ),
file('<stdin>',fact_321_zero__reorient) ).
fof(c_0_1076,axiom,
! [X1] :
( one(X1)
=> ! [X6] :
( one_one(X1) = ti(X1,X6)
<=> ti(X1,X6) = one_one(X1) ) ),
file('<stdin>',fact_171_one__reorient) ).
fof(c_0_1077,axiom,
! [X116,X117] : ti(X116,ti(X116,X117)) = ti(X116,X117),
file('<stdin>',help_ti_idem) ).
fof(c_0_1078,axiom,
! [X1] : ti(fun(X1,X1),combi(X1)) = combi(X1),
file('<stdin>',tsy_c_COMBI_res) ).
fof(c_0_1079,axiom,
! [X114,X115] :
( ( finite_finite(X115)
& finite_finite(X114) )
=> finite_finite(product_prod(X114,X115)) ),
file('<stdin>',arity_prod___Finite__Set_Ofinite) ).
fof(c_0_1080,axiom,
! [X114,X115] :
( ( finite_finite(X115)
& finite_finite(X114) )
=> finite_finite(sum_sum(X114,X115)) ),
file('<stdin>',arity_sum___Finite__Set_Ofinite) ).
fof(c_0_1081,axiom,
! [X114,X115] :
( ( finite_finite(X115)
& finite_finite(X114) )
=> finite_finite(fun(X114,X115)) ),
file('<stdin>',arity_fun___Finite__Set_Ofinite) ).
fof(c_0_1082,axiom,
ti(fun(nat,nat),size_size(nat)) = size_size(nat),
file('<stdin>',tsy_c_Nat_Osize__class_Osize_res) ).
fof(c_0_1083,axiom,
! [X114,X115] :
( ord(X115)
=> ord(fun(X114,X115)) ),
file('<stdin>',arity_fun___Orderings_Oord) ).
fof(c_0_1084,axiom,
! [X114,X115] :
( top(X115)
=> top(fun(X114,X115)) ),
file('<stdin>',arity_fun___Orderings_Otop) ).
fof(c_0_1085,axiom,
! [X114,X115] :
( order(X115)
=> order(fun(X114,X115)) ),
file('<stdin>',arity_fun___Orderings_Oorder) ).
fof(c_0_1086,axiom,
! [X114,X115] :
( lattice(X115)
=> lattice(fun(X114,X115)) ),
file('<stdin>',arity_fun___Lattices_Olattice) ).
fof(c_0_1087,axiom,
! [X114,X115] :
( preorder(X115)
=> preorder(fun(X114,X115)) ),
file('<stdin>',arity_fun___Orderings_Opreorder) ).
fof(c_0_1088,axiom,
! [X114,X115] :
( distrib_lattice(X115)
=> distrib_lattice(fun(X114,X115)) ),
file('<stdin>',arity_fun___Lattices_Odistrib__lattice) ).
fof(c_0_1089,axiom,
! [X114,X115] :
( lattice(X115)
=> semilattice_inf(fun(X114,X115)) ),
file('<stdin>',arity_fun___Lattices_Osemilattice__inf) ).
fof(c_0_1090,axiom,
! [X114,X115] :
( lattice(X115)
=> semilattice_sup(fun(X114,X115)) ),
file('<stdin>',arity_fun___Lattices_Osemilattice__sup) ).
fof(c_0_1091,axiom,
! [X114,X115] :
( bounded_lattice(X115)
=> bounded_lattice_top(fun(X114,X115)) ),
file('<stdin>',arity_fun___Lattices_Obounded__lattice__top) ).
fof(c_0_1092,axiom,
! [X114,X115] :
( bounded_lattice(X115)
=> bounded_lattice(fun(X114,X115)) ),
file('<stdin>',arity_fun___Lattices_Obounded__lattice) ).
fof(c_0_1093,axiom,
ti(fun(arrow_1998540521e_indi,nat),h) = h,
file('<stdin>',tsy_v_h_____res) ).
fof(c_0_1094,axiom,
ti(fun(bool,bool),fNot) = fNot,
file('<stdin>',tsy_c_fNot_res) ).
fof(c_0_1095,axiom,
ti(fun(nat,nat),nat_size) = nat_size,
file('<stdin>',tsy_c_Nat_Onat_Onat__size_res) ).
fof(c_0_1096,axiom,
ti(fun(nat,nat),suc) = suc,
file('<stdin>',tsy_c_Nat_OSuc_res) ).
fof(c_0_1097,axiom,
ti(fun(bool,nat),bool_size) = bool_size,
file('<stdin>',tsy_c_HOL_Obool_Obool__size_res) ).
fof(c_0_1098,axiom,
! [X1] :
( top(X1)
=> ti(X1,top_top(X1)) = top_top(X1) ),
file('<stdin>',tsy_c_Orderings_Otop__class_Otop_res) ).
fof(c_0_1099,axiom,
! [X1] :
( zero(X1)
=> ti(X1,zero_zero(X1)) = zero_zero(X1) ),
file('<stdin>',tsy_c_Groups_Ozero__class_Ozero_res) ).
fof(c_0_1100,axiom,
! [X1] :
( one(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
file('<stdin>',tsy_c_Groups_Oone__class_Oone_res) ).
fof(c_0_1101,axiom,
! [X118] :
( ti(bool,X118) = fTrue
| ti(bool,X118) = fFalse ),
file('<stdin>',help_fFalse_1_1_T) ).
fof(c_0_1102,axiom,
! [X118] :
( ti(bool,X118) = fTrue
| ti(bool,X118) = fFalse ),
file('<stdin>',help_fTrue_1_1_T) ).
fof(c_0_1103,axiom,
! [X118] :
( ti(bool,X118) = fTrue
| ti(bool,X118) = fFalse ),
file('<stdin>',help_If_3_1_T) ).
fof(c_0_1104,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
file('<stdin>',tsy_c_HOL_Oundefined_res) ).
fof(c_0_1105,axiom,
! [X1] :
( zero_neq_one(X1)
=> one_one(X1) != zero_zero(X1) ),
file('<stdin>',fact_328_one__neq__zero) ).
fof(c_0_1106,axiom,
! [X1] :
( zero_neq_one(X1)
=> zero_zero(X1) != one_one(X1) ),
file('<stdin>',fact_327_zero__neq__one) ).
fof(c_0_1107,axiom,
! [X115] :
( finite_finite(X115)
=> finite_finite(option(X115)) ),
file('<stdin>',arity_Option_Ooption___Finite__Set_Ofinite) ).
fof(c_0_1108,axiom,
ti(nat,n) = n,
file('<stdin>',tsy_v_n_____res) ).
fof(c_0_1109,axiom,
ti(arrow_2142409994le_alt,e) = e,
file('<stdin>',tsy_v_e_____res) ).
fof(c_0_1110,axiom,
ti(arrow_2142409994le_alt,b) = b,
file('<stdin>',tsy_v_b_____res) ).
fof(c_0_1111,axiom,
ti(arrow_2142409994le_alt,a) = a,
file('<stdin>',tsy_v_a_____res) ).
fof(c_0_1112,axiom,
ti(bool,fTrue) = fTrue,
file('<stdin>',tsy_c_fTrue_res) ).
fof(c_0_1113,axiom,
ti(bool,fFalse) = fFalse,
file('<stdin>',tsy_c_fFalse_res) ).
fof(c_0_1114,axiom,
~ hBOOL(fFalse),
file('<stdin>',help_fFalse_1_1_U) ).
fof(c_0_1115,axiom,
hBOOL(fTrue),
file('<stdin>',help_fTrue_1_1_U) ).
fof(c_0_1116,axiom,
finite_finite(product_unit),
file('<stdin>',arity_Product__Type_Ounit___Finite__Set_Ofinite) ).
fof(c_0_1117,axiom,
ord(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Oord) ).
fof(c_0_1118,axiom,
top(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Otop) ).
fof(c_0_1119,axiom,
order(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Oorder) ).
fof(c_0_1120,axiom,
lattice(bool),
file('<stdin>',arity_HOL_Obool___Lattices_Olattice) ).
fof(c_0_1121,axiom,
finite_finite(bool),
file('<stdin>',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(c_0_1122,axiom,
preorder(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Opreorder) ).
fof(c_0_1123,axiom,
distrib_lattice(bool),
file('<stdin>',arity_HOL_Obool___Lattices_Odistrib__lattice) ).
fof(c_0_1124,axiom,
semilattice_inf(bool),
file('<stdin>',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
fof(c_0_1125,axiom,
semilattice_sup(bool),
file('<stdin>',arity_HOL_Obool___Lattices_Osemilattice__sup) ).
fof(c_0_1126,axiom,
bounded_lattice_top(bool),
file('<stdin>',arity_HOL_Obool___Lattices_Obounded__lattice__top) ).
fof(c_0_1127,axiom,
one(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oone) ).
fof(c_0_1128,axiom,
zero(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ozero) ).
fof(c_0_1129,axiom,
ord(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Oord) ).
fof(c_0_1130,axiom,
semiring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Osemiring) ).
fof(c_0_1131,axiom,
order(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Oorder) ).
fof(c_0_1132,axiom,
mult_zero(nat),
file('<stdin>',arity_Nat_Onat___Rings_Omult__zero) ).
fof(c_0_1133,axiom,
lattice(nat),
file('<stdin>',arity_Nat_Onat___Lattices_Olattice) ).
fof(c_0_1134,axiom,
semiring_0(nat),
file('<stdin>',arity_Nat_Onat___Rings_Osemiring__0) ).
fof(c_0_1135,axiom,
monoid_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(c_0_1136,axiom,
monoid_mult(nat),
file('<stdin>',arity_Nat_Onat___Groups_Omonoid__mult) ).
fof(c_0_1137,axiom,
linorder(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Olinorder) ).
fof(c_0_1138,axiom,
preorder(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Opreorder) ).
fof(c_0_1139,axiom,
zero_neq_one(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ozero__neq__one) ).
fof(c_0_1140,axiom,
comm_semiring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ocomm__semiring) ).
fof(c_0_1141,axiom,
comm_semiring_1(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
fof(c_0_1142,axiom,
comm_monoid_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
fof(c_0_1143,axiom,
no_zero_divisors(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
fof(c_0_1144,axiom,
ordered_semiring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Oordered__semiring) ).
fof(c_0_1145,axiom,
ab_semigroup_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
fof(c_0_1146,axiom,
comm_monoid_mult(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
fof(c_0_1147,axiom,
ab_semigroup_mult(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
fof(c_0_1148,axiom,
distrib_lattice(nat),
file('<stdin>',arity_Nat_Onat___Lattices_Odistrib__lattice) ).
fof(c_0_1149,axiom,
semilattice_inf(nat),
file('<stdin>',arity_Nat_Onat___Lattices_Osemilattice__inf) ).
fof(c_0_1150,axiom,
semilattice_sup(nat),
file('<stdin>',arity_Nat_Onat___Lattices_Osemilattice__sup) ).
fof(c_0_1151,axiom,
linordered_semidom(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semidom) ).
fof(c_0_1152,axiom,
linordered_semiring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semiring) ).
fof(c_0_1153,axiom,
cancel_semigroup_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
fof(c_0_1154,axiom,
ordere1490568538miring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).
fof(c_0_1155,axiom,
ordere453448008miring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).
fof(c_0_1156,axiom,
cancel146912293up_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_1157,axiom,
ordere216010020id_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
fof(c_0_1158,axiom,
ordere779506340up_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
fof(c_0_1159,axiom,
linord20386208strict(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).
fof(c_0_1160,axiom,
linord893533164strict(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_1161,axiom,
ordere236663937imp_le(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_1162,axiom,
ordere223160158up_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_1163,axiom,
semiri456707255roduct(nat),
file('<stdin>',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(c_0_1164,axiom,
bounded_lattice(bool),
file('<stdin>',arity_HOL_Obool___Lattices_Obounded__lattice) ).
fof(c_0_1165,axiom,
a != b,
file('<stdin>',fact_37__096a_A_126_061_Ab_096) ).
fof(c_0_1166,axiom,
c != d,
file('<stdin>',fact_2__096c_A_126_061_Ad_096) ).
fof(c_0_1167,axiom,
! [X2,X1,X39,X63,X76,X57,X103,X41,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
=> ( ! [X46] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),X103))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X2,X2,X57,X46)),X41))
& hAPP(X2,X2,X76,hAPP(X2,X2,X57,X46)) = ti(X2,X46) ) )
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X2,X2,X76,X26)),X103))
& hAPP(X2,X2,X57,hAPP(X2,X2,X76,X26)) = ti(X2,X26)
& hAPP(X2,X1,X39,hAPP(X2,X2,X76,X26)) = hAPP(X2,X1,X63,X26) ) )
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X63),X41) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X103) ) ) ) ),
c_0_0 ).
fof(c_0_1168,axiom,
! [X2,X1,X3] :
( comm_monoid_mult(X3)
=> ! [X99,X39,X38,X76,X57,X103,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ! [X46] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),X103))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X57,X46)),X41))
& hAPP(X1,X2,X76,hAPP(X2,X1,X57,X46)) = ti(X2,X46) ) )
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X41))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X76,X26)),X103))
& hAPP(X2,X1,X57,hAPP(X1,X2,X76,X26)) = ti(X1,X26)
& hAPP(X2,X3,X39,hAPP(X1,X2,X76,X26)) = hAPP(X1,X3,X38,X26) ) )
=> hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X38),X99),X41) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X39),X99),X103) ) ) ) ),
c_0_1 ).
fof(c_0_1169,axiom,
! [X2,X1,X76,X39,X41,X42,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X9),X9))
=> ( ! [X18,X100,X101,X102] :
( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X18),X101))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X100),X102)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X18),X100)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X101),X102))) )
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X2,X1,X76,X26)),hAPP(X2,X1,X39,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X41)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X41))) ) ) ) ) ),
c_0_2 ).
fof(c_0_1170,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
c_0_3 ).
fof(c_0_1171,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
c_0_4 ).
fof(c_0_1172,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
c_0_5 ).
fof(c_0_1173,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_6 ).
fof(c_0_1174,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_7 ).
fof(c_0_1175,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_8 ).
fof(c_0_1176,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
c_0_9 ).
fof(c_0_1177,axiom,
! [X2,X1,X42,X41,X26,X27] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X42)),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)))),X41)),X26),X27))
<=> 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),X26),X27)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X42),X41))) ),
c_0_10 ).
fof(c_0_1178,axiom,
! [X2,X1,X42,X41,X26,X27] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X42)),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)))),X41)),X26),X27))
<=> 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),X26),X27)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X42),X41))) ),
c_0_11 ).
fof(c_0_1179,axiom,
! [X2,X1] :
( comm_monoid_mult(X1)
=> ! [X76,X39,X41,X42,X99] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X99),X99))
=> ( ! [X18,X100,X101,X102] :
( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X18),X101))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X100),X102)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X18),X100)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X101),X102))) )
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X2,X1,X76,X26)),hAPP(X2,X1,X39,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X76),X99),X41)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X39),X99),X41))) ) ) ) ) ),
c_0_12 ).
fof(c_0_1180,plain,
~ ! [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
=> ( ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
=> ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_13]) ).
fof(c_0_1181,axiom,
? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
& ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
& hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ),
c_0_14 ).
fof(c_0_1182,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
c_0_15 ).
fof(c_0_1183,axiom,
! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) ),
c_0_16 ).
fof(c_0_1184,axiom,
! [X30] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X30))),lab)),lba)),arrow_301600364e_Prof)),
c_0_17 ).
fof(c_0_1185,axiom,
! [X1,X2,X42,X41] :
( 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)))),X42)),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)))),X41)))
<=> 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)),X42),X41)) ),
c_0_18 ).
fof(c_0_1186,axiom,
! [X2,X1,X3] :
( comm_monoid_add(X3)
=> ! [X38,X42,X103,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X103))
=> hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),hAPP(fun(X1,fun(X2,bool)),fun(X1,X3),hAPP(fun(X1,fun(fun(X2,bool),X3)),fun(fun(X1,fun(X2,bool)),fun(X1,X3)),combs(X1,fun(X2,bool),X3),hAPP(fun(X1,fun(X2,X3)),fun(X1,fun(fun(X2,bool),X3)),hAPP(fun(fun(X2,X3),fun(fun(X2,bool),X3)),fun(fun(X1,fun(X2,X3)),fun(X1,fun(fun(X2,bool),X3))),combb(fun(X2,X3),fun(fun(X2,bool),X3),X1),big_co1399186613setsum(X2,X3)),X38)),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X1),collect(X2)),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X1),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X103)))),X42)))),X41) = hAPP(fun(X2,bool),X3,hAPP(fun(X2,X3),fun(fun(X2,bool),X3),big_co1399186613setsum(X2,X3),hAPP(fun(X2,fun(X1,bool)),fun(X2,X3),hAPP(fun(X2,fun(fun(X1,bool),X3)),fun(fun(X2,fun(X1,bool)),fun(X2,X3)),combs(X2,fun(X1,bool),X3),hAPP(fun(X2,fun(X1,X3)),fun(X2,fun(fun(X1,bool),X3)),hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),fun(fun(X2,fun(X1,X3)),fun(X2,fun(fun(X1,bool),X3))),combb(fun(X1,X3),fun(fun(X1,bool),X3),X2),big_co1399186613setsum(X1,X3)),hAPP(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)),combc(X1,X2,X3),X38))),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X2),collect(X1)),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X2),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),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)),X41)))),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),X42))))),X103) ) ) ),
c_0_19 ).
fof(c_0_1187,axiom,
! [X2,X1,X39,X76,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40))
=> hAPP(X2,X1,X39,X26) = hAPP(X2,X1,X76,X26) )
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X40) ) ) ),
c_0_20 ).
fof(c_0_1188,axiom,
! [X2,X3,X1] :
( semiring_0(X1)
=> ! [X38,X40,X39,X43] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X39),X43)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),hAPP(fun(X3,X1),fun(X2,fun(X3,X1)),hAPP(fun(X2,fun(fun(X3,X1),fun(X3,X1))),fun(fun(X3,X1),fun(X2,fun(X3,X1))),combc(X2,fun(X3,X1),fun(X3,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X3,X1),fun(X3,X1))),hAPP(fun(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X3,X1),fun(X3,X1)))),combb(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),X2),combb(X1,X1,X3)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X38))),X39))),X43)),X40) ),
c_0_21 ).
fof(c_0_1189,axiom,
! [X29,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)),X29))))) = 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,X29))))) ),
c_0_22 ).
fof(c_0_1190,axiom,
! [X3,X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X38,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X41) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combb(fun(X1,bool),X2,X3),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X41)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X38)))))),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),X41)) ) ),
c_0_23 ).
fof(c_0_1191,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),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),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)),X40))),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)),X43)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X43))),X38)),zero_zero(X2))),X40) ) ),
c_0_24 ).
fof(c_0_1192,plain,
! [X2,X1,X38,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( 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),X38),X40)))
=> ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& ~ 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),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)),X40))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X38)),hAPP(X1,X2,X38,X26)))))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_1193,plain,
! [X29,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)),X29)))) = 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,X29))))) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_1194,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X43))),X38)),zero_zero(X2))),X40) ) ),
c_0_27 ).
fof(c_0_1195,plain,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X15,X14,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_1196,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X11,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),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),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)),X40))),X11))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X11)),X38)),zero_zero(X2))),X40) ) ),
c_0_29 ).
fof(c_0_1197,axiom,
! [X2,X1,X11,X38,X39,X41] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),X11)),X38)),X39)),X41) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X41),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),X11)))),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X41),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),fNot),X11))))),
c_0_30 ).
fof(c_0_1198,plain,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X15,X14,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_1199,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X38,X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X15)),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X46))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X38,X46))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X14)),X17)) ) ) ) ),
c_0_32 ).
fof(c_0_1200,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X38,X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X15)),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X46))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X38,X46))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X14)),X17)) ) ) ) ),
c_0_33 ).
fof(c_0_1201,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X15)),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X17),X15))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X46),X26))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X46)),hAPP(X2,X1,X38,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X17)),X14)) ) ) ) ),
c_0_34 ).
fof(c_0_1202,axiom,
! [X2,X1] :
( ( order(X1)
& ord(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X15)),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),X15))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X46),X26))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X46)),hAPP(X2,X1,X38,X26))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X17)),X14)) ) ) ) ),
c_0_35 ).
fof(c_0_1203,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X17,X14,X38,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X15)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X15),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X26),X46))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X26)),hAPP(X2,X1,X38,X46))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X17))) ) ) ) ),
c_0_36 ).
fof(c_0_1204,axiom,
! [X1,X2] :
( ( order(X2)
& order(X1) )
=> ! [X17,X14,X38,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),hAPP(X2,X1,X38,X15)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X15),X17))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X26),X46))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X26)),hAPP(X2,X1,X38,X46))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X17))) ) ) ) ),
c_0_37 ).
fof(c_0_1205,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X15)))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X46),X26))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X46)),hAPP(X1,X2,X38,X26))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X14))) ) ) ) ),
c_0_38 ).
fof(c_0_1206,axiom,
! [X2,X1] :
( ( order(X1)
& order(X2) )
=> ! [X17,X38,X15,X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X17),hAPP(X1,X2,X38,X15)))
=> ( ! [X26,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),X26))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X46)),hAPP(X1,X2,X38,X26))) )
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X14))) ) ) ) ),
c_0_39 ).
fof(c_0_1207,axiom,
! [X10,X11,X12,X13,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X12)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
c_0_40 ).
fof(c_0_1208,axiom,
! [X10,X11,X12,X13,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X13)
=> ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X12)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
c_0_41 ).
fof(c_0_1209,axiom,
! [X10,X11,X12,X13,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ),
c_0_42 ).
fof(c_0_1210,axiom,
! [X29,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,X29))))) != zero_zero(nat) ),
c_0_43 ).
fof(c_0_1211,plain,
! [X16] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_1212,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X39)),X76)),one_one(X2)),X40) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X40)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X76),one_one(X2)),X40)) ) ),
c_0_45 ).
fof(c_0_1213,axiom,
! [X2,X3,X1] :
( comm_monoid_add(X1)
=> ! [X38,X43,X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),X38)),X43)),X40) = hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X2,bool),fun(X3,X1),hAPP(fun(X3,fun(fun(X2,bool),X1)),fun(fun(X2,bool),fun(X3,X1)),combc(X3,fun(X2,bool),X1),hAPP(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1)),hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),fun(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1))),combb(fun(X2,X1),fun(fun(X2,bool),X1),X3),big_co1399186613setsum(X2,X1)),hAPP(fun(X2,fun(X3,X1)),fun(X3,fun(X2,X1)),combc(X2,X3,X1),X38))),X40)),X43) ),
c_0_46 ).
fof(c_0_1214,axiom,
! [X29,X25] :
( hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X25),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
=> ( ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> ! [X19,X20] :
( ti(arrow_2142409994le_alt,X19) != ti(arrow_2142409994le_alt,X20)
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X29)))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26))) ) ) )
=> hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X25),X29)) ) ),
c_0_47 ).
fof(c_0_1215,plain,
! [X16] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_1216,plain,
! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
=> ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_1217,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X39,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X40)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X43)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ) ),
c_0_50 ).
fof(c_0_1218,axiom,
! [X25] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X25))
<=> ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> ! [X27] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X27),arrow_301600364e_Prof))
=> ! [X19,X20] :
( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X27,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X27))) ) ) ) ) ),
c_0_51 ).
fof(c_0_1219,axiom,
! [X10,X11,X17,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X17)
=> ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X17)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X17)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X17)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ),
c_0_52 ).
fof(c_0_1220,axiom,
! [X1,X11,X53] :
( 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),X11)),X53))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) ) ),
c_0_53 ).
fof(c_0_1221,axiom,
! [X10,X11,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
=> ( ! [X16] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ),
c_0_54 ).
fof(c_0_1222,axiom,
! [X87,X3,X1,X2,X76,X88,X39,X52,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X39),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X43),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X52))))
=> ( hBOOL(hAPP(fun(fun(X3,X87),bool),bool,hAPP(fun(X3,X87),fun(fun(fun(X3,X87),bool),bool),member(fun(X3,X87)),X76),hAPP(fun(X3,fun(X87,bool)),fun(fun(X3,X87),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X87,bool)),fun(fun(X3,X87),bool)),pi(X3,X87),X52),hAPP(fun(X87,bool),fun(X3,fun(X87,bool)),combk(fun(X87,bool),X3),X88))))
=> hAPP(fun(X1,X3),fun(X1,X87),hAPP(fun(X3,X87),fun(fun(X1,X3),fun(X1,X87)),hAPP(fun(X1,bool),fun(fun(X3,X87),fun(fun(X1,X3),fun(X1,X87))),compose(X1,X3,X87),X40),X76),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X40),X39),X38)) = hAPP(fun(X1,X2),fun(X1,X87),hAPP(fun(X2,X87),fun(fun(X1,X2),fun(X1,X87)),hAPP(fun(X1,bool),fun(fun(X2,X87),fun(fun(X1,X2),fun(X1,X87))),compose(X1,X2,X87),X40),hAPP(fun(X2,X3),fun(X2,X87),hAPP(fun(X3,X87),fun(fun(X2,X3),fun(X2,X87)),hAPP(fun(X2,bool),fun(fun(X3,X87),fun(fun(X2,X3),fun(X2,X87))),compose(X2,X3,X87),X43),X76),X39)),X38) ) ) ),
c_0_55 ).
fof(c_0_1223,axiom,
! [X3,X1,X2,X39,X52,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X39),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X43),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X52))))
=> hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X40),X39),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),X40),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X52)))) ) ),
c_0_56 ).
fof(c_0_1224,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X38,X103,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X103))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X41),X103)))
=> hAPP(X1,X2,X38,X26) = one_one(X2) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X41),X103)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X41)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X103)) ) ) ) ),
c_0_57 ).
fof(c_0_1225,axiom,
! [X11,X29] : 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)),X29))))),
c_0_58 ).
fof(c_0_1226,axiom,
! [X1,X2,X3,X6,X38,X39,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)))
=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40))))
=> hAPP(X2,X3,hAPP(fun(X3,X2),fun(X2,X3),hAPP(fun(X3,bool),fun(fun(X3,X2),fun(X2,X3)),the_inv_into(X3,X2),X40),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),X6) = hAPP(X2,X3,hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),the_inv_into(X3,X1),X40),X39)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)),X38)),X6) ) ) ),
c_0_59 ).
fof(c_0_1227,axiom,
! [X1,X2,X3,X6,X38,X39,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)))
=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40))))
=> hAPP(X2,X3,hAPP(fun(X3,X2),fun(X2,X3),hAPP(fun(X3,bool),fun(fun(X3,X2),fun(X2,X3)),hilbert_inv_into(X3,X2),X40),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),X6) = hAPP(X2,X3,hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X40),X39)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)),X38)),X6) ) ) ),
c_0_60 ).
fof(c_0_1228,axiom,
! [X1,X42,X41,X26] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X42)),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)),X41)),X26))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X42),X41))) ),
c_0_61 ).
fof(c_0_1229,axiom,
! [X1,X42,X41,X26] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X42)),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)),X41)),X26))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X42),X41))) ),
c_0_62 ).
fof(c_0_1230,axiom,
! [X6,X7,X8,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X8),X14),X15)))
<=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
& ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X14)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X15)),X8)) )
& ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X14)
=> ( ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X14)
=> ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X15)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X7)),X8)) ) )
& ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X14)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
c_0_63 ).
fof(c_0_1231,axiom,
! [X6,X7,X8,X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X8),X14),X15)))
<=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
& ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X15)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X7)),X8)) )
& ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X15)
=> ( ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X15)
=> ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X14)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X14)),X8)) ) )
& ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X15)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
c_0_64 ).
fof(c_0_1232,axiom,
! [X2,X1,X43,X52,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> 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),X43,X26)),hAPP(X1,fun(X2,bool),X52,X26))) )
=> 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),X40),X43)),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),X40),X52))) ),
c_0_65 ).
fof(c_0_1233,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7))),zero_zero(X1)))
<=> ( ti(X1,X6) = zero_zero(X1)
& ti(X1,X7) = zero_zero(X1) ) ) ),
c_0_66 ).
fof(c_0_1234,plain,
! [X1] :
( linordered_ring(X1)
=> ! [X34,X35] : ~ 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),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35))),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_1235,axiom,
! [X2,X1,X43,X38,X39,X40] :
( ! [X47] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X47),X40))
=> hAPP(X1,X2,X38,X47) = hAPP(X1,X2,X39,X47) )
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
<=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),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),X40),X43))) ) ),
c_0_68 ).
fof(c_0_1236,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X40)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X40)),
c_0_69 ).
fof(c_0_1237,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),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),X40),X43))) ),
c_0_70 ).
fof(c_0_1238,axiom,
! [X1,X2,X41,X42] :
( ! [X26,X27] :
( 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),X26),X27)),X42))
<=> 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),X26),X27)),X41)) )
<=> ti(fun(product_prod(X1,X2),bool),X42) = ti(fun(product_prod(X1,X2),bool),X41) ),
c_0_71 ).
fof(c_0_1239,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
c_0_72 ).
fof(c_0_1240,axiom,
! [X1,X2] :
( ab_semigroup_mult(X2)
=> ! [X9,X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X1,X2,X39,X26) = hAPP(X1,X2,X76,X26) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),X9),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X76),X9),X40) ) ) ),
c_0_73 ).
fof(c_0_1241,axiom,
! [X1,X53,X11] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) )
=> 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),X11)),X53)))) ),
c_0_74 ).
fof(c_0_1242,axiom,
! [X66,X38] :
( ! [X44] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),hAPP(nat,nat,X38,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)),X38)),X66)))) ),
c_0_75 ).
fof(c_0_1243,axiom,
! [X2,X1,X39,X76,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),X38),X39)),X76)),X40) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X40)) ) ),
c_0_76 ).
fof(c_0_1244,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43))) ),
c_0_77 ).
fof(c_0_1245,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43))) ),
c_0_78 ).
fof(c_0_1246,axiom,
! [X1,X2,X38,X40,X43] : 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),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X40),X43))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X43)))),
c_0_79 ).
fof(c_0_1247,axiom,
! [X2,X1,X38,X40,X43] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X40),X38)),X43)),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),X43),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X40)))) ),
c_0_80 ).
fof(c_0_1248,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),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)),X14)),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ) ),
c_0_81 ).
fof(c_0_1249,axiom,
! [X1] :
( linord1278240602ring_1(X1)
=> ! [X89,X90,X35,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X90))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X89))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X90),X89) = one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X90),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X89),X35))),X21)) ) ) ) ) ) ),
c_0_82 ).
fof(c_0_1250,axiom,
! [X1] :
( linord626643107strict(X1)
=> ! [X89,X90,X35,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X90))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X89))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X90),X89) = one_one(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),times_times(X1),X90),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X89),X35))),X21)) ) ) ) ) ) ),
c_0_83 ).
fof(c_0_1251,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43)))) ),
c_0_84 ).
fof(c_0_1252,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)))) ),
c_0_85 ).
fof(c_0_1253,axiom,
! [X2,X1,X38,X39,X71,X60] :
( ti(fun(X1,bool),X71) = ti(fun(X1,bool),X60)
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X60))
=> hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X71) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X39),X60) ) ),
c_0_86 ).
fof(c_0_1254,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = 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),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)),X40))),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)),X43))),
c_0_87 ).
fof(c_0_1255,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = 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),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)),X40))),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)),X43))),
c_0_88 ).
fof(c_0_1256,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X113,X54,X30] :
( 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),X30),one_one(nat))))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X113))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X113)))) ) ),
c_0_89 ).
fof(c_0_1257,axiom,
! [X2,X1,X43,X40,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X43),X40))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,X25,X43)),hAPP(fun(X2,bool),X1,X25,X40)) = hAPP(fun(X2,bool),X1,X25,X40) ) ) ),
c_0_90 ).
fof(c_0_1258,axiom,
! [X2,X1,X43,X40,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hAPP(fun(X2,bool),X1,X25,hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X40),X43)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,X25,X40)),hAPP(fun(X2,bool),X1,X25,X43)) ) ) ),
c_0_91 ).
fof(c_0_1259,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43)))) ),
c_0_92 ).
fof(c_0_1260,axiom,
! [X2,X1,X6,X40,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X40))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(X2,X1,X39,X6)),hAPP(fun(X2,bool),X1,X25,X40)) = hAPP(fun(X2,bool),X1,X25,X40) ) ) ),
c_0_93 ).
fof(c_0_1261,axiom,
! [X1,X2,X39,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X39),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),X43),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X40))))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X39),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X2,bool),nat,finite_card(X2),X43) ) ) ) ) ) ),
c_0_94 ).
fof(c_0_1262,axiom,
! [X2,X1,X38,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
=> 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),X38),X40)),X43)) ),
c_0_95 ).
fof(c_0_1263,axiom,
! [X25] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X25))
<=> ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> ! [X19,X20] :
( ! [X16] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X16)))
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26))) ) ) ),
c_0_96 ).
fof(c_0_1264,axiom,
! [X1,X2,X39,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( 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),X38),X40)),X43))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),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(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),X43)),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X2,bool),nat,finite_card(X2),X43) ) ) ) ) ) ),
c_0_97 ).
fof(c_0_1265,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)))) ),
c_0_98 ).
fof(c_0_1266,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X39)),X76)),X40) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X76),X40)) ) ),
c_0_99 ).
fof(c_0_1267,axiom,
! [X2,X1,X6,X38,X9,X39,X25] :
( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X6),X6) = ti(X1,X6) ),
c_0_100 ).
fof(c_0_1268,axiom,
! [X2,X1] :
( comm_monoid_add(X1)
=> ! [X38,X39,X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),plus_plus(X1)),X38)),X39)),X40) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X39),X40)) ),
c_0_101 ).
fof(c_0_1269,axiom,
! [X2,X1,X39,X38,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( hAPP(X1,X2,X39,hAPP(X1,X1,X38,X26)) = hAPP(X1,X2,X39,hAPP(X1,X1,X38,X27))
<=> hAPP(X1,X2,X39,X26) = hAPP(X1,X2,X39,X27) ) ) )
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),X40)) ) ) ),
c_0_102 ).
fof(c_0_1270,axiom,
! [X1,X42,X38,X6,X7] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7)))
=> ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),X42))
=> hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X38),X42))) ) ),
c_0_103 ).
fof(c_0_1271,axiom,
! [X2,X1] :
( semiring_0(X1)
=> ! [X38,X40,X106] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),X106) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X38)),X106)),X40) ),
c_0_104 ).
fof(c_0_1272,plain,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),X38),X40))),hAPP(fun(X2,bool),nat,finite_card(X2),X40)))
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_1273,axiom,
! [X8,X6,X7] :
( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X8),X6),X7)),arrow_1568854078le_Lin)) ) ),
c_0_106 ).
fof(c_0_1274,axiom,
! [X8,X6,X7] :
( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X8),X6),X7)),arrow_1568854078le_Lin)) ) ),
c_0_107 ).
fof(c_0_1275,axiom,
! [X1,X2,X43,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> 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)),the_inv_into(X1,X2),X40),X38),X6)),X43)) ) ) ),
c_0_108 ).
fof(c_0_1276,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X7] :
( 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7))))
<=> ( ti(X1,X6) != zero_zero(X1)
| ti(X1,X7) != zero_zero(X1) ) ) ),
c_0_109 ).
fof(c_0_1277,axiom,
! [X1,X2,X6,X11,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( ! [X46] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),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)))))
=> hBOOL(hAPP(X1,bool,X11,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),top_top(fun(X1,bool))),X38),X46))) )
=> hBOOL(hAPP(X1,bool,X11,X6)) ) ),
c_0_110 ).
fof(c_0_1278,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
c_0_111 ).
fof(c_0_1279,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
c_0_112 ).
fof(c_0_1280,plain,
! [X6,X7,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
=> ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X7),X6)),X8)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_1281,plain,
! [X14,X15,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X8))
=> ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),X8)) ) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_1282,axiom,
! [X1,X42,X41] :
( 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)),X42)),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)),X41)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X42),X41)) ),
c_0_115 ).
fof(c_0_1283,axiom,
! [X2,X1,X39,X76,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X2),fun(fun(X2,bool),bool),inj_on(X2,X2),X76),X40))
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,bool)),image(X2,X2),X76),X40)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,hAPP(fun(X2,X2),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X2),fun(X2,X1)),comp(X2,X1,X2),X39),X76)),X40) ) ) ),
c_0_116 ).
fof(c_0_1284,axiom,
! [X1,X2,X3,X40,X38,X39] : hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X38),X39)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40))),
c_0_117 ).
fof(c_0_1285,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X40),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X43)),X38) = ti(fun(X1,X2),X38) ) ),
c_0_118 ).
fof(c_0_1286,axiom,
! [X3,X1,X2,X38,X39] :
( 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),X39),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),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),combb(X1,X3,X2),X38),X39)),top_top(fun(X2,bool))))) ),
c_0_119 ).
fof(c_0_1287,axiom,
! [X2,X1,X3] :
( ab_semigroup_mult(X3)
=> ! [X39,X9,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X76),X40))
=> hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X39),X9),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X76),X40)) = hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X39),X76)),X9),X40) ) ) ),
c_0_120 ).
fof(c_0_1288,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X40),X43)),finite_psubset(X1)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ) ),
c_0_121 ).
fof(c_0_1289,axiom,
! [X2,X1,X39,X40,X38,X9,X25] :
( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
=> hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),X38),X39),X9),X40) ) ),
c_0_122 ).
fof(c_0_1290,axiom,
! [X6,X7,X8,X9] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X8),X9)))
<=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X9)
& ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X9)
=> ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7) )
& ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X9)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ),
c_0_123 ).
fof(c_0_1291,axiom,
! [X6,X7,X8,X9] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X8),X9)))
<=> ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X9)
& ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X9)
=> ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7) )
& ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X9)
=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ),
c_0_124 ).
fof(c_0_1292,axiom,
! [X1,X2,X39,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X40),X39),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X40)) = ti(fun(X1,X2),X39) ) ),
c_0_125 ).
fof(c_0_1293,axiom,
! [X1,X2,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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),X40),X38),X6)),X40)) ),
c_0_126 ).
fof(c_0_1294,axiom,
! [X54,X57,X38] :
( ! [X33,X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X44))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X38,X33)),hAPP(nat,nat,X38,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,X38,X54)),X57)),hAPP(nat,nat,X38,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)))) ),
c_0_127 ).
fof(c_0_1295,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
c_0_128 ).
fof(c_0_1296,axiom,
! [X1] :
( order(X1)
=> ! [X30,X54,X38] :
( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X54)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54)) ) ) ),
c_0_129 ).
fof(c_0_1297,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> 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),X38),X40)),X43)) ),
c_0_130 ).
fof(c_0_1298,plain,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_1299,axiom,
! [X1,X2,X40,X43,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ) ),
c_0_132 ).
fof(c_0_1300,axiom,
! [X1] :
( order(X1)
=> ! [X30,X72,X38] :
( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X72))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X72))) ) ) ),
c_0_133 ).
fof(c_0_1301,axiom,
! [X1] :
( order(X1)
=> ! [X30,X72,X38] :
( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X72))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X72))) ) ) ),
c_0_134 ).
fof(c_0_1302,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X57,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) ),
c_0_135 ).
fof(c_0_1303,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X57,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) ),
c_0_136 ).
fof(c_0_1304,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X43)) ) ) ),
c_0_137 ).
fof(c_0_1305,axiom,
! [X3,X1,X2,X105,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X105),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X105),X38)),X40)) ) ),
c_0_138 ).
fof(c_0_1306,axiom,
! [X1] :
( semiring(X1)
=> ! [X21,X96,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X96)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X96)),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X96)),X37) ),
c_0_139 ).
fof(c_0_1307,axiom,
! [X40,X57] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X40),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),X40)))))
=> X40 = 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),X40))) ),
c_0_140 ).
fof(c_0_1308,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) ),
c_0_141 ).
fof(c_0_1309,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ),
c_0_142 ).
fof(c_0_1310,plain,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
=> ~ ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_1311,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
c_0_144 ).
fof(c_0_1312,axiom,
! [X2,X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> ( ? [X84] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X84),X40))
& 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),X84),X40)),X43)) )
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
c_0_145 ).
fof(c_0_1313,axiom,
! [X58,X90,X59,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X90)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X90)),X50)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X90)),X50),
c_0_146 ).
fof(c_0_1314,axiom,
! [X2,X1,X40,X38,X6,X7] :
( 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),X40),X38),X6) = 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),X40),X38),X7)
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> ti(X2,X6) = ti(X2,X7) ) ) ),
c_0_147 ).
fof(c_0_1315,plain,
! [X1] :
( order(X1)
=> ! [X14,X15,X17,X81] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81))
& ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X14))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) )
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X81)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_1316,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( 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),X38),X40)),X43))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
c_0_149 ).
fof(c_0_1317,axiom,
! [X1,X2,X6,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),X43)) ) ),
c_0_150 ).
fof(c_0_1318,axiom,
! [X1,X2,X3,X39,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X39),X38)),X40))
=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X39),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),X40))) ),
c_0_151 ).
fof(c_0_1319,axiom,
! [X2,X1,X43,X48,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X48),X40))
=> 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),X40),X43)),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),X48),X43))) ),
c_0_152 ).
fof(c_0_1320,axiom,
! [X3,X1,X2,X39,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X39),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X39),X38)),X40)) ) ),
c_0_153 ).
fof(c_0_1321,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X113,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X113))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X30),X113))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X113)) ) ) ),
c_0_154 ).
fof(c_0_1322,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
c_0_155 ).
fof(c_0_1323,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) ) ),
c_0_156 ).
fof(c_0_1324,plain,
! [X1] :
( order(X1)
=> ! [X14,X15,X17,X81] :
( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_1325,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr1471790799AtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
c_0_158 ).
fof(c_0_1326,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr676655987ssThan(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
c_0_159 ).
fof(c_0_1327,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr676655987ssThan(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
c_0_160 ).
fof(c_0_1328,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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_gr1471790799AtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) ) ),
c_0_161 ).
fof(c_0_1329,axiom,
! [X1,X2,X39,X38,X40] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
=> ti(fun(X1,X2),X38) = ti(fun(X1,X2),X39) ) ) ),
c_0_162 ).
fof(c_0_1330,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X34,X35] : 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35)))) ),
c_0_163 ).
fof(c_0_1331,axiom,
! [X1,X42,X38,X6,X7] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7)))
=> hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X38),X42))) ),
c_0_164 ).
fof(c_0_1332,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X15,X17,X81] :
( 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),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14))
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
c_0_165 ).
fof(c_0_1333,axiom,
! [X2,X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),X38),X40))),hAPP(fun(X1,bool),nat,finite_card(X1),X40))) ),
c_0_166 ).
fof(c_0_1334,axiom,
! [X1,X6,X7,X38] :
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X38)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7))) ),
c_0_167 ).
fof(c_0_1335,axiom,
! [X2,X1,X38,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> ? [X85] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X85),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X85))
& ti(fun(X1,bool),X43) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X85) ) ) ),
c_0_168 ).
fof(c_0_1336,axiom,
! [X1,X43,X88,X40,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X88))
=> 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X88))) ) ),
c_0_169 ).
fof(c_0_1337,axiom,
! [X1,X43,X88,X40,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X88))
=> 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X88))) ) ),
c_0_170 ).
fof(c_0_1338,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( 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),X38),X40)),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40) = ti(fun(X1,bool),X40) ) ) ),
c_0_171 ).
fof(c_0_1339,axiom,
! [X2,X1,X43,X40,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ) ),
c_0_172 ).
fof(c_0_1340,axiom,
! [X1,X2,X6,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6))) ) ),
c_0_173 ).
fof(c_0_1341,plain,
! [X1,X2,X6,X38,X40,X43] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
=> ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6)))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40)) ) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_1342,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
<=> ? [X79] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X79),X40))
& ti(fun(X1,bool),X43) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X79) ) ),
c_0_175 ).
fof(c_0_1343,axiom,
! [X1,X2,X40,X38,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43))) ) ),
c_0_176 ).
fof(c_0_1344,axiom,
! [X1,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
=> ( 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),X11))))
<=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ) ),
c_0_177 ).
fof(c_0_1345,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ) ),
c_0_178 ).
fof(c_0_1346,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ) ),
c_0_179 ).
fof(c_0_1347,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
c_0_180 ).
fof(c_0_1348,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
c_0_181 ).
fof(c_0_1349,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
c_0_182 ).
fof(c_0_1350,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
c_0_183 ).
fof(c_0_1351,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ) ),
c_0_184 ).
fof(c_0_1352,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ) ),
c_0_185 ).
fof(c_0_1353,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14)) ) ) ),
c_0_186 ).
fof(c_0_1354,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ),
c_0_187 ).
fof(c_0_1355,axiom,
! [X1,X2,X3,X105,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X105),X38)),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X38),X40)) ),
c_0_188 ).
fof(c_0_1356,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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),X40),X38)),X43)) ),
c_0_189 ).
fof(c_0_1357,plain,
! [X1,X2,X15,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> ~ ! [X26] :
( ti(X1,X15) = hAPP(X2,X1,X38,X26)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40)) ) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_1358,axiom,
! [X1,X2,X9,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X9),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
<=> ? [X26] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40))
& ti(X1,X9) = hAPP(X2,X1,X38,X26) ) ),
c_0_191 ).
fof(c_0_1359,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
c_0_192 ).
fof(c_0_1360,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
c_0_193 ).
fof(c_0_1361,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
c_0_194 ).
fof(c_0_1362,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
c_0_195 ).
fof(c_0_1363,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
c_0_196 ).
fof(c_0_1364,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
c_0_197 ).
fof(c_0_1365,axiom,
! [X2,X1,X42,X6,X7] :
( 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),X42),X6),X7))
<=> 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),X6),X7)),X42)) ),
c_0_198 ).
fof(c_0_1366,axiom,
! [X54,X30,X57] :
( 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ) ),
c_0_199 ).
fof(c_0_1367,axiom,
! [X54,X30,X57] :
( 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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ) ),
c_0_200 ).
fof(c_0_1368,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> ( 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_eq(nat),X54),X30)) ) ),
c_0_201 ).
fof(c_0_1369,axiom,
! [X54,X57,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)))
<=> ( 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_eq(nat),X54),X30)) ) ),
c_0_202 ).
fof(c_0_1370,axiom,
! [X1,X2,X43,X40,X38,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) ) ) ),
c_0_203 ).
fof(c_0_1371,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ) ),
c_0_204 ).
fof(c_0_1372,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X17,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X17)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ) ),
c_0_205 ).
fof(c_0_1373,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> 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))),X40)))) ),
c_0_206 ).
fof(c_0_1374,axiom,
! [X3,X2,X1,X39,X52,X38,X40,X43] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
=> ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X39),X43) = ti(fun(X3,bool),X52)
=> 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)),hAPP(fun(X2,bool),fun(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3))),compose(X2,X1,X3),X40),X39),X38)),X40) = ti(fun(X3,bool),X52) ) ),
c_0_207 ).
fof(c_0_1375,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ),
c_0_208 ).
fof(c_0_1376,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
c_0_209 ).
fof(c_0_1377,axiom,
! [X3,X1,X2,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,bool),bool),inj_on(X1,fun(X3,X2)),hAPP(fun(X1,X2),fun(X1,fun(X3,X2)),hAPP(fun(X2,fun(X3,X2)),fun(fun(X1,X2),fun(X1,fun(X3,X2))),combb(X2,fun(X3,X2),X1),combk(X2,X3)),X38)),top_top(fun(X1,bool)))) ),
c_0_210 ).
fof(c_0_1378,plain,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X30,X54] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X30))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_1379,axiom,
! [X3,X1,X2,X39,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X39),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))),X38))),X38) = ti(fun(X1,X3),X39) ),
c_0_212 ).
fof(c_0_1380,axiom,
! [X2,X1,X40,X43,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
c_0_213 ).
fof(c_0_1381,axiom,
! [X2,X1,X43,X40,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
c_0_214 ).
fof(c_0_1382,plain,
! [X2,X1,X40,X43,X6,X7] :
( ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) )
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_1383,axiom,
! [X6,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X8),X6)),arrow_1568854078le_Lin)) ),
c_0_216 ).
fof(c_0_1384,axiom,
! [X6,X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X8),X6)),arrow_1568854078le_Lin)) ),
c_0_217 ).
fof(c_0_1385,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),X40))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
c_0_218 ).
fof(c_0_1386,axiom,
! [X3,X1,X2,X39,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),top_top(fun(X3,bool))))
=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),top_top(fun(X3,bool)))) ) ),
c_0_219 ).
fof(c_0_1387,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X14,X17,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X17)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ),
c_0_220 ).
fof(c_0_1388,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ),
c_0_221 ).
fof(c_0_1389,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
c_0_222 ).
fof(c_0_1390,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
c_0_223 ).
fof(c_0_1391,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X14,X17,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X17)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ),
c_0_224 ).
fof(c_0_1392,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X17,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X15)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ),
c_0_225 ).
fof(c_0_1393,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X21,X37,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ),
c_0_226 ).
fof(c_0_1394,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ),
c_0_227 ).
fof(c_0_1395,axiom,
! [X1,X11,X53] : 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),X11)),X53)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53)),
c_0_228 ).
fof(c_0_1396,axiom,
! [X1,X11,X53] : 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),X11)),X53)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53)),
c_0_229 ).
fof(c_0_1397,axiom,
! [X2,X1,X38,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> 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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43))) ),
c_0_230 ).
fof(c_0_1398,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ),
c_0_231 ).
fof(c_0_1399,axiom,
! [X57,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
<=> ( 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),X54),X30)) ) ),
c_0_232 ).
fof(c_0_1400,axiom,
! [X54,X57,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)))
<=> ( 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),X54),X30)) ) ),
c_0_233 ).
fof(c_0_1401,axiom,
! [X57,X54,X30] :
( 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),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
c_0_234 ).
fof(c_0_1402,axiom,
! [X57,X54,X30] :
( 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),X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
c_0_235 ).
fof(c_0_1403,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X38,X39] :
( ! [X26] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)))
=> hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39)) ) ),
c_0_236 ).
fof(c_0_1404,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
<=> ! [X26] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26))) ) ),
c_0_237 ).
fof(c_0_1405,axiom,
! [X1,X11,X40,X43] :
( ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
& hBOOL(hAPP(X1,bool,X11,X26)) )
<=> ( ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& hBOOL(hAPP(X1,bool,X11,X26)) )
| ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43))
& hBOOL(hAPP(X1,bool,X11,X26)) ) ) ),
c_0_238 ).
fof(c_0_1406,axiom,
! [X1,X2,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> hAPP(X1,X2,X38,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X7)) = ti(X2,X7) ) ),
c_0_239 ).
fof(c_0_1407,axiom,
! [X2,X1,X38,X40,X43] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
=> hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X43),X38),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X40),X38)),X43)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X43) ),
c_0_240 ).
fof(c_0_1408,axiom,
! [X1,X11,X40,X43] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
=> hBOOL(hAPP(X1,bool,X11,X26)) )
<=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(X1,bool,X11,X26)) )
& ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43))
=> hBOOL(hAPP(X1,bool,X11,X26)) ) ) ),
c_0_241 ).
fof(c_0_1409,axiom,
! [X1,X2,X14,X40,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X40)) ) ),
c_0_242 ).
fof(c_0_1410,axiom,
! [X1,X43,X40,X52] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),X52)) ) ),
c_0_243 ).
fof(c_0_1411,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X17,X81,X14,X15] :
( ( ti(X1,X14) != ti(X1,X15)
& ti(X1,X17) != ti(X1,X81) )
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X81)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X81)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X17)) ) ),
c_0_244 ).
fof(c_0_1412,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X91,X7,X6,X9] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X91),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X9)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X91),X9)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X7))
<=> ( ti(X1,X91) = ti(X1,X6)
| ti(X1,X7) = ti(X1,X9) ) ) ),
c_0_245 ).
fof(c_0_1413,axiom,
! [X2,X1,X82,X38,X40,X48] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X48)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X82),X48))
=> hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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),X40),X38)),X82)) = ti(fun(X1,bool),X82) ) ),
c_0_246 ).
fof(c_0_1414,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X54))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X30)) ) ),
c_0_247 ).
fof(c_0_1415,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51))) ) ),
c_0_248 ).
fof(c_0_1416,plain,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X30,X54] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(nat,X1,X38,X30)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_1417,axiom,
! [X8] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
=> hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X8)),arrow_301600364e_Prof)) ),
c_0_250 ).
fof(c_0_1418,axiom,
! [X1] :
( linord1117847801e_zero(X1)
=> ! [X34,X35] :
( ! [X98] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X98))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X98),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X98),X34)),X35)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
c_0_251 ).
fof(c_0_1419,axiom,
! [X1,X40,X43,X52] :
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X40)) ),
c_0_252 ).
fof(c_0_1420,axiom,
! [X2,X1,X38,X39,X40] :
( ! [X19] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40))
=> hAPP(X1,X2,X38,X19) = hAPP(X1,X2,X39,X19) )
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),X40)) ) ),
c_0_253 ).
fof(c_0_1421,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X38,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X54)),X30))) ) ),
c_0_254 ).
fof(c_0_1422,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X38,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X54)),X30))) ) ),
c_0_255 ).
fof(c_0_1423,axiom,
! [X25,X29] :
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X25),X29))
<=> ! [X26] :
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
=> hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X29) ) ),
c_0_256 ).
fof(c_0_1424,axiom,
! [X1] :
( linord893533164strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
c_0_257 ).
fof(c_0_1425,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
c_0_258 ).
fof(c_0_1426,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
c_0_259 ).
fof(c_0_1427,axiom,
! [X1] :
( ordere1490568538miring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
c_0_260 ).
fof(c_0_1428,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
c_0_261 ).
fof(c_0_1429,axiom,
! [X1] :
( ordered_semiring(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
c_0_262 ).
fof(c_0_1430,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
c_0_263 ).
fof(c_0_1431,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
c_0_264 ).
fof(c_0_1432,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
c_0_265 ).
fof(c_0_1433,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
c_0_266 ).
fof(c_0_1434,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X45,X21,X37] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X37),X45))) ) ) ),
c_0_267 ).
fof(c_0_1435,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X45,X21,X37] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X37),X45))) ) ) ),
c_0_268 ).
fof(c_0_1436,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
c_0_269 ).
fof(c_0_1437,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
c_0_270 ).
fof(c_0_1438,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
c_0_271 ).
fof(c_0_1439,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X45,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
c_0_272 ).
fof(c_0_1440,axiom,
! [X29,X63,X38] :
( ! [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,X38,X16)),hAPP(nat,nat,X38,X64))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X63))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X38,X29)),hAPP(nat,nat,X38,X63))) ) ),
c_0_273 ).
fof(c_0_1441,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)),zero_zero(X1)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X15)) ) ) ) ),
c_0_274 ).
fof(c_0_1442,axiom,
! [X50,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),zero_zero(nat)),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X50))) ) ),
c_0_275 ).
fof(c_0_1443,axiom,
! [X50,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),zero_zero(nat)),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X59))) ) ),
c_0_276 ).
fof(c_0_1444,axiom,
! [X50,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),X50),X61))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X61))) ) ),
c_0_277 ).
fof(c_0_1445,axiom,
! [X50,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),X50),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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
c_0_278 ).
fof(c_0_1446,axiom,
! [X50,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),X50),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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
c_0_279 ).
fof(c_0_1447,axiom,
! [X1,X6,X40,X11] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11))))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
& hBOOL(hAPP(X1,bool,X11,X6)) ) ),
c_0_280 ).
fof(c_0_1448,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X49))) ) ),
c_0_281 ).
fof(c_0_1449,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51))) ) ),
c_0_282 ).
fof(c_0_1450,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)),X34)) ) ) ) ),
c_0_283 ).
fof(c_0_1451,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)),X34)) ) ) ) ),
c_0_284 ).
fof(c_0_1452,axiom,
! [X38] :
( ! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X38,hAPP(nat,nat,suc,X16))),hAPP(nat,nat,X38,X16)))
=> ? [X16] :
! [X62] : hAPP(nat,nat,X38,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X62)) = hAPP(nat,nat,X38,X16) ),
c_0_285 ).
fof(c_0_1453,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_1454,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_1455,axiom,
! [X2,X1,X40,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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))),X38)),X40)) = ti(fun(X1,bool),X40) ),
c_0_288 ).
fof(c_0_1456,axiom,
! [X1,X2,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
=> hAPP(X2,X1,X38,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),X40),X38),X7)) = ti(X1,X7) ),
c_0_289 ).
fof(c_0_1457,axiom,
! [X1,X2,X40,X43,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) ),
c_0_290 ).
fof(c_0_1458,axiom,
! [X3,X1,X2,X6,X39,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),X39)) = hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),X39) ),
c_0_291 ).
fof(c_0_1459,axiom,
! [X2,X1,X39,X38,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X2,X1,X39,hAPP(X1,X2,X38,X26)) = ti(X1,X26) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
c_0_292 ).
fof(c_0_1460,axiom,
! [X1,X2,X15,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X15),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)))))
<=> ? [X26] :
( ti(X2,X15) = hAPP(X1,X2,X38,X26)
& ! [X46] :
( ti(X2,X15) = hAPP(X1,X2,X38,X46)
=> ti(X1,X46) = ti(X1,X26) ) ) ) ),
c_0_293 ).
fof(c_0_1461,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X94)) ),
c_0_294 ).
fof(c_0_1462,axiom,
! [X1,X2,X41,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X41),X40))
=> 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),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X41)) = ti(fun(X1,bool),X41) ) ),
c_0_295 ).
fof(c_0_1463,axiom,
! [X57,X29,X63] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X63))
=> hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X63),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57))) ),
c_0_296 ).
fof(c_0_1464,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ),
c_0_297 ).
fof(c_0_1465,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ),
c_0_298 ).
fof(c_0_1466,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1))) ) ),
c_0_299 ).
fof(c_0_1467,plain,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34))
=> ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_1468,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X6,X7,X9] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X6),X7)),X9))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X9))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X9)) ) ) ),
c_0_301 ).
fof(c_0_1469,axiom,
! [X1,X2,X38,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
=> ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)
<=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
c_0_302 ).
fof(c_0_1470,axiom,
! [X1] :
( ring_1(X1)
=> ! [X15,X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),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),times_times(X1),X14),X15)),ring_1_Ints(X1))) ) ) ),
c_0_303 ).
fof(c_0_1471,axiom,
! [X1] :
( ring_1(X1)
=> ! [X15,X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),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),X14),X15)),ring_1_Ints(X1))) ) ) ),
c_0_304 ).
fof(c_0_1472,axiom,
! [X1,X43,X52,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)),X40) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X40)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X40)),
c_0_305 ).
fof(c_0_1473,axiom,
! [X1,X43,X52,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)),X40) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X40)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X40)),
c_0_306 ).
fof(c_0_1474,axiom,
! [X2,X1,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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))),X38)),top_top(fun(X1,bool)))) ),
c_0_307 ).
fof(c_0_1475,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ? [X44,X84] :
( ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X84),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)),X44)))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),X84),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)),X44)))) ) ),
c_0_308 ).
fof(c_0_1476,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X43))) ) ),
c_0_309 ).
fof(c_0_1477,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43)) ) ) ),
c_0_310 ).
fof(c_0_1478,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
c_0_311 ).
fof(c_0_1479,plain,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_1480,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54)),X30)) ),
c_0_313 ).
fof(c_0_1481,axiom,
! [X49,X50,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
c_0_314 ).
fof(c_0_1482,axiom,
! [X49,X50,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ),
c_0_315 ).
fof(c_0_1483,axiom,
! [X58,X59,X50] :
( 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)),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X50)) ),
c_0_316 ).
fof(c_0_1484,plain,
! [X49,X50,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
=> ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_1485,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37))) ) ),
c_0_318 ).
fof(c_0_1486,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22))) ) ),
c_0_319 ).
fof(c_0_1487,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37))) ) ),
c_0_320 ).
fof(c_0_1488,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22))) ) ),
c_0_321 ).
fof(c_0_1489,axiom,
! [X2,X1,X38,X39,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
=> hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X39),X40) ),
c_0_322 ).
fof(c_0_1490,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( ( ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> one_one(nat) = zero_zero(nat) )
=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ) ),
c_0_323 ).
fof(c_0_1491,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X76,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X76),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X76),X40)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X39),X76)),X40) ) ) ),
c_0_324 ).
fof(c_0_1492,axiom,
! [X2,X1] :
( semiring_0(X1)
=> ! [X106,X38,X40] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X106),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X1,X1),fun(fun(X2,X1),fun(X2,X1)),combb(X1,X1,X2),hAPP(X1,fun(X1,X1),times_times(X1),X106)),X38)),X40) ),
c_0_325 ).
fof(c_0_1493,axiom,
! [X1,X2] :
( comm_monoid_mult(X2)
=> ! [X38,X41] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
=> ( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X41))
=> hAPP(X1,X2,X38,X26) = one_one(X2) )
=> hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X41) = one_one(X2) ) ) ),
c_0_326 ).
fof(c_0_1494,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) ),
c_0_327 ).
fof(c_0_1495,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X38,X54,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) ),
c_0_328 ).
fof(c_0_1496,axiom,
! [X1,X43,X52,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
c_0_329 ).
fof(c_0_1497,axiom,
! [X50,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),times_times(nat),X50),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X59))) ),
c_0_330 ).
fof(c_0_1498,axiom,
! [X50,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),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X50))) ),
c_0_331 ).
fof(c_0_1499,axiom,
! [X50,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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X50))) ),
c_0_332 ).
fof(c_0_1500,axiom,
! [X50,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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X50))) ),
c_0_333 ).
fof(c_0_1501,axiom,
! [X1,X2,X38,X40] : hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40))),
c_0_334 ).
fof(c_0_1502,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40)) ) ),
c_0_335 ).
fof(c_0_1503,axiom,
! [X57,X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)),
c_0_336 ).
fof(c_0_1504,axiom,
! [X57,X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)),
c_0_337 ).
fof(c_0_1505,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
c_0_338 ).
fof(c_0_1506,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)),zero_zero(X1))) ) ) ),
c_0_339 ).
fof(c_0_1507,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
c_0_340 ).
fof(c_0_1508,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ),
c_0_341 ).
fof(c_0_1509,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
c_0_342 ).
fof(c_0_1510,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)),zero_zero(X1))) ) ) ),
c_0_343 ).
fof(c_0_1511,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
c_0_344 ).
fof(c_0_1512,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
c_0_345 ).
fof(c_0_1513,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
c_0_346 ).
fof(c_0_1514,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
c_0_347 ).
fof(c_0_1515,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
c_0_348 ).
fof(c_0_1516,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)),X34)) ) ) ),
c_0_349 ).
fof(c_0_1517,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X21,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34)) ) ) ),
c_0_350 ).
fof(c_0_1518,axiom,
! [X1,X2,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
c_0_351 ).
fof(c_0_1519,axiom,
! [X1,X2,X3] :
( comm_monoid_add(X3)
=> ! [X76,X38,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> hAPP(fun(X2,bool),X3,hAPP(fun(X2,X3),fun(fun(X2,bool),X3),big_co1399186613setsum(X2,X3),X76),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X76),X38)),X43) ) ),
c_0_352 ).
fof(c_0_1520,plain,
! [X1] :
( linordered_ring(X1)
=> ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21)),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_1521,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66) ) ) ),
c_0_354 ).
fof(c_0_1522,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66) ) ) ),
c_0_355 ).
fof(c_0_1523,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66) ) ) ),
c_0_356 ).
fof(c_0_1524,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66) ) ) ),
c_0_357 ).
fof(c_0_1525,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66) ) ) ),
c_0_358 ).
fof(c_0_1526,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66) ) ) ),
c_0_359 ).
fof(c_0_1527,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66) ) ) ),
c_0_360 ).
fof(c_0_1528,axiom,
! [X1] :
( linorder(X1)
=> ! [X66,X77,X54] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X54))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66) ) ) ),
c_0_361 ).
fof(c_0_1529,axiom,
! [X1,X2,X43,X40,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(fun(X1,bool),fun(X2,X2),X25,X43)) = hAPP(fun(X1,bool),fun(X2,X2),X25,X40) ) ) ),
c_0_362 ).
fof(c_0_1530,axiom,
! [X1,X2,X43,X40,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hAPP(fun(X1,bool),fun(X2,X2),X25,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(fun(X1,bool),fun(X2,X2),X25,X43)) ) ) ),
c_0_363 ).
fof(c_0_1531,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X11,X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X11),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X11,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X11),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X54),X30))) ) ),
c_0_364 ).
fof(c_0_1532,axiom,
! [X1,X40] : 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),X40),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X40)))),
c_0_365 ).
fof(c_0_1533,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_366]) ).
fof(c_0_1534,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_367]) ).
fof(c_0_1535,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
c_0_368 ).
fof(c_0_1536,axiom,
! [X1,X43,X17,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
c_0_369 ).
fof(c_0_1537,axiom,
! [X1,X2,X6,X40,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(X1,fun(X2,X2),X38,X6)) = hAPP(fun(X1,bool),fun(X2,X2),X25,X40) ) ) ),
c_0_370 ).
fof(c_0_1538,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) ),
c_0_371 ).
fof(c_0_1539,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ),
c_0_372 ).
fof(c_0_1540,plain,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_1541,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) ),
c_0_374 ).
fof(c_0_1542,plain,
! [X1,X40] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_1543,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X43)),hAPP(fun(X1,bool),nat,finite_card(X1),X40)))
=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ) ),
c_0_376 ).
fof(c_0_1544,axiom,
! [X2,X1,X43,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X43),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ) ),
c_0_377 ).
fof(c_0_1545,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22)) ) ) ),
c_0_378 ).
fof(c_0_1546,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22)) ) ) ),
c_0_379 ).
fof(c_0_1547,axiom,
! [X2,X3,X1,X39,X38,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X39),X38),X6) = hAPP(X3,X2,X39,hAPP(X1,X3,X38,X6)) ),
c_0_380 ).
fof(c_0_1548,axiom,
! [X1,X2,X40,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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))),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)) = ti(fun(X1,bool),X40) ),
c_0_381 ).
fof(c_0_1549,axiom,
! [X1,X2,X83,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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))),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X83)) = ti(fun(X1,bool),X83) ),
c_0_382 ).
fof(c_0_1550,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X52)),
c_0_383 ).
fof(c_0_1551,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X52)),
c_0_384 ).
fof(c_0_1552,axiom,
! [X1,X2,X38,X40] :
( 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),X38),X40)))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40)) ) ),
c_0_385 ).
fof(c_0_1553,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_386 ).
fof(c_0_1554,axiom,
! [X1,X40,X43] : 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X40)),
c_0_387 ).
fof(c_0_1555,axiom,
! [X1,X40,X43] : 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X43)),
c_0_388 ).
fof(c_0_1556,axiom,
! [X2,X1,X38,X40,X43] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X43)),
c_0_389 ).
fof(c_0_1557,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_390 ).
fof(c_0_1558,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_391 ).
fof(c_0_1559,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),X94)) ),
c_0_392 ).
fof(c_0_1560,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94))) ),
c_0_393 ).
fof(c_0_1561,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45)) ),
c_0_394 ).
fof(c_0_1562,axiom,
! [X2,X1,X38,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ),
c_0_395 ).
fof(c_0_1563,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> 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)),the_inv_into(X1,X2),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)) = ti(fun(X1,bool),X40) ),
c_0_396 ).
fof(c_0_1564,axiom,
! [X1,X2,X15,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool)))))
=> ~ ! [X26] : ti(X1,X15) != hAPP(X2,X1,X38,X26) ),
c_0_397 ).
fof(c_0_1565,axiom,
! [X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X49)))),
c_0_398 ).
fof(c_0_1566,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
<=> ? [X44,X84] : ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X84),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)),X44))) ),
c_0_399 ).
fof(c_0_1567,axiom,
! [X1,X40,X38,X30] :
( ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X38),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)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
c_0_400 ).
fof(c_0_1568,axiom,
! [X11,X30] :
( ? [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X30))
& hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ? [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X30)))
& hBOOL(hAPP(nat,bool,X11,X26)) ) ),
c_0_401 ).
fof(c_0_1569,axiom,
! [X11,X30] :
( ? [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X30))
& hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ? [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X30)))
& hBOOL(hAPP(nat,bool,X11,X26)) ) ),
c_0_402 ).
fof(c_0_1570,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X15)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),zero_zero(X1))) ) ) ) ),
c_0_403 ).
fof(c_0_1571,axiom,
! [X2,X1,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
<=> ! [X26] : hAPP(X2,X1,X38,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))),X38),X26)) = ti(X1,X26) ),
c_0_404 ).
fof(c_0_1572,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) ) ),
c_0_405 ).
fof(c_0_1573,plain,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X40] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) )
& ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_1574,axiom,
! [X11,X30] :
( ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X30))
=> hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ! [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X30)))
=> hBOOL(hAPP(nat,bool,X11,X26)) ) ),
c_0_407 ).
fof(c_0_1575,axiom,
! [X11,X30] :
( ! [X33] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X30))
=> hBOOL(hAPP(nat,bool,X11,X33)) )
<=> ! [X26] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X30)))
=> hBOOL(hAPP(nat,bool,X11,X26)) ) ),
c_0_408 ).
fof(c_0_1576,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
c_0_409 ).
fof(c_0_1577,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X21,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
c_0_410 ).
fof(c_0_1578,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X21,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
c_0_411 ).
fof(c_0_1579,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
c_0_412 ).
fof(c_0_1580,axiom,
! [X1,X3,X2,X87,X38,X39,X76] : hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X38),hAPP(fun(X1,X87),fun(X1,X3),hAPP(fun(X87,X3),fun(fun(X1,X87),fun(X1,X3)),comp(X87,X3,X1),X39),X76)) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),hAPP(fun(X87,X3),fun(X87,X2),hAPP(fun(X3,X2),fun(fun(X87,X3),fun(X87,X2)),comp(X3,X2,X87),X38),X39)),X76),
c_0_413 ).
fof(c_0_1581,axiom,
! [X54,X30] :
( 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),X30)))
<=> ( 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)),X30)) ) ),
c_0_414 ).
fof(c_0_1582,axiom,
! [X1,X2,X40,X43] :
( 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),X40),X43)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ) ),
c_0_415 ).
fof(c_0_1583,axiom,
! [X1,X2,X40,X43] :
( 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),X40),X43)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
c_0_416 ).
fof(c_0_1584,axiom,
! [X1,X2,X40,X43] :
( 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),X40),X43)))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ),
c_0_417 ).
fof(c_0_1585,axiom,
! [X1,X3,X2,X40,X39,X38] : hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X39),X38) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X39),X38)),X40),
c_0_418 ).
fof(c_0_1586,axiom,
! [X2,X1,X53,X11] :
( ! [X26,X46] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X26),X46))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X26),X46)) )
=> 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))),X11),X53)) ),
c_0_419 ).
fof(c_0_1587,axiom,
! [X3,X2,X1,X39,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X39),top_top(fun(X1,bool))) = top_top(fun(X3,bool))
=> 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)),comp(X1,X3,X2),X39),X38)),top_top(fun(X2,bool))) = top_top(fun(X3,bool)) ) ),
c_0_420 ).
fof(c_0_1588,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( 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),ord_atLeast(X1),X6)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
c_0_421 ).
fof(c_0_1589,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( 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),ord_greaterThan(X1),X6)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
c_0_422 ).
fof(c_0_1590,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X51,X49] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X49))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X51))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X49),X51))) ) ) ),
c_0_423 ).
fof(c_0_1591,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
c_0_424 ).
fof(c_0_1592,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X22,X21] :
( ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22)) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(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),times_times(X1),X21),X22))) ) ),
c_0_425 ).
fof(c_0_1593,axiom,
! [X1] :
( ordere453448008miring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
c_0_426 ).
fof(c_0_1594,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
c_0_427 ).
fof(c_0_1595,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
c_0_428 ).
fof(c_0_1596,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
c_0_429 ).
fof(c_0_1597,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
=> 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),X21),X22))) ) ) ),
c_0_430 ).
fof(c_0_1598,axiom,
! [X2,X1,X3,X38,X39] : 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),X38),X39)),top_top(fun(X2,bool))) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X38),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X39),top_top(fun(X2,bool)))),
c_0_431 ).
fof(c_0_1599,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
c_0_432 ).
fof(c_0_1600,axiom,
! [X1] :
( ordered_ring(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(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),times_times(X1),X21),X22))) ) ) ),
c_0_433 ).
fof(c_0_1601,axiom,
! [X14,X15] :
( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
=> ? [X26] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X26),arrow_1568854078le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X26)) ) ),
c_0_434 ).
fof(c_0_1602,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
c_0_435 ).
fof(c_0_1603,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
c_0_436 ).
fof(c_0_1604,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
c_0_437 ).
fof(c_0_1605,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X37,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
c_0_438 ).
fof(c_0_1606,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X22,X21,X37] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
c_0_439 ).
fof(c_0_1607,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X6,X7,X9] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X7),X9)))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X9)) ) ) ),
c_0_440 ).
fof(c_0_1608,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22))) ) ) ),
c_0_441 ).
fof(c_0_1609,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36))) ) ) ),
c_0_442 ).
fof(c_0_1610,axiom,
! [X1] :
( linordered_field(X1)
=> ! [X34,X35] :
( ! [X75] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X75))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X75))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
c_0_443 ).
fof(c_0_1611,plain,
~ ! [X32] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),X32))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X32),arrow_1568854078le_Lin)) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_1612,plain,
~ ! [X31] :
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),X31))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X31),arrow_1568854078le_Lin)) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_1613,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
c_0_446 ).
fof(c_0_1614,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
c_0_447 ).
fof(c_0_1615,axiom,
! [X2,X1,X3,X38,X39,X106] : 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)),comp(X3,X1,X2),X38),X39)),X106) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X38),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X39),X106)),
c_0_448 ).
fof(c_0_1616,axiom,
! [X2,X1,X3,X38,X39,X40] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X39),X40)) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),combb(X2,X1,X3),X38),X39)),X40),
c_0_449 ).
fof(c_0_1617,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( ! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X47))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X36)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36)) ) ) ),
c_0_450 ).
fof(c_0_1618,axiom,
! [X1,X2,X6,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
=> ti(X1,X6) = ti(X1,X7) ) ) ) ),
c_0_451 ).
fof(c_0_1619,axiom,
! [X1,X2,X7,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
<=> ti(X1,X6) = ti(X1,X7) ) ) ) ),
c_0_452 ).
fof(c_0_1620,axiom,
! [X1,X2,X6,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( ti(X1,X6) != ti(X1,X7)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
=> hAPP(X1,X2,X38,X6) != hAPP(X1,X2,X38,X7) ) ) ) ),
c_0_453 ).
fof(c_0_1621,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
<=> ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X27)
=> ti(X1,X26) = ti(X1,X27) ) ) ) ),
c_0_454 ).
fof(c_0_1622,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X35,X36,X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X36),X34)) ),
c_0_455 ).
fof(c_0_1623,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X35,X36,X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X36),X34)) ),
c_0_456 ).
fof(c_0_1624,axiom,
! [X1] :
( comm_semiring(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
c_0_457 ).
fof(c_0_1625,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
c_0_458 ).
fof(c_0_1626,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X49,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X49)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X49) ),
c_0_459 ).
fof(c_0_1627,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)))
<=> ( 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)),X30)) ) ),
c_0_460 ).
fof(c_0_1628,axiom,
! [X2,X1,X15,X38,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( ti(X2,X15) = hAPP(X1,X2,X38,X6)
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X15),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ) ),
c_0_461 ).
fof(c_0_1629,axiom,
! [X1,X2,X40,X15,X38,X6] :
( ti(X1,X15) = hAPP(X2,X1,X38,X6)
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40))) ) ),
c_0_462 ).
fof(c_0_1630,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X40) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& hAPP(X1,nat,X38,X26) = hAPP(nat,nat,suc,zero_zero(nat))
& ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( ti(X1,X26) != ti(X1,X27)
=> hAPP(X1,nat,X38,X27) = zero_zero(nat) ) ) ) ) ),
c_0_463 ).
fof(c_0_1631,axiom,
! [X1,X2,X11] :
( ! [X18] : hBOOL(hAPP(product_prod(X1,X2),bool,X11,X18))
<=> ! [X19,X20] : hBOOL(hAPP(product_prod(X1,X2),bool,X11,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X19),X20))) ),
c_0_464 ).
fof(c_0_1632,axiom,
! [X1,X2,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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))),X38)),top_top(fun(X2,bool))) = top_top(fun(X1,bool)) ),
c_0_465 ).
fof(c_0_1633,axiom,
! [X1,X40,X17,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
c_0_466 ).
fof(c_0_1634,axiom,
! [X1,X43,X17,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
c_0_467 ).
fof(c_0_1635,plain,
! [X1,X40,X17,X43] :
( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1636,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)),
c_0_469 ).
fof(c_0_1637,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)),
c_0_470 ).
fof(c_0_1638,axiom,
! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X50)),
c_0_471 ).
fof(c_0_1639,axiom,
! [X1] :
( ring_char_0(X1)
=> ! [X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(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)),X14)),X14) != zero_zero(X1) ) ),
c_0_472 ).
fof(c_0_1640,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( 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),X14),X14)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X14)) ) ),
c_0_473 ).
fof(c_0_1641,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( 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),X14),X14)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14)) ) ),
c_0_474 ).
fof(c_0_1642,plain,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)))
=> ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1643,plain,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6))
=> ( ~ hBOOL(hAPP(X1,bool,X40,X6))
=> hBOOL(hAPP(X1,bool,X43,X6)) ) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1644,axiom,
! [X1,X2,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ) ),
c_0_477 ).
fof(c_0_1645,axiom,
! [X1,X2,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> 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),X40),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ) ),
c_0_478 ).
fof(c_0_1646,axiom,
! [X1,X2,X6,X7,X11,X53] :
( 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))),X11),X53))
=> ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X6),X7))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X6),X7)) ) ),
c_0_479 ).
fof(c_0_1647,axiom,
! [X2,X1,X53,X11,X6,X7] :
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X6),X7))
=> ( 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))),X11),X53))
=> hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X6),X7)) ) ),
c_0_480 ).
fof(c_0_1648,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ),
c_0_481 ).
fof(c_0_1649,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ),
c_0_482 ).
fof(c_0_1650,axiom,
! [X1,X2,X6,X7,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X7) = ti(X1,X6) ) ) ),
c_0_483 ).
fof(c_0_1651,axiom,
! [X1,X2,X7,X6,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
=> 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),X40),X38),X7) = ti(X1,X6) ) ) ),
c_0_484 ).
fof(c_0_1652,axiom,
! [X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X40) = one_one(nat)
<=> ? [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
& hAPP(X1,nat,X38,X26) = one_one(nat)
& ! [X27] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
=> ( ti(X1,X26) != ti(X1,X27)
=> hAPP(X1,nat,X38,X27) = zero_zero(nat) ) ) ) ) ),
c_0_485 ).
fof(c_0_1653,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7)) = zero_zero(X1)
<=> ( ti(X1,X6) = zero_zero(X1)
& ti(X1,X7) = zero_zero(X1) ) ) ),
c_0_486 ).
fof(c_0_1654,axiom,
! [X11,X54,X30] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
=> ( ( X54 = X30
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) ) ) ),
c_0_487 ).
fof(c_0_1655,axiom,
! [X1,X25,X112] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X25),X112)))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112)) ) ),
c_0_488 ).
fof(c_0_1656,axiom,
! [X58,X49] : 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),X49),X58)))),
c_0_489 ).
fof(c_0_1657,axiom,
! [X58,X49] : 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),X49)))),
c_0_490 ).
fof(c_0_1658,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
c_0_491 ).
fof(c_0_1659,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52)) ) ),
c_0_492 ).
fof(c_0_1660,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
c_0_493 ).
fof(c_0_1661,axiom,
! [X1,X52,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
c_0_494 ).
fof(c_0_1662,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
=> hBOOL(hAPP(X1,bool,X40,X6)) ),
c_0_495 ).
fof(c_0_1663,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
=> hBOOL(hAPP(X1,bool,X43,X6)) ),
c_0_496 ).
fof(c_0_1664,plain,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
=> ~ ( hBOOL(hAPP(X1,bool,X40,X6))
=> ~ hBOOL(hAPP(X1,bool,X43,X6)) ) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1665,axiom,
! [X30,X54] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),hAPP(nat,nat,suc,X54)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X54)) ),
c_0_498 ).
fof(c_0_1666,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
c_0_499 ).
fof(c_0_1667,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),hAPP(nat,nat,suc,X51)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
c_0_500 ).
fof(c_0_1668,axiom,
! [X1,X2,X38,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X38,X6)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))))),
c_0_501 ).
fof(c_0_1669,axiom,
! [X1,X2,X40,X38,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ) ),
c_0_502 ).
fof(c_0_1670,axiom,
! [X50,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),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X50)) ) ),
c_0_503 ).
fof(c_0_1671,axiom,
! [X1,X2,X6,X38,X25] :
( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
=> hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(X1,fun(X2,X2),X38,X6)),hAPP(X1,fun(X2,X2),X38,X6)) = hAPP(X1,fun(X2,X2),X38,X6) ),
c_0_504 ).
fof(c_0_1672,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X66)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X77) ) ),
c_0_505 ).
fof(c_0_1673,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X66)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X77) ) ),
c_0_506 ).
fof(c_0_1674,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X66)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X77) ) ),
c_0_507 ).
fof(c_0_1675,axiom,
! [X1] :
( linorder(X1)
=> ! [X77,X66] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X66)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X77) ) ),
c_0_508 ).
fof(c_0_1676,axiom,
! [X1,X2,X39,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( ! [X26] : hAPP(X1,X2,X38,hAPP(X2,X1,X39,X26)) = ti(X2,X26)
=> 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))),X38) = ti(fun(X2,X1),X39) ) ),
c_0_509 ).
fof(c_0_1677,axiom,
! [X2,X1,X3,X87,X109,X38,X39,X6,X105,X110,X111] :
( hAPP(X2,X1,X38,hAPP(X3,X2,X39,X6)) = hAPP(X87,X1,X105,hAPP(X109,X87,X110,X111))
=> hAPP(X3,X1,hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),comp(X2,X1,X3),X38),X39),X6) = hAPP(X109,X1,hAPP(fun(X109,X87),fun(X109,X1),hAPP(fun(X87,X1),fun(fun(X109,X87),fun(X109,X1)),comp(X87,X1,X109),X105),X110),X111) ),
c_0_510 ).
fof(c_0_1678,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X49] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)),X49) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1))),X49) ),
c_0_511 ).
fof(c_0_1679,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
c_0_512 ).
fof(c_0_1680,axiom,
! [X1] :
( distrib_lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
c_0_513 ).
fof(c_0_1681,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X93) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),X95) ),
c_0_514 ).
fof(c_0_1682,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X36)) ),
c_0_515 ).
fof(c_0_1683,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),X22) ),
c_0_516 ).
fof(c_0_1684,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X34)) ),
c_0_517 ).
fof(c_0_1685,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X34)) ),
c_0_518 ).
fof(c_0_1686,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X35)) ),
c_0_519 ).
fof(c_0_1687,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X35)) ),
c_0_520 ).
fof(c_0_1688,axiom,
! [X2,X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> 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),X40),X43))) ) ),
c_0_521 ).
fof(c_0_1689,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
c_0_522 ).
fof(c_0_1690,axiom,
! [X1,X6,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
c_0_523 ).
fof(c_0_1691,axiom,
! [X1,X43,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
c_0_524 ).
fof(c_0_1692,axiom,
! [X1,X6,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
c_0_525 ).
fof(c_0_1693,axiom,
! [X1,X17,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
c_0_526 ).
fof(c_0_1694,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X6,X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,X2,X39,X6))) ) ),
c_0_527 ).
fof(c_0_1695,axiom,
! [X1,X2] :
( ord(X2)
=> ! [X6,X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,X2,X39,X6))) ) ),
c_0_528 ).
fof(c_0_1696,plain,
! [X54,X30] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
inference(fof_simplification,[status(thm)],[c_0_529]) ).
fof(c_0_1697,axiom,
! [X1] :
( linorder(X1)
=> ! [X17,X81,X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
=> ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
<=> ( ti(X1,X14) = ti(X1,X17)
& ti(X1,X15) = ti(X1,X81) ) ) ) ) ),
c_0_530 ).
fof(c_0_1698,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X15,X17,X81] :
( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
=> ti(X1,X14) = ti(X1,X17) ) ) ) ),
c_0_531 ).
fof(c_0_1699,axiom,
! [X1] :
( linorder(X1)
=> ! [X14,X15,X17,X81] :
( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
=> ti(X1,X15) = ti(X1,X81) ) ) ) ),
c_0_532 ).
fof(c_0_1700,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X57,X38] :
( hAPP(nat,X1,X38,zero_zero(nat)) = zero_zero(X1)
=> hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X57)) ) ),
c_0_533 ).
fof(c_0_1701,axiom,
! [X57,X38] :
( hAPP(nat,nat,X38,zero_zero(nat)) = zero_zero(nat)
=> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X57)) ),
c_0_534 ).
fof(c_0_1702,axiom,
! [X50,X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X49)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X51)),
c_0_535 ).
fof(c_0_1703,plain,
! [X1,X2] :
( ord(X2)
=> ! [X38,X39] :
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X38),X39))
<=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
& ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X39),X38)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1704,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
=> hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40) = ti(fun(X1,X2),X38) ),
c_0_537 ).
fof(c_0_1705,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X37,X45,X21,X22,X97] :
( ti(X1,X97) != zero_zero(X1)
=> ( ( ti(X1,X21) = ti(X1,X22)
& ti(X1,X37) != ti(X1,X45) )
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X97),X37)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X97),X45)) ) ) ),
c_0_538 ).
fof(c_0_1706,axiom,
! [X2,X1,X7,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> hAPP(X2,X1,X38,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))),X38),X7)) = ti(X1,X7) ),
c_0_539 ).
fof(c_0_1707,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
c_0_540 ).
fof(c_0_1708,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X34,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
c_0_541 ).
fof(c_0_1709,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X34,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
c_0_542 ).
fof(c_0_1710,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X34,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
c_0_543 ).
fof(c_0_1711,axiom,
! [X2,X1,X43,X40] :
( ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) )
=> 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),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43)) )
& ( ~ ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) )
=> 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),X40),X43)) = zero_zero(nat) ) ),
c_0_544 ).
fof(c_0_1712,axiom,
! [X2,X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
=> 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),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43)) ) ),
c_0_545 ).
fof(c_0_1713,axiom,
! [X2,X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
<=> 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40) ) ),
c_0_546 ).
fof(c_0_1714,axiom,
! [X2,X1,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ) ),
c_0_547 ).
fof(c_0_1715,axiom,
! [X36,X34,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
c_0_548 ).
fof(c_0_1716,axiom,
! [X35,X34,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X36))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
c_0_549 ).
fof(c_0_1717,axiom,
! [X35,X34,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X36))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
c_0_550 ).
fof(c_0_1718,axiom,
! [X36,X34,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
c_0_551 ).
fof(c_0_1719,axiom,
! [X49,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),X49),X59))) ),
c_0_552 ).
fof(c_0_1720,axiom,
! [X49,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),X49))) ),
c_0_553 ).
fof(c_0_1721,axiom,
! [X49,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),X49),X59))) ),
c_0_554 ).
fof(c_0_1722,axiom,
! [X49,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),X49))) ),
c_0_555 ).
fof(c_0_1723,axiom,
! [X58,X50] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X50))
=> ~ ! [X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
=> X50 != hAPP(nat,nat,suc,X64) ) ),
c_0_556 ).
fof(c_0_1724,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
c_0_557 ).
fof(c_0_1725,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
c_0_558 ).
fof(c_0_1726,axiom,
! [X30,X54] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
c_0_559 ).
fof(c_0_1727,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
c_0_560 ).
fof(c_0_1728,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
c_0_561 ).
fof(c_0_1729,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X52)),
c_0_562 ).
fof(c_0_1730,axiom,
! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X52)),
c_0_563 ).
fof(c_0_1731,axiom,
! [X1,X112,X25] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X25),X112))) ) ),
c_0_564 ).
fof(c_0_1732,axiom,
! [X1,X2,X15,X38,X6] :
( ti(X1,X15) = hAPP(X2,X1,X38,X6)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))))) ),
c_0_565 ).
fof(c_0_1733,axiom,
! [X1,X2,X40,X43,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)
<=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
c_0_566 ).
fof(c_0_1734,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),hAPP(nat,nat,suc,X51))) ),
c_0_567 ).
fof(c_0_1735,axiom,
! [X1,X54,X11,X57] :
( hBOOL(hAPP(X1,bool,X11,X57))
=> ? [X26] :
( hBOOL(hAPP(X1,bool,X11,X26))
& ! [X46] :
( hBOOL(hAPP(X1,bool,X11,X46))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X54,X26)),hAPP(X1,nat,X54,X46))) ) ) ),
c_0_568 ).
fof(c_0_1736,axiom,
! [X2,X1,X38,X40] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(X2,X1),X38),X40)),X40) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40),
c_0_569 ).
fof(c_0_1737,axiom,
! [X1,X53,X11] :
( ! [X26] :
( hBOOL(hAPP(X1,bool,X11,X26))
=> hBOOL(hAPP(X1,bool,X53,X26)) )
=> 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),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) ),
c_0_570 ).
fof(c_0_1738,axiom,
! [X1,X43,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),
c_0_571 ).
fof(c_0_1739,axiom,
! [X1,X40,X43] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),
c_0_572 ).
fof(c_0_1740,axiom,
! [X1,X43,X40,X6] :
( hBOOL(hAPP(X1,bool,X40,X6))
=> ( hBOOL(hAPP(X1,bool,X43,X6))
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6)) ) ),
c_0_573 ).
fof(c_0_1741,axiom,
! [X2,X1,X39,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ( ! [X26] : hAPP(X1,X2,X39,hAPP(X2,X1,X38,X26)) = ti(X2,X26)
=> 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))),X38) = ti(fun(X1,X2),X39) ) ),
c_0_574 ).
fof(c_0_1742,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
c_0_575 ).
fof(c_0_1743,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
c_0_576 ).
fof(c_0_1744,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
c_0_577 ).
fof(c_0_1745,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
c_0_578 ).
fof(c_0_1746,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
c_0_579 ).
fof(c_0_1747,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
c_0_580 ).
fof(c_0_1748,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X36)) ) ) ),
c_0_581 ).
fof(c_0_1749,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X34)) ) ) ),
c_0_582 ).
fof(c_0_1750,axiom,
! [X1] :
( preorder(X1)
=> ! [X36,X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X36))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
c_0_583 ).
fof(c_0_1751,axiom,
! [X1] :
( order(X1)
=> ! [X36,X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
c_0_584 ).
fof(c_0_1752,axiom,
! [X1,X2,X6,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),top_top(fun(X1,bool))),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ),
c_0_585 ).
fof(c_0_1753,axiom,
! [X1,X2,X6,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> 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),top_top(fun(X1,bool))),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ),
c_0_586 ).
fof(c_0_1754,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
c_0_587 ).
fof(c_0_1755,axiom,
! [X1,X2,X6,X7,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
=> 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),top_top(fun(X1,bool))),X38),X7) = ti(X1,X6) ) ),
c_0_588 ).
fof(c_0_1756,axiom,
! [X50,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),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X50)) ) ),
c_0_589 ).
fof(c_0_1757,axiom,
arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
c_0_590 ).
fof(c_0_1758,axiom,
! [X49,X51,X50,X61] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X50),X61))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X61) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X50),X51)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ) ),
c_0_591 ).
fof(c_0_1759,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49,X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X49),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1))),X49) ),
c_0_592 ).
fof(c_0_1760,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X37)) ),
c_0_593 ).
fof(c_0_1761,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) ),
c_0_594 ).
fof(c_0_1762,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) ),
c_0_595 ).
fof(c_0_1763,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) ),
c_0_596 ).
fof(c_0_1764,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) ),
c_0_597 ).
fof(c_0_1765,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X37)) ),
c_0_598 ).
fof(c_0_1766,axiom,
! [X1] :
( ab_semigroup_mult(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
c_0_599 ).
fof(c_0_1767,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X95,X93] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X93) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),X93)) ),
c_0_600 ).
fof(c_0_1768,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),X94) ),
c_0_601 ).
fof(c_0_1769,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)) ),
c_0_602 ).
fof(c_0_1770,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),X45) ),
c_0_603 ).
fof(c_0_1771,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)) ),
c_0_604 ).
fof(c_0_1772,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
<=> X30 = X54 ) ),
c_0_605 ).
fof(c_0_1773,plain,
! [X54,X30] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54))) ),
inference(fof_simplification,[status(thm)],[c_0_606]) ).
fof(c_0_1774,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X7,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X7))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X6),X7) = zero_zero(X1)
<=> ( ti(X1,X6) = zero_zero(X1)
& ti(X1,X7) = zero_zero(X1) ) ) ) ) ),
c_0_607 ).
fof(c_0_1775,axiom,
! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X50)),
c_0_608 ).
fof(c_0_1776,axiom,
! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X50)),
c_0_609 ).
fof(c_0_1777,axiom,
! [X1] :
( ord(X1)
=> ! [X29,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X29),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X57)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X57),X29)) ) ),
c_0_610 ).
fof(c_0_1778,axiom,
! [X1] :
( ord(X1)
=> ! [X29,X57] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X29),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X57)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X57),X29)) ) ),
c_0_611 ).
fof(c_0_1779,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> ( hAPP(nat,nat,suc,X49) != X51
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),X51)) ) ),
c_0_612 ).
fof(c_0_1780,axiom,
! [X1,X112,X25] :
( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112)) )
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X25),X112))) ),
c_0_613 ).
fof(c_0_1781,axiom,
! [X1,X2,X38,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
=> 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40) ),
c_0_614 ).
fof(c_0_1782,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51)) ),
c_0_615 ).
fof(c_0_1783,axiom,
! [X1,X40,X43,X6] :
( hBOOL(hAPP(X1,bool,X43,X6))
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
c_0_616 ).
fof(c_0_1784,axiom,
! [X1,X43,X40,X6] :
( hBOOL(hAPP(X1,bool,X40,X6))
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
c_0_617 ).
fof(c_0_1785,plain,
! [X1,X40,X43,X6] :
( ( ~ hBOOL(hAPP(X1,bool,X43,X6))
=> hBOOL(hAPP(X1,bool,X40,X6)) )
=> hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_618]) ).
fof(c_0_1786,axiom,
! [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),
c_0_619 ).
fof(c_0_1787,axiom,
! [X2,X1,X76,X25] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
=> 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),X76),X25))) ),
c_0_620 ).
fof(c_0_1788,axiom,
! [X2,X1,X38,X40] :
( ! [X26,X46] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X46),X40))
=> ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X46)
=> ti(X1,X26) = ti(X1,X46) ) ) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
c_0_621 ).
fof(c_0_1789,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X30)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
| X54 = hAPP(nat,nat,suc,X30) ) ),
c_0_622 ).
fof(c_0_1790,plain,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> X49 = hAPP(nat,nat,suc,X51) ) ),
inference(fof_simplification,[status(thm)],[c_0_623]) ).
fof(c_0_1791,axiom,
! [X51,X73] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X73))
=> ? [X33] : X73 = hAPP(nat,nat,suc,X33) ),
c_0_624 ).
fof(c_0_1792,axiom,
! [X11,X29,X63] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),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,X29)) ) ) ),
c_0_625 ).
fof(c_0_1793,plain,
! [X1] :
( preorder(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_626]) ).
fof(c_0_1794,axiom,
! [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,
c_0_627 ).
fof(c_0_1795,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
<=> ( X54 = zero_zero(nat)
| ? [X64] :
( X54 = hAPP(nat,nat,suc,X64)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X30)) ) ) ),
c_0_628 ).
fof(c_0_1796,axiom,
! [X1,X43,X40] :
( ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
c_0_629 ).
fof(c_0_1797,axiom,
! [X1,X3,X2,X87,X14,X15,X17,X81] :
( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),X17),X81)
=> ! [X108] : hAPP(X3,X2,X14,hAPP(X1,X3,X15,X108)) = hAPP(X87,X2,X17,hAPP(X1,X87,X81,X108)) ),
c_0_630 ).
fof(c_0_1798,axiom,
! [X1,X3,X2,X87,X107,X14,X15,X17,X81] :
( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),X17),X81)
=> hAPP(X3,X2,X14,hAPP(X1,X3,X15,X107)) = hAPP(X87,X2,X17,hAPP(X1,X87,X81,X107)) ),
c_0_631 ).
fof(c_0_1799,axiom,
! [X1,X38] :
( 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),X38),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),X38),top_top(fun(X1,bool))) = top_top(fun(X1,bool)) ) ),
c_0_632 ).
fof(c_0_1800,axiom,
! [X1,X38,X25] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
=> ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X25) = zero_zero(nat)
<=> ! [X26] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X25))
=> hAPP(X1,nat,X38,X26) = zero_zero(nat) ) ) ),
c_0_633 ).
fof(c_0_1801,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
| X54 = X30 ) ),
c_0_634 ).
fof(c_0_1802,plain,
! [X30,X54] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
<=> X30 = X54 ) ),
inference(fof_simplification,[status(thm)],[c_0_635]) ).
fof(c_0_1803,plain,
! [X51,X49] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X49)))
=> X49 = X51 ) ),
inference(fof_simplification,[status(thm)],[c_0_636]) ).
fof(c_0_1804,plain,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> X49 = X51 ) ),
inference(fof_simplification,[status(thm)],[c_0_637]) ).
fof(c_0_1805,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
c_0_638 ).
fof(c_0_1806,plain,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X51)),
inference(fof_simplification,[status(thm)],[c_0_639]) ).
fof(c_0_1807,axiom,
! [X57,X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)
<=> X54 = X30 ),
c_0_640 ).
fof(c_0_1808,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
| ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
c_0_641 ).
fof(c_0_1809,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
& ti(fun(X1,bool),X40) != ti(fun(X1,bool),X43) ) ),
c_0_642 ).
fof(c_0_1810,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
c_0_643 ).
fof(c_0_1811,axiom,
! [X1,X2,X3,X17,X38,X26] : hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X17)),X38),X26) = ti(X2,X17),
c_0_644 ).
fof(c_0_1812,axiom,
! [X60] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
<=> ? [X33] :
! [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),X33)) ) ),
c_0_645 ).
fof(c_0_1813,axiom,
! [X60] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
<=> ? [X33] :
! [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),X33)) ) ),
c_0_646 ).
fof(c_0_1814,axiom,
! [X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X63)),
c_0_647 ).
fof(c_0_1815,axiom,
! [X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X63)),
c_0_648 ).
fof(c_0_1816,plain,
! [X30,X11] :
( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X11,X30))
=> ? [X62] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X30))
& ! [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_649]) ).
fof(c_0_1817,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_650]) ).
fof(c_0_1818,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( ti(X1,X6) = ti(X1,X7)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
c_0_651 ).
fof(c_0_1819,axiom,
! [X1] :
( order(X1)
=> ! [X7,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
c_0_652 ).
fof(c_0_1820,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ti(X1,X34) = ti(X1,X35) ) ) ),
c_0_653 ).
fof(c_0_1821,axiom,
! [X1] :
( order(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ti(X1,X34) = ti(X1,X35) ) ) ),
c_0_654 ).
fof(c_0_1822,axiom,
! [X1,X38] :
( 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),X38),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),X38),top_top(fun(X1,bool)))) ) ),
c_0_655 ).
fof(c_0_1823,axiom,
! [X1] :
( preorder(X1)
=> ! [X11,X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
=> hBOOL(X11) ) ) ),
c_0_656 ).
fof(c_0_1824,plain,
! [X1] :
( linorder(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
inference(fof_simplification,[status(thm)],[c_0_657]) ).
fof(c_0_1825,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ),
inference(fof_simplification,[status(thm)],[c_0_658]) ).
fof(c_0_1826,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
inference(fof_simplification,[status(thm)],[c_0_659]) ).
fof(c_0_1827,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
| ti(X1,X6) = ti(X1,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_660]) ).
fof(c_0_1828,plain,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[c_0_661]) ).
fof(c_0_1829,plain,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[c_0_662]) ).
fof(c_0_1830,plain,
! [X1] :
( preorder(X1)
=> ! [X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ),
inference(fof_simplification,[status(thm)],[c_0_663]) ).
fof(c_0_1831,plain,
! [X1] :
( order(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
inference(fof_simplification,[status(thm)],[c_0_664]) ).
fof(c_0_1832,plain,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[c_0_665]) ).
fof(c_0_1833,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51))) ),
c_0_666 ).
fof(c_0_1834,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51))) ),
c_0_667 ).
fof(c_0_1835,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51))) ),
c_0_668 ).
fof(c_0_1836,axiom,
! [X1,X2] :
( lattice(X2)
=> ! [X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X38),X39),X26) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)) ),
c_0_669 ).
fof(c_0_1837,axiom,
! [X2,X1] :
( lattice(X1)
=> ! [X38,X39,X6] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_inf_inf(fun(X2,X1)),X38),X39),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X2,X1,X38,X6)),hAPP(X2,X1,X39,X6)) ),
c_0_670 ).
fof(c_0_1838,axiom,
! [X1,X2] :
( lattice(X2)
=> ! [X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X38),X39),X26) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)) ),
c_0_671 ).
fof(c_0_1839,axiom,
! [X2,X1] :
( lattice(X1)
=> ! [X38,X39,X6] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_sup_sup(fun(X2,X1)),X38),X39),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X2,X1,X38,X6)),hAPP(X2,X1,X39,X6)) ),
c_0_672 ).
fof(c_0_1840,axiom,
! [X54,X30,X57] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
<=> X54 = X30 ) ),
c_0_673 ).
fof(c_0_1841,axiom,
! [X1] :
( 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)))) ),
c_0_674 ).
fof(c_0_1842,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X49))
=> X49 = X51 ) ),
c_0_675 ).
fof(c_0_1843,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X49),X49) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X49) ),
c_0_676 ).
fof(c_0_1844,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21))) ),
c_0_677 ).
fof(c_0_1845,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1)))) ),
c_0_678 ).
fof(c_0_1846,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X22,X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X37)) ),
c_0_679 ).
fof(c_0_1847,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
c_0_680 ).
fof(c_0_1848,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
c_0_681 ).
fof(c_0_1849,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
c_0_682 ).
fof(c_0_1850,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
c_0_683 ).
fof(c_0_1851,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X22,X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X37)) ),
c_0_684 ).
fof(c_0_1852,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X92,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X94)) ),
c_0_685 ).
fof(c_0_1853,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X45)) ),
c_0_686 ).
fof(c_0_1854,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X35,X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
c_0_687 ).
fof(c_0_1855,axiom,
! [X1] :
( lattice(X1)
=> ! [X35,X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
c_0_688 ).
fof(c_0_1856,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
c_0_689 ).
fof(c_0_1857,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
c_0_690 ).
fof(c_0_1858,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X36,X35] :
( ! [X26] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X36)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36)) ) ),
c_0_691 ).
fof(c_0_1859,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ? [X84,X44] :
( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),X84),X40) = 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)),X44))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),X84),X40)) ) ),
c_0_692 ).
fof(c_0_1860,axiom,
! [X1,X40] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X40)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
c_0_693 ).
fof(c_0_1861,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ) ),
c_0_694 ).
fof(c_0_1862,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ) ),
c_0_695 ).
fof(c_0_1863,axiom,
! [X2,X1,X39,X38] :
( ! [X26] : hAPP(X2,X1,X39,hAPP(X1,X2,X38,X26)) = ti(X1,X26)
=> hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),top_top(fun(X2,bool))) = top_top(fun(X1,bool)) ),
c_0_696 ).
fof(c_0_1864,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),
c_0_697 ).
fof(c_0_1865,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),
c_0_698 ).
fof(c_0_1866,axiom,
! [X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X49))),
c_0_699 ).
fof(c_0_1867,axiom,
! [X51,X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X49))),
c_0_700 ).
fof(c_0_1868,axiom,
! [X51,X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51))),
c_0_701 ).
fof(c_0_1869,axiom,
! [X34,X35,X36] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X36)),
c_0_702 ).
fof(c_0_1870,plain,
! [X30,X11] :
( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X11,X30))
=> ? [X62] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X30))
& ! [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_703]) ).
fof(c_0_1871,axiom,
! [X1,X53,X11,X6] :
( hBOOL(hAPP(X1,bool,X11,X6))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53))
=> hBOOL(hAPP(X1,bool,X53,X6)) ) ),
c_0_704 ).
fof(c_0_1872,axiom,
! [X1,X6,X11,X53] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53))
=> ( hBOOL(hAPP(X1,bool,X11,X6))
=> hBOOL(hAPP(X1,bool,X53,X6)) ) ),
c_0_705 ).
fof(c_0_1873,plain,
! [X1,X40] :
( ~ 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),X40))
=> ? [X19] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40)) ) ),
inference(fof_simplification,[status(thm)],[c_0_706]) ).
fof(c_0_1874,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X40) ),
c_0_707 ).
fof(c_0_1875,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
c_0_708 ).
fof(c_0_1876,axiom,
! [X1,X43,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X40) ),
c_0_709 ).
fof(c_0_1877,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
c_0_710 ).
fof(c_0_1878,axiom,
! [X1,X40,X43] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
<=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
c_0_711 ).
fof(c_0_1879,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
<=> ? [X62] : X30 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62)) ),
c_0_712 ).
fof(c_0_1880,axiom,
! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3)),combs(X1,X2,X3),X118),X119),X120) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X118,X120),hAPP(X1,X2,X119,X120)),
c_0_713 ).
fof(c_0_1881,axiom,
! [X58,X50] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X50))
=> ( X50 != hAPP(nat,nat,suc,X58)
=> ~ ! [X64] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
=> X50 != hAPP(nat,nat,suc,X64) ) ) ),
c_0_714 ).
fof(c_0_1882,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> ? [X62] : X51 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X62)) ),
c_0_715 ).
fof(c_0_1883,axiom,
! [X1] :
( ring_char_0(X1)
=> ! [X14] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
=> ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14) = zero_zero(X1)
<=> ti(X1,X14) = zero_zero(X1) ) ) ),
c_0_716 ).
fof(c_0_1884,axiom,
! [X1] :
( order(X1)
=> ! [X37,X21,X22] :
( ti(X1,X21) = ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X21)) ) ) ),
c_0_717 ).
fof(c_0_1885,axiom,
! [X1] :
( order(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( ti(X1,X22) = ti(X1,X37)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X21)) ) ) ),
c_0_718 ).
fof(c_0_1886,plain,
! [X1] :
( linorder(X1)
=> ! [X7,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_1887,axiom,
! [X1] :
( order(X1)
=> ! [X37,X21,X22] :
( ti(X1,X21) = ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X21)) ) ) ),
c_0_720 ).
fof(c_0_1888,axiom,
! [X1] :
( order(X1)
=> ! [X37,X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
=> ( ti(X1,X22) = ti(X1,X37)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X21)) ) ) ),
c_0_721 ).
fof(c_0_1889,axiom,
! [X1] :
( order(X1)
=> ! [X22,X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> ( ti(X1,X21) != ti(X1,X22)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ) ),
c_0_722 ).
fof(c_0_1890,axiom,
! [X1] :
( order(X1)
=> ! [X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( ti(X1,X21) != ti(X1,X22)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
c_0_723 ).
fof(c_0_1891,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
| ti(X1,X34) = ti(X1,X35) ) ) ),
c_0_724 ).
fof(c_0_1892,axiom,
! [X1] :
( order(X1)
=> ! [X21,X22] :
( ti(X1,X21) != ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ) ),
c_0_725 ).
fof(c_0_1893,axiom,
! [X1] :
( order(X1)
=> ! [X21,X22] :
( ti(X1,X21) != ti(X1,X22)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
c_0_726 ).
fof(c_0_1894,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> ti(X1,X6) = ti(X1,X7) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_727]) ).
fof(c_0_1895,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
| ti(X1,X6) = ti(X1,X7) ) ) ),
c_0_728 ).
fof(c_0_1896,axiom,
! [X1] :
( order(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
& ti(X1,X6) != ti(X1,X7) ) ) ),
c_0_729 ).
fof(c_0_1897,axiom,
! [X1,X2,X6,X7,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
=> ti(X1,X6) = ti(X1,X7) ) ),
c_0_730 ).
fof(c_0_1898,axiom,
! [X1,X2,X6,X7,X38] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
=> ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
<=> ti(X1,X6) = ti(X1,X7) ) ),
c_0_731 ).
fof(c_0_1899,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( X21 = X22
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37)) ) ) ),
c_0_732 ).
fof(c_0_1900,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
=> ( X22 = X37
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37)) ) ) ),
c_0_733 ).
fof(c_0_1901,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( X21 = X22
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X37)) ) ) ),
c_0_734 ).
fof(c_0_1902,axiom,
! [X1] :
( ord(X1)
=> ! [X37,X21,X22] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
=> ( X22 = X37
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X37)) ) ) ),
c_0_735 ).
fof(c_0_1903,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
c_0_736 ).
fof(c_0_1904,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),
c_0_737 ).
fof(c_0_1905,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_atLeastAtMost(nat),X77),X66))),
c_0_738 ).
fof(c_0_1906,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_gr676655987ssThan(nat),X77),X66))),
c_0_739 ).
fof(c_0_1907,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_gr1471790799AtMost(nat),X77),X66))),
c_0_740 ).
fof(c_0_1908,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_741 ).
fof(c_0_1909,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_742 ).
fof(c_0_1910,axiom,
! [X2,X3,X1,X28,X14,X15] : hAPP(product_prod(X2,X3),X1,hAPP(fun(X2,fun(X3,X1)),fun(product_prod(X2,X3),X1),product_prod_rec(X2,X3,X1),X28),hAPP(X3,product_prod(X2,X3),hAPP(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X14),X15)) = hAPP(X3,X1,hAPP(X2,fun(X3,X1),X28,X14),X15),
c_0_743 ).
fof(c_0_1911,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
=> ( X49 != X51
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ) ),
c_0_744 ).
fof(c_0_1912,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
| X54 = X30 ) ),
c_0_745 ).
fof(c_0_1913,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
& X54 != X30 ) ),
c_0_746 ).
fof(c_0_1914,axiom,
! [X34,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35)) ),
c_0_747 ).
fof(c_0_1915,axiom,
! [X49,X51] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
| X49 = X51 )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
c_0_748 ).
fof(c_0_1916,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
c_0_749 ).
fof(c_0_1917,axiom,
! [X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,zero_zero(nat))))
<=> X30 = zero_zero(nat) ),
c_0_750 ).
fof(c_0_1918,axiom,
! [X1] :
( 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))))) ),
c_0_751 ).
fof(c_0_1919,axiom,
? [X65] : hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X65),arrow_1568854078le_Lin)),
c_0_752 ).
fof(c_0_1920,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
c_0_753 ).
fof(c_0_1921,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
c_0_754 ).
fof(c_0_1922,axiom,
! [X30,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,X30)) ) ),
c_0_755 ).
fof(c_0_1923,axiom,
! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(X2,fun(X1,X3),hAPP(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)),combc(X1,X2,X3),X118),X119),X120) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X118,X120),X119),
c_0_756 ).
fof(c_0_1924,axiom,
! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X118),X119),X120) = hAPP(X2,X3,X118,hAPP(X1,X2,X119,X120)),
c_0_757 ).
fof(c_0_1925,axiom,
! [X3,X1,X2,X38,X39,X6] : hAPP(X3,X1,hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),comp(X2,X1,X3),X38),X39),X6) = hAPP(X2,X1,X38,hAPP(X3,X2,X39,X6)),
c_0_758 ).
fof(c_0_1926,axiom,
! [X1,X2,X3,X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X38),X39),X26) = hAPP(X3,X2,X38,hAPP(X1,X3,X39,X26)),
c_0_759 ).
fof(c_0_1927,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,suc,X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),
c_0_760 ).
fof(c_0_1928,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),
c_0_761 ).
fof(c_0_1929,axiom,
! [X1,X6,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
<=> hBOOL(hAPP(X1,bool,X40,X6)) ),
c_0_762 ).
fof(c_0_1930,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X6),X7) = ti(X1,X6) ) ),
c_0_763 ).
fof(c_0_1931,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = ti(X1,X34) ) ),
c_0_764 ).
fof(c_0_1932,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = ti(X1,X35) ) ),
c_0_765 ).
fof(c_0_1933,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X35,X34] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = ti(X1,X34) ) ),
c_0_766 ).
fof(c_0_1934,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = ti(X1,X35) ) ),
c_0_767 ).
fof(c_0_1935,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
<=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X6),X7) = ti(X1,X7) ) ),
c_0_768 ).
fof(c_0_1936,axiom,
! [X54,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
<=> ? [X62] : X30 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62) ),
c_0_769 ).
fof(c_0_1937,plain,
! [X1] :
( linordered_idom(X1)
=> ! [X34,X35] :
( ti(X1,X34) != ti(X1,X35)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_770]) ).
fof(c_0_1938,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ti(X1,X6) != ti(X1,X7)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ) ),
c_0_771 ).
fof(c_0_1939,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
| ti(X1,X34) = ti(X1,X35)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
c_0_772 ).
fof(c_0_1940,plain,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ti(X1,X34) != ti(X1,X35)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_773]) ).
fof(c_0_1941,plain,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ( ti(X1,X34) != ti(X1,X35)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_774]) ).
fof(c_0_1942,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22) ),
c_0_775 ).
fof(c_0_1943,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) ),
c_0_776 ).
fof(c_0_1944,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) ),
c_0_777 ).
fof(c_0_1945,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) ),
c_0_778 ).
fof(c_0_1946,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) ),
c_0_779 ).
fof(c_0_1947,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22) ),
c_0_780 ).
fof(c_0_1948,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) ),
c_0_781 ).
fof(c_0_1949,axiom,
! [X1,X53,X11] :
( ! [X26] :
( hBOOL(hAPP(X1,bool,X11,X26))
=> hBOOL(hAPP(X1,bool,X53,X26)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53)) ),
c_0_782 ).
fof(c_0_1950,plain,
! [X1] :
( linorder(X1)
=> ! [X35,X34] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
inference(fof_simplification,[status(thm)],[c_0_783]) ).
fof(c_0_1951,plain,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[c_0_784]) ).
fof(c_0_1952,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
c_0_785 ).
fof(c_0_1953,axiom,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
c_0_786 ).
fof(c_0_1954,plain,
! [X1] :
( linorder(X1)
=> ! [X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[c_0_787]) ).
fof(c_0_1955,axiom,
! [X30,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),X30)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60)) ),
c_0_788 ).
fof(c_0_1956,axiom,
! [X2,X1] :
( 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)))) ) ),
c_0_789 ).
fof(c_0_1957,axiom,
! [X1,X2] :
( 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))))
& hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ) ),
c_0_790 ).
fof(c_0_1958,plain,
! [X34,X35] :
( X34 != X35
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[c_0_791]) ).
fof(c_0_1959,axiom,
! [X54,X30] :
( X54 != X30
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54)) ) ),
c_0_792 ).
fof(c_0_1960,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X49)) ),
c_0_793 ).
fof(c_0_1961,axiom,
! [X1,X3,X2,X107,X14,X15,X17] :
( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = ti(fun(X1,X2),X17)
=> hAPP(X3,X2,X14,hAPP(X1,X3,X15,X107)) = hAPP(X1,X2,X17,X107) ),
c_0_794 ).
fof(c_0_1962,axiom,
! [X1,X40] :
( ! [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> top_top(fun(X1,bool)) = ti(fun(X1,bool),X40) ),
c_0_795 ).
fof(c_0_1963,axiom,
! [X2,X1,X14,X15,X12,X13] :
( hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X14),X15) = hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X12),X13)
<=> ( ti(X1,X14) = ti(X1,X12)
& ti(X2,X15) = ti(X2,X13) ) ),
c_0_796 ).
fof(c_0_1964,axiom,
! [X2,X1,X21,X22,X23,X24] :
( hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X21),X22) = hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X23),X24)
=> ~ ( ti(X1,X21) = ti(X1,X23)
=> ti(X2,X22) != ti(X2,X24) ) ),
c_0_797 ).
fof(c_0_1965,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> ( ( ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
=> one_one(nat) = zero_zero(nat) )
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
c_0_798 ).
fof(c_0_1966,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,suc,X51)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),
c_0_799 ).
fof(c_0_1967,axiom,
! [X1,X28,X86,X67] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X28),X86),hAPP(nat,nat,suc,X67)) = hAPP(nat,X1,X86,X67),
c_0_800 ).
fof(c_0_1968,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,suc,X51)),
c_0_801 ).
fof(c_0_1969,axiom,
! [X104] : hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X104)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X104)),hAPP(nat,nat,suc,zero_zero(nat))),
c_0_802 ).
fof(c_0_1970,axiom,
! [X104] : hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X104)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X104)),hAPP(nat,nat,suc,zero_zero(nat))),
c_0_803 ).
fof(c_0_1971,axiom,
! [X1,X2] :
( 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)))) ) ),
c_0_804 ).
fof(c_0_1972,axiom,
! [X1,X2,X38] :
( ! [X26,X46] :
( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X46)
=> ti(X1,X26) = ti(X1,X46) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool)))) ),
c_0_805 ).
fof(c_0_1973,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
c_0_806 ).
fof(c_0_1974,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_807 ).
fof(c_0_1975,axiom,
! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X77)),X66) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X77),X66),
c_0_808 ).
fof(c_0_1976,axiom,
! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X77)),X66) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X77),X66),
c_0_809 ).
fof(c_0_1977,axiom,
! [X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51))
=> ? [X33] : X51 = hAPP(nat,nat,suc,X33) ),
c_0_810 ).
fof(c_0_1978,axiom,
! [X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30))
<=> ? [X33] : X30 = hAPP(nat,nat,suc,X33) ),
c_0_811 ).
fof(c_0_1979,axiom,
! [X2,X1,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
<=> ! [X46] :
? [X26] : ti(X1,X46) = hAPP(X2,X1,X38,X26) ),
c_0_812 ).
fof(c_0_1980,axiom,
! [X2,X1,X7,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ? [X26] : ti(X1,X7) = hAPP(X2,X1,X38,X26) ),
c_0_813 ).
fof(c_0_1981,axiom,
! [X2,X1,X7,X38] :
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
=> ~ ! [X26] : ti(X1,X7) != hAPP(X2,X1,X38,X26) ),
c_0_814 ).
fof(c_0_1982,axiom,
~ ! [X78] :
( hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),X78),top_top(fun(arrow_1998540521e_indi,bool))))
=> hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),X78),top_top(fun(arrow_1998540521e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) ),
c_0_815 ).
fof(c_0_1983,axiom,
hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_816 ).
fof(c_0_1984,axiom,
! [X1,X2,X40] : 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),X40),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_817 ).
fof(c_0_1985,plain,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_818]) ).
fof(c_0_1986,plain,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_819]) ).
fof(c_0_1987,axiom,
! [X1] :
( top(X1)
=> ! [X21] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X21))
=> ti(X1,X21) = top_top(X1) ) ),
c_0_820 ).
fof(c_0_1988,axiom,
! [X1] :
( top(X1)
=> ! [X14] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X14))
<=> ti(X1,X14) = top_top(X1) ) ),
c_0_821 ).
fof(c_0_1989,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X14,X15,X17] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X15) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)
<=> ti(X1,X15) = ti(X1,X17) ) ),
c_0_822 ).
fof(c_0_1990,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X15,X14,X17] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X14) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)
<=> ti(X1,X15) = ti(X1,X17) ) ),
c_0_823 ).
fof(c_0_1991,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X21,X22,X37] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)
=> ti(X1,X22) = ti(X1,X37) ) ),
c_0_824 ).
fof(c_0_1992,axiom,
! [X1] :
( cancel146912293up_add(X1)
=> ! [X21,X22,X37] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)
=> ti(X1,X22) = ti(X1,X37) ) ),
c_0_825 ).
fof(c_0_1993,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X22,X21,X37] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X21) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)
=> ti(X1,X22) = ti(X1,X37) ) ),
c_0_826 ).
fof(c_0_1994,axiom,
! [X1] :
( top(X1)
=> ! [X14] :
( ti(X1,X14) != top_top(X1)
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),top_top(X1))) ) ),
c_0_827 ).
fof(c_0_1995,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ti(X1,X34) != ti(X1,X35) ) ),
c_0_828 ).
fof(c_0_1996,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ti(X1,X34) != ti(X1,X35) ) ),
c_0_829 ).
fof(c_0_1997,axiom,
! [X1] :
( order(X1)
=> ! [X34,X35] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
=> ti(X1,X35) != ti(X1,X34) ) ),
c_0_830 ).
fof(c_0_1998,plain,
! [X1] :
( top(X1)
=> ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X21)) ),
inference(fof_simplification,[status(thm)],[c_0_831]) ).
fof(c_0_1999,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X51))),
c_0_832 ).
fof(c_0_2000,plain,
! [X1,X34,X35] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35))
| ti(X1,X34) = ti(X1,X35) ),
inference(fof_simplification,[status(thm)],[c_0_833]) ).
fof(c_0_2001,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X51))),
c_0_834 ).
fof(c_0_2002,plain,
! [X1] :
( preorder(X1)
=> ! [X34] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_835]) ).
fof(c_0_2003,axiom,
! [X30] :
( X30 != zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30)) ),
c_0_836 ).
fof(c_0_2004,axiom,
! [X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),zero_zero(nat)))
<=> X30 = zero_zero(nat) ),
c_0_837 ).
fof(c_0_2005,plain,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[c_0_838]) ).
fof(c_0_2006,plain,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[c_0_839]) ).
fof(c_0_2007,plain,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[c_0_840]) ).
fof(c_0_2008,axiom,
! [X49,X51] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
=> X51 != zero_zero(nat) ),
c_0_841 ).
fof(c_0_2009,axiom,
! [X55,X56] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
=> X55 != X56 ),
c_0_842 ).
fof(c_0_2010,axiom,
! [X51,X49] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
=> X49 != X51 ),
c_0_843 ).
fof(c_0_2011,axiom,
! [X57,X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
<=> ( X57 = zero_zero(nat)
| X54 = X30 ) ),
c_0_844 ).
fof(c_0_2012,axiom,
! [X57,X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
<=> ( X54 = X30
| X57 = zero_zero(nat) ) ),
c_0_845 ).
fof(c_0_2013,axiom,
! [X54,X57,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)
<=> ( X54 = X30
| X57 = zero_zero(nat) ) ),
c_0_846 ).
fof(c_0_2014,plain,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
inference(fof_simplification,[status(thm)],[c_0_847]) ).
fof(c_0_2015,plain,
! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
inference(fof_simplification,[status(thm)],[c_0_848]) ).
fof(c_0_2016,axiom,
! [X54,X57,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57)
<=> X54 = X30 ),
c_0_849 ).
fof(c_0_2017,axiom,
! [X57,X54,X30] :
( 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),X30)
<=> X54 = X30 ),
c_0_850 ).
fof(c_0_2018,axiom,
! [X1,X40] : hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X40),
c_0_851 ).
fof(c_0_2019,plain,
! [X118,X119] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119))
| hBOOL(X118)
| hBOOL(X119) ),
inference(fof_simplification,[status(thm)],[c_0_852]) ).
fof(c_0_2020,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = ti(X1,X34) ),
c_0_853 ).
fof(c_0_2021,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = ti(X1,X34) ),
c_0_854 ).
fof(c_0_2022,plain,
! [X118,X119] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
| hBOOL(X119) ),
inference(fof_simplification,[status(thm)],[c_0_855]) ).
fof(c_0_2023,plain,
! [X118,X119] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
| hBOOL(X118) ),
inference(fof_simplification,[status(thm)],[c_0_856]) ).
fof(c_0_2024,axiom,
! [X1,X2,X38,X39] :
( ! [X26] : hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26)
=> ti(fun(X1,X2),X38) = ti(fun(X1,X2),X39) ),
c_0_857 ).
fof(c_0_2025,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X40),
c_0_858 ).
fof(c_0_2026,axiom,
! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X40),
c_0_859 ).
fof(c_0_2027,axiom,
! [X1,X2] :
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool))))
=> hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
c_0_860 ).
fof(c_0_2028,axiom,
! [X1,X28,X86] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X28),X86),zero_zero(nat)) = ti(X1,X28),
c_0_861 ).
fof(c_0_2029,axiom,
! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X77),hAPP(nat,nat,suc,X66)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X77),X66),
c_0_862 ).
fof(c_0_2030,axiom,
! [X2,X1] :
( comm_monoid_add(X1)
=> ! [X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),combk(X1,X2),zero_zero(X1))),X40) = zero_zero(X1) ),
c_0_863 ).
fof(c_0_2031,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
c_0_864 ).
fof(c_0_2032,axiom,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ),
c_0_865 ).
fof(c_0_2033,plain,
! [X1,X40,X43] :
( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
=> ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
inference(fof_simplification,[status(thm)],[c_0_866]) ).
fof(c_0_2034,axiom,
! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),top_top(fun(X1,bool)))),
c_0_867 ).
fof(c_0_2035,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
c_0_868 ).
fof(c_0_2036,axiom,
! [X1,X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X34),X35) = ti(X1,X35),
c_0_869 ).
fof(c_0_2037,axiom,
! [X1,X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X34),X35) = ti(X1,X34),
c_0_870 ).
fof(c_0_2038,axiom,
! [X54,X30] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30)
<=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
& X30 = zero_zero(nat) )
| ( X54 = zero_zero(nat)
& X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
c_0_871 ).
fof(c_0_2039,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
& X30 = zero_zero(nat) )
| ( X54 = zero_zero(nat)
& X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
c_0_872 ).
fof(c_0_2040,axiom,
! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X40)),
c_0_873 ).
fof(c_0_2041,axiom,
! [X1,X40] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
=> ( hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
=> ti(fun(X1,bool),X40) = top_top(fun(X1,bool)) ) ),
c_0_874 ).
fof(c_0_2042,axiom,
! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X40)),
c_0_875 ).
fof(c_0_2043,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_876 ).
fof(c_0_2044,axiom,
! [X1] :
? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),top_top(fun(X1,bool)))),
c_0_877 ).
fof(c_0_2045,axiom,
! [X1,X2] : 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_878 ).
fof(c_0_2046,axiom,
! [X1,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),top_top(fun(X1,bool)))),
c_0_879 ).
fof(c_0_2047,axiom,
! [X1,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),top_top(fun(X1,bool)))),
c_0_880 ).
fof(c_0_2048,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_881 ).
fof(c_0_2049,axiom,
! [X1] :
( 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))) ),
c_0_882 ).
fof(c_0_2050,axiom,
! [X1] :
( 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))) ),
c_0_883 ).
fof(c_0_2051,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
& X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
c_0_884 ).
fof(c_0_2052,axiom,
! [X1] :
( 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_885 ).
fof(c_0_2053,axiom,
! [X1,X34,X35] :
( ti(X1,X34) != ti(X1,X35)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35)) ),
c_0_886 ).
fof(c_0_2054,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
c_0_887 ).
fof(c_0_2055,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
c_0_888 ).
fof(c_0_2056,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X21) ),
c_0_889 ).
fof(c_0_2057,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34) ),
c_0_890 ).
fof(c_0_2058,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34) ),
c_0_891 ).
fof(c_0_2059,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34) ),
c_0_892 ).
fof(c_0_2060,axiom,
! [X1] :
( lattice(X1)
=> ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34) ),
c_0_893 ).
fof(c_0_2061,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X21) ),
c_0_894 ).
fof(c_0_2062,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21) ),
c_0_895 ).
fof(c_0_2063,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21) ),
c_0_896 ).
fof(c_0_2064,axiom,
! [X1] :
( top(X1)
=> ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),top_top(X1))) ),
c_0_897 ).
fof(c_0_2065,axiom,
! [X2,X1] : 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),top_top(fun(X1,bool))),top_top(fun(X2,bool))) = top_top(fun(sum_sum(X1,X2),bool)),
c_0_898 ).
fof(c_0_2066,axiom,
! [X1] :
( preorder(X1)
=> ! [X34,X35] :
( X34 = X35
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
c_0_899 ).
fof(c_0_2067,axiom,
! [X1] :
( preorder(X1)
=> ! [X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X34)) ),
c_0_900 ).
fof(c_0_2068,axiom,
! [X51] :
( X51 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51)) ),
c_0_901 ).
fof(c_0_2069,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X51)),
c_0_902 ).
fof(c_0_2070,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X51)),
c_0_903 ).
fof(c_0_2071,plain,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X39,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_904]) ).
fof(c_0_2072,plain,
! [X1,X2] :
( comm_monoid_add(X2)
=> ! [X38,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),X40) = zero_zero(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_905]) ).
fof(c_0_2073,axiom,
! [X49,X51] :
( X49 = X51
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
c_0_906 ).
fof(c_0_2074,axiom,
! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X51)),
c_0_907 ).
fof(c_0_2075,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X49),
c_0_908 ).
fof(c_0_2076,axiom,
! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X49),
c_0_909 ).
fof(c_0_2077,plain,
! [X119,X118] :
( ~ hBOOL(X118)
| ~ hBOOL(X119)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119)) ),
inference(fof_simplification,[status(thm)],[c_0_910]) ).
fof(c_0_2078,plain,
! [X118,X119] :
( ~ hBOOL(X119)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
inference(fof_simplification,[status(thm)],[c_0_911]) ).
fof(c_0_2079,plain,
! [X119,X118] :
( ~ hBOOL(X118)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
inference(fof_simplification,[status(thm)],[c_0_912]) ).
fof(c_0_2080,axiom,
hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
c_0_913 ).
fof(c_0_2081,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
c_0_914 ).
fof(c_0_2082,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
c_0_915 ).
fof(c_0_2083,axiom,
! [X1] :
( ring_n68954251visors(X1)
=> ! [X14,X15] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15) = zero_zero(X1)
<=> ( ti(X1,X14) = zero_zero(X1)
| ti(X1,X15) = zero_zero(X1) ) ) ),
c_0_916 ).
fof(c_0_2084,axiom,
! [X1] :
( no_zero_divisors(X1)
=> ! [X22,X21] :
( ti(X1,X21) != zero_zero(X1)
=> ( ti(X1,X22) != zero_zero(X1)
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) != zero_zero(X1) ) ) ),
c_0_917 ).
fof(c_0_2085,axiom,
! [X1] :
( no_zero_divisors(X1)
=> ! [X21,X22] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) = zero_zero(X1)
=> ( ti(X1,X21) = zero_zero(X1)
| ti(X1,X22) = zero_zero(X1) ) ) ),
c_0_918 ).
fof(c_0_2086,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X15,X14] :
( ti(X1,X15) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X14)
<=> ti(X1,X14) = zero_zero(X1) ) ),
c_0_919 ).
fof(c_0_2087,axiom,
! [X1,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X43) = ti(fun(X1,bool),X43),
c_0_920 ).
fof(c_0_2088,axiom,
! [X1,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X43) = top_top(fun(X1,bool)),
c_0_921 ).
fof(c_0_2089,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X6),X7) = top_top(X1)
<=> ( ti(X1,X6) = top_top(X1)
& ti(X1,X7) = top_top(X1) ) ) ),
c_0_922 ).
fof(c_0_2090,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14) = zero_zero(X1)
<=> ti(X1,X14) = zero_zero(X1) ) ),
c_0_923 ).
fof(c_0_2091,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X14] :
( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)
<=> ti(X1,X14) = zero_zero(X1) ) ),
c_0_924 ).
fof(c_0_2092,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),top_top(fun(X1,bool))) = ti(fun(X1,bool),X40),
c_0_925 ).
fof(c_0_2093,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
c_0_926 ).
fof(c_0_2094,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = zero_zero(nat)
<=> ( X54 = zero_zero(nat)
| X30 = zero_zero(nat) ) ),
c_0_927 ).
fof(c_0_2095,axiom,
! [X49,X51] :
( X49 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)
=> ( X51 = one_one(nat)
| X49 = zero_zero(nat) ) ),
c_0_928 ).
fof(c_0_2096,axiom,
! [X54,X30] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)
<=> ( X54 = one_one(nat)
& X30 = one_one(nat) ) ),
c_0_929 ).
fof(c_0_2097,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = one_one(nat)
<=> ( X54 = one_one(nat)
& X30 = one_one(nat) ) ),
c_0_930 ).
fof(c_0_2098,axiom,
! [X54,X30] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30) = zero_zero(nat)
<=> ( X54 = zero_zero(nat)
& X30 = zero_zero(nat) ) ),
c_0_931 ).
fof(c_0_2099,axiom,
! [X49,X51] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51) = X49
=> X51 = zero_zero(nat) ),
c_0_932 ).
fof(c_0_2100,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X40) = ti(fun(X1,bool),X40),
c_0_933 ).
fof(c_0_2101,axiom,
! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X40) = ti(fun(X1,bool),X40),
c_0_934 ).
fof(c_0_2102,axiom,
! [X1,X80] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X80) = ti(fun(X1,bool),X80),
c_0_935 ).
fof(c_0_2103,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
c_0_936 ).
fof(c_0_2104,axiom,
! [X51] : hAPP(nat,nat,suc,X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X51),
c_0_937 ).
fof(c_0_2105,axiom,
! [X51] : hAPP(nat,nat,suc,X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),one_one(nat)),
c_0_938 ).
fof(c_0_2106,axiom,
! [X57] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X57)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X57),
c_0_939 ).
fof(c_0_2107,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_940 ).
fof(c_0_2108,plain,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
inference(fof_simplification,[status(thm)],[c_0_941]) ).
fof(c_0_2109,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
c_0_942 ).
fof(c_0_2110,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
c_0_943 ).
fof(c_0_2111,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
c_0_944 ).
fof(c_0_2112,axiom,
! [X1,X3,X2] : ti(fun(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)))),compose(X1,X3,X2)) = compose(X1,X3,X2),
c_0_945 ).
fof(c_0_2113,axiom,
! [X1] : top_top(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)),
c_0_946 ).
fof(c_0_2114,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X6) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X7)
<=> ti(X1,X6) = ti(X1,X7) ) ),
c_0_947 ).
fof(c_0_2115,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X6) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X7)
<=> ti(X1,X6) = ti(X1,X7) ) ),
c_0_948 ).
fof(c_0_2116,axiom,
! [X2,X1,X118,X119] : hAPP(X2,X1,hAPP(X1,fun(X2,X1),combk(X1,X2),X118),X119) = ti(X1,X118),
c_0_949 ).
fof(c_0_2117,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X34) = ti(X1,X34) ),
c_0_950 ).
fof(c_0_2118,axiom,
! [X1] :
( comm_monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
c_0_951 ).
fof(c_0_2119,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
c_0_952 ).
fof(c_0_2120,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
c_0_953 ).
fof(c_0_2121,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
c_0_954 ).
fof(c_0_2122,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
c_0_955 ).
fof(c_0_2123,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
c_0_956 ).
fof(c_0_2124,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),top_top(X1)) = ti(X1,X34) ),
c_0_957 ).
fof(c_0_2125,axiom,
! [X1] :
( comm_monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
c_0_958 ).
fof(c_0_2126,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
c_0_959 ).
fof(c_0_2127,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
c_0_960 ).
fof(c_0_2128,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
c_0_961 ).
fof(c_0_2129,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
c_0_962 ).
fof(c_0_2130,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
c_0_963 ).
fof(c_0_2131,plain,
! [X1,X40] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
=> hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ),
inference(fof_simplification,[status(thm)],[c_0_964]) ).
fof(c_0_2132,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X34) = top_top(X1) ),
c_0_965 ).
fof(c_0_2133,axiom,
! [X1] :
( mult_zero(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X21) = zero_zero(X1) ),
c_0_966 ).
fof(c_0_2134,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X21) = zero_zero(X1) ),
c_0_967 ).
fof(c_0_2135,axiom,
! [X1] :
( lattice(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X34) = ti(X1,X34) ),
c_0_968 ).
fof(c_0_2136,axiom,
! [X1] :
( lattice(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X34) = ti(X1,X34) ),
c_0_969 ).
fof(c_0_2137,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X21) = ti(X1,X21) ),
c_0_970 ).
fof(c_0_2138,axiom,
! [X1] :
( semilattice_inf(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X34) = ti(X1,X34) ),
c_0_971 ).
fof(c_0_2139,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X34) = ti(X1,X34) ),
c_0_972 ).
fof(c_0_2140,axiom,
! [X1] :
( semilattice_sup(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X21) = ti(X1,X21) ),
c_0_973 ).
fof(c_0_2141,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X34) = ti(X1,X34) ),
c_0_974 ).
fof(c_0_2142,axiom,
! [X1] :
( ab_sem1668676832m_mult(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21) = ti(X1,X21) ),
c_0_975 ).
fof(c_0_2143,axiom,
! [X1] :
( bounded_lattice_top(X1)
=> ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),top_top(X1)) = top_top(X1) ),
c_0_976 ).
fof(c_0_2144,axiom,
! [X1] :
( mult_zero(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),zero_zero(X1)) = zero_zero(X1) ),
c_0_977 ).
fof(c_0_2145,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),zero_zero(X1)) = zero_zero(X1) ),
c_0_978 ).
fof(c_0_2146,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
c_0_979 ).
fof(c_0_2147,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
c_0_980 ).
fof(c_0_2148,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X51) = zero_zero(nat),
c_0_981 ).
fof(c_0_2149,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X51) = X51,
c_0_982 ).
fof(c_0_2150,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X51) = X51,
c_0_983 ).
fof(c_0_2151,axiom,
! [X49] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),zero_zero(nat)) = zero_zero(nat),
c_0_984 ).
fof(c_0_2152,axiom,
! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),one_one(nat)) = X51,
c_0_985 ).
fof(c_0_2153,axiom,
! [X49] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),zero_zero(nat)) = X49,
c_0_986 ).
fof(c_0_2154,axiom,
! [X1,X2] : ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
c_0_987 ).
fof(c_0_2155,plain,
! [X118] :
( ~ hBOOL(hAPP(bool,bool,fNot,X118))
| ~ hBOOL(X118) ),
inference(fof_simplification,[status(thm)],[c_0_988]) ).
fof(c_0_2156,axiom,
! [X67,X68] :
( hAPP(nat,nat,suc,X67) = hAPP(nat,nat,suc,X68)
<=> X67 = X68 ),
c_0_989 ).
fof(c_0_2157,axiom,
! [X34,X35] :
( hAPP(nat,nat,suc,X34) = hAPP(nat,nat,suc,X35)
=> X34 = X35 ),
c_0_990 ).
fof(c_0_2158,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
c_0_991 ).
fof(c_0_2159,axiom,
! [X3,X1,X4,X5] : ti(X3,hAPP(X1,X3,X4,X5)) = hAPP(X1,X3,X4,X5),
c_0_992 ).
fof(c_0_2160,axiom,
! [X1] : ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
c_0_993 ).
fof(c_0_2161,axiom,
! [X1] :
( finite_finite(X1)
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
c_0_994 ).
fof(c_0_2162,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_995 ).
fof(c_0_2163,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
c_0_996 ).
fof(c_0_2164,axiom,
! [X1,X6] : hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X6)),
c_0_997 ).
fof(c_0_2165,axiom,
! [X1,X3,X4,X5] : hAPP(X1,X3,ti(fun(X1,X3),X4),X5) = hAPP(X1,X3,X4,X5),
c_0_998 ).
fof(c_0_2166,axiom,
! [X1,X2] : 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_999 ).
fof(c_0_2167,axiom,
! [X1] :
( finite_finite(X1)
=> ! [X40] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
c_0_1000 ).
fof(c_0_2168,axiom,
! [X1] :
( finite_finite(X1)
=> ! [X40] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
c_0_1001 ).
fof(c_0_2169,axiom,
! [X1,X3,X4,X5] : hAPP(X1,X3,X4,ti(X1,X5)) = hAPP(X1,X3,X4,X5),
c_0_1002 ).
fof(c_0_2170,axiom,
! [X2,X3,X1] : ti(fun(fun(X2,fun(X3,X1)),fun(product_prod(X2,X3),X1)),product_prod_rec(X2,X3,X1)) = product_prod_rec(X2,X3,X1),
c_0_1003 ).
fof(c_0_2171,axiom,
! [X1,X3,X2] : ti(fun(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3))),comp(X1,X3,X2)) = comp(X1,X3,X2),
c_0_1004 ).
fof(c_0_2172,axiom,
! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
c_0_1005 ).
fof(c_0_2173,axiom,
! [X2,X3,X1] : ti(fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),combb(X2,X3,X1)) = combb(X2,X3,X1),
c_0_1006 ).
fof(c_0_2174,axiom,
! [X118] :
( hBOOL(X118)
| hBOOL(hAPP(bool,bool,fNot,X118)) ),
c_0_1007 ).
fof(c_0_2175,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
c_0_1008 ).
fof(c_0_2176,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
c_0_1009 ).
fof(c_0_2177,axiom,
! [X49] : zero_zero(nat) != hAPP(nat,nat,suc,X49),
c_0_1010 ).
fof(c_0_2178,axiom,
! [X70] : zero_zero(nat) != hAPP(nat,nat,suc,X70),
c_0_1011 ).
fof(c_0_2179,axiom,
! [X49] : hAPP(nat,nat,suc,X49) != zero_zero(nat),
c_0_1012 ).
fof(c_0_2180,axiom,
! [X69] : hAPP(nat,nat,suc,X69) != zero_zero(nat),
c_0_1013 ).
fof(c_0_2181,axiom,
! [X49] : zero_zero(nat) != hAPP(nat,nat,suc,X49),
c_0_1014 ).
fof(c_0_2182,axiom,
! [X49] : hAPP(nat,nat,suc,X49) != zero_zero(nat),
c_0_1015 ).
fof(c_0_2183,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
c_0_1016 ).
fof(c_0_2184,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
c_0_1017 ).
fof(c_0_2185,axiom,
! [X51] : X51 != hAPP(nat,nat,suc,X51),
c_0_1018 ).
fof(c_0_2186,axiom,
! [X51] : hAPP(nat,nat,suc,X51) != X51,
c_0_1019 ).
fof(c_0_2187,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
c_0_1020 ).
fof(c_0_2188,axiom,
! [X1,X2] : ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
c_0_1021 ).
fof(c_0_2189,axiom,
! [X2,X1] : ti(fun(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool))),image(X2,X1)) = image(X2,X1),
c_0_1022 ).
fof(c_0_2190,axiom,
! [X1,X11] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11) = ti(fun(X1,bool),X11),
c_0_1023 ).
fof(c_0_2191,axiom,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
c_0_1024 ).
fof(c_0_2192,axiom,
hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
c_0_1025 ).
fof(c_0_2193,axiom,
! [X2,X1] :
( top(X1)
=> ! [X6] : hAPP(X2,X1,top_top(fun(X2,X1)),X6) = top_top(X1) ),
c_0_1026 ).
fof(c_0_2194,axiom,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
c_0_1027 ).
fof(c_0_2195,axiom,
! [X1] : ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
c_0_1028 ).
fof(c_0_2196,axiom,
! [X1,X2] :
( comm_monoid_add(X2)
=> ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2) ),
c_0_1029 ).
fof(c_0_2197,axiom,
! [X1] : ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
c_0_1030 ).
fof(c_0_2198,axiom,
! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
c_0_1031 ).
fof(c_0_2199,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
c_0_1032 ).
fof(c_0_2200,axiom,
! [X1,X118] : hAPP(X1,X1,combi(X1),X118) = ti(X1,X118),
c_0_1033 ).
fof(c_0_2201,axiom,
! [X35] :
( X35 != zero_zero(nat)
=> ~ ! [X74] : X35 != hAPP(nat,nat,suc,X74) ),
c_0_1034 ).
fof(c_0_2202,axiom,
! [X51] :
( X51 != zero_zero(nat)
=> ? [X33] : X51 = hAPP(nat,nat,suc,X33) ),
c_0_1035 ).
fof(c_0_2203,axiom,
hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
c_0_1036 ).
fof(c_0_2204,axiom,
! [X51] : hAPP(nat,nat,size_size(nat),X51) = X51,
c_0_1037 ).
fof(c_0_2205,axiom,
hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
c_0_1038 ).
fof(c_0_2206,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
c_0_1039 ).
fof(c_0_2207,axiom,
! [X1] : ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
c_0_1040 ).
fof(c_0_2208,axiom,
hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
c_0_1041 ).
fof(c_0_2209,axiom,
hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
c_0_1042 ).
fof(c_0_2210,axiom,
! [X1,X2] : ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
c_0_1043 ).
fof(c_0_2211,axiom,
! [X1] : ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
c_0_1044 ).
fof(c_0_2212,axiom,
! [X1] :
( linorder(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1) ),
c_0_1045 ).
fof(c_0_2213,axiom,
! [X1] :
( linorder(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1) ),
c_0_1046 ).
fof(c_0_2214,axiom,
! [X1] :
( linorder(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1) ),
c_0_1047 ).
fof(c_0_2215,axiom,
! [X1] :
( order(X1)
=> ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1) ),
c_0_1048 ).
fof(c_0_2216,axiom,
! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
c_0_1049 ).
fof(c_0_2217,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
c_0_1050 ).
fof(c_0_2218,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
c_0_1051 ).
fof(c_0_2219,axiom,
! [X1,X2] : ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
c_0_1052 ).
fof(c_0_2220,axiom,
! [X1] :
( semilattice_sup(X1)
=> ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1) ),
c_0_1053 ).
fof(c_0_2221,axiom,
! [X1] :
( semilattice_inf(X1)
=> ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1) ),
c_0_1054 ).
fof(c_0_2222,axiom,
! [X1] :
( no_zero_divisors(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
c_0_1055 ).
fof(c_0_2223,axiom,
! [X1] :
( mult_zero(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
c_0_1056 ).
fof(c_0_2224,axiom,
! [X1] :
( ab_semigroup_mult(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
c_0_1057 ).
fof(c_0_2225,axiom,
! [X1] :
( monoid_mult(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
c_0_1058 ).
fof(c_0_2226,axiom,
! [X1] :
( semiring(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
c_0_1059 ).
fof(c_0_2227,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
c_0_1060 ).
fof(c_0_2228,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
c_0_1061 ).
fof(c_0_2229,axiom,
! [X1] :
( monoid_add(X1)
=> ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
c_0_1062 ).
fof(c_0_2230,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1) ),
c_0_1063 ).
fof(c_0_2231,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1) ),
c_0_1064 ).
fof(c_0_2232,axiom,
! [X2] :
( ord(X2)
=> ti(fun(X2,fun(X2,bool)),ord_less_eq(X2)) = ord_less_eq(X2) ),
c_0_1065 ).
fof(c_0_2233,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
c_0_1066 ).
fof(c_0_2234,axiom,
! [X1] : ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
c_0_1067 ).
fof(c_0_2235,axiom,
! [X2] : ti(fun(fun(X2,bool),bool),finite_finite_1(X2)) = finite_finite_1(X2),
c_0_1068 ).
fof(c_0_2236,axiom,
! [X1] : ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
c_0_1069 ).
fof(c_0_2237,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
c_0_1070 ).
fof(c_0_2238,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
c_0_1071 ).
fof(c_0_2239,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
c_0_1072 ).
fof(c_0_2240,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
c_0_1073 ).
fof(c_0_2241,axiom,
! [X1] :
( ring_1(X1)
=> ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1) ),
c_0_1074 ).
fof(c_0_2242,axiom,
! [X1] :
( zero(X1)
=> ! [X6] :
( zero_zero(X1) = ti(X1,X6)
<=> ti(X1,X6) = zero_zero(X1) ) ),
c_0_1075 ).
fof(c_0_2243,axiom,
! [X1] :
( one(X1)
=> ! [X6] :
( one_one(X1) = ti(X1,X6)
<=> ti(X1,X6) = one_one(X1) ) ),
c_0_1076 ).
fof(c_0_2244,axiom,
! [X116,X117] : ti(X116,ti(X116,X117)) = ti(X116,X117),
c_0_1077 ).
fof(c_0_2245,axiom,
! [X1] : ti(fun(X1,X1),combi(X1)) = combi(X1),
c_0_1078 ).
fof(c_0_2246,axiom,
! [X114,X115] :
( ( finite_finite(X115)
& finite_finite(X114) )
=> finite_finite(product_prod(X114,X115)) ),
c_0_1079 ).
fof(c_0_2247,axiom,
! [X114,X115] :
( ( finite_finite(X115)
& finite_finite(X114) )
=> finite_finite(sum_sum(X114,X115)) ),
c_0_1080 ).
fof(c_0_2248,axiom,
! [X114,X115] :
( ( finite_finite(X115)
& finite_finite(X114) )
=> finite_finite(fun(X114,X115)) ),
c_0_1081 ).
fof(c_0_2249,axiom,
ti(fun(nat,nat),size_size(nat)) = size_size(nat),
c_0_1082 ).
fof(c_0_2250,axiom,
! [X114,X115] :
( ord(X115)
=> ord(fun(X114,X115)) ),
c_0_1083 ).
fof(c_0_2251,axiom,
! [X114,X115] :
( top(X115)
=> top(fun(X114,X115)) ),
c_0_1084 ).
fof(c_0_2252,axiom,
! [X114,X115] :
( order(X115)
=> order(fun(X114,X115)) ),
c_0_1085 ).
fof(c_0_2253,axiom,
! [X114,X115] :
( lattice(X115)
=> lattice(fun(X114,X115)) ),
c_0_1086 ).
fof(c_0_2254,axiom,
! [X114,X115] :
( preorder(X115)
=> preorder(fun(X114,X115)) ),
c_0_1087 ).
fof(c_0_2255,axiom,
! [X114,X115] :
( distrib_lattice(X115)
=> distrib_lattice(fun(X114,X115)) ),
c_0_1088 ).
fof(c_0_2256,axiom,
! [X114,X115] :
( lattice(X115)
=> semilattice_inf(fun(X114,X115)) ),
c_0_1089 ).
fof(c_0_2257,axiom,
! [X114,X115] :
( lattice(X115)
=> semilattice_sup(fun(X114,X115)) ),
c_0_1090 ).
fof(c_0_2258,axiom,
! [X114,X115] :
( bounded_lattice(X115)
=> bounded_lattice_top(fun(X114,X115)) ),
c_0_1091 ).
fof(c_0_2259,axiom,
! [X114,X115] :
( bounded_lattice(X115)
=> bounded_lattice(fun(X114,X115)) ),
c_0_1092 ).
fof(c_0_2260,axiom,
ti(fun(arrow_1998540521e_indi,nat),h) = h,
c_0_1093 ).
fof(c_0_2261,axiom,
ti(fun(bool,bool),fNot) = fNot,
c_0_1094 ).
fof(c_0_2262,axiom,
ti(fun(nat,nat),nat_size) = nat_size,
c_0_1095 ).
fof(c_0_2263,axiom,
ti(fun(nat,nat),suc) = suc,
c_0_1096 ).
fof(c_0_2264,axiom,
ti(fun(bool,nat),bool_size) = bool_size,
c_0_1097 ).
fof(c_0_2265,axiom,
! [X1] :
( top(X1)
=> ti(X1,top_top(X1)) = top_top(X1) ),
c_0_1098 ).
fof(c_0_2266,axiom,
! [X1] :
( zero(X1)
=> ti(X1,zero_zero(X1)) = zero_zero(X1) ),
c_0_1099 ).
fof(c_0_2267,axiom,
! [X1] :
( one(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
c_0_1100 ).
fof(c_0_2268,axiom,
! [X118] :
( ti(bool,X118) = fTrue
| ti(bool,X118) = fFalse ),
c_0_1101 ).
fof(c_0_2269,axiom,
! [X118] :
( ti(bool,X118) = fTrue
| ti(bool,X118) = fFalse ),
c_0_1102 ).
fof(c_0_2270,axiom,
! [X118] :
( ti(bool,X118) = fTrue
| ti(bool,X118) = fFalse ),
c_0_1103 ).
fof(c_0_2271,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
c_0_1104 ).
fof(c_0_2272,axiom,
! [X1] :
( zero_neq_one(X1)
=> one_one(X1) != zero_zero(X1) ),
c_0_1105 ).
fof(c_0_2273,axiom,
! [X1] :
( zero_neq_one(X1)
=> zero_zero(X1) != one_one(X1) ),
c_0_1106 ).
fof(c_0_2274,axiom,
! [X115] :
( finite_finite(X115)
=> finite_finite(option(X115)) ),
c_0_1107 ).
fof(c_0_2275,axiom,
ti(nat,n) = n,
c_0_1108 ).
fof(c_0_2276,axiom,
ti(arrow_2142409994le_alt,e) = e,
c_0_1109 ).
fof(c_0_2277,axiom,
ti(arrow_2142409994le_alt,b) = b,
c_0_1110 ).
fof(c_0_2278,axiom,
ti(arrow_2142409994le_alt,a) = a,
c_0_1111 ).
fof(c_0_2279,axiom,
ti(bool,fTrue) = fTrue,
c_0_1112 ).
fof(c_0_2280,axiom,
ti(bool,fFalse) = fFalse,
c_0_1113 ).
fof(c_0_2281,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[c_0_1114]) ).
fof(c_0_2282,axiom,
hBOOL(fTrue),
c_0_1115 ).
fof(c_0_2283,axiom,
finite_finite(product_unit),
c_0_1116 ).
fof(c_0_2284,axiom,
ord(bool),
c_0_1117 ).
fof(c_0_2285,axiom,
top(bool),
c_0_1118 ).
fof(c_0_2286,axiom,
order(bool),
c_0_1119 ).
fof(c_0_2287,axiom,
lattice(bool),
c_0_1120 ).
fof(c_0_2288,axiom,
finite_finite(bool),
c_0_1121 ).
fof(c_0_2289,axiom,
preorder(bool),
c_0_1122 ).
fof(c_0_2290,axiom,
distrib_lattice(bool),
c_0_1123 ).
fof(c_0_2291,axiom,
semilattice_inf(bool),
c_0_1124 ).
fof(c_0_2292,axiom,
semilattice_sup(bool),
c_0_1125 ).
fof(c_0_2293,axiom,
bounded_lattice_top(bool),
c_0_1126 ).
fof(c_0_2294,axiom,
one(nat),
c_0_1127 ).
fof(c_0_2295,axiom,
zero(nat),
c_0_1128 ).
fof(c_0_2296,axiom,
ord(nat),
c_0_1129 ).
fof(c_0_2297,axiom,
semiring(nat),
c_0_1130 ).
fof(c_0_2298,axiom,
order(nat),
c_0_1131 ).
fof(c_0_2299,axiom,
mult_zero(nat),
c_0_1132 ).
fof(c_0_2300,axiom,
lattice(nat),
c_0_1133 ).
fof(c_0_2301,axiom,
semiring_0(nat),
c_0_1134 ).
fof(c_0_2302,axiom,
monoid_add(nat),
c_0_1135 ).
fof(c_0_2303,axiom,
monoid_mult(nat),
c_0_1136 ).
fof(c_0_2304,axiom,
linorder(nat),
c_0_1137 ).
fof(c_0_2305,axiom,
preorder(nat),
c_0_1138 ).
fof(c_0_2306,axiom,
zero_neq_one(nat),
c_0_1139 ).
fof(c_0_2307,axiom,
comm_semiring(nat),
c_0_1140 ).
fof(c_0_2308,axiom,
comm_semiring_1(nat),
c_0_1141 ).
fof(c_0_2309,axiom,
comm_monoid_add(nat),
c_0_1142 ).
fof(c_0_2310,axiom,
no_zero_divisors(nat),
c_0_1143 ).
fof(c_0_2311,axiom,
ordered_semiring(nat),
c_0_1144 ).
fof(c_0_2312,axiom,
ab_semigroup_add(nat),
c_0_1145 ).
fof(c_0_2313,axiom,
comm_monoid_mult(nat),
c_0_1146 ).
fof(c_0_2314,axiom,
ab_semigroup_mult(nat),
c_0_1147 ).
fof(c_0_2315,axiom,
distrib_lattice(nat),
c_0_1148 ).
fof(c_0_2316,axiom,
semilattice_inf(nat),
c_0_1149 ).
fof(c_0_2317,axiom,
semilattice_sup(nat),
c_0_1150 ).
fof(c_0_2318,axiom,
linordered_semidom(nat),
c_0_1151 ).
fof(c_0_2319,axiom,
linordered_semiring(nat),
c_0_1152 ).
fof(c_0_2320,axiom,
cancel_semigroup_add(nat),
c_0_1153 ).
fof(c_0_2321,axiom,
ordere1490568538miring(nat),
c_0_1154 ).
fof(c_0_2322,axiom,
ordere453448008miring(nat),
c_0_1155 ).
fof(c_0_2323,axiom,
cancel146912293up_add(nat),
c_0_1156 ).
fof(c_0_2324,axiom,
ordere216010020id_add(nat),
c_0_1157 ).
fof(c_0_2325,axiom,
ordere779506340up_add(nat),
c_0_1158 ).
fof(c_0_2326,axiom,
linord20386208strict(nat),
c_0_1159 ).
fof(c_0_2327,axiom,
linord893533164strict(nat),
c_0_1160 ).
fof(c_0_2328,axiom,
ordere236663937imp_le(nat),
c_0_1161 ).
fof(c_0_2329,axiom,
ordere223160158up_add(nat),
c_0_1162 ).
fof(c_0_2330,axiom,
semiri456707255roduct(nat),
c_0_1163 ).
fof(c_0_2331,axiom,
bounded_lattice(bool),
c_0_1164 ).
fof(c_0_2332,axiom,
a != b,
c_0_1165 ).
fof(c_0_2333,axiom,
c != d,
c_0_1166 ).
fof(c_0_2334,plain,
! [X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114] :
( ( hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114)),X111))
| hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X107),X111) = hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X106),X110)
| hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114)),X110))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X111))
| ~ hBOOL(hAPP(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool,hAPP(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool),hAPP(fun(X105,fun(X105,X105)),fun(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool)),finite_folding_image(X105,X104),X112),X113),X114)) )
& ( ~ hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),hAPP(X104,X104,X108,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))),X110))
| hAPP(X104,X104,X109,hAPP(X104,X104,X108,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))) != ti(X104,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))
| hAPP(X104,X105,X106,hAPP(X104,X104,X108,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))) != hAPP(X104,X105,X107,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))
| hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X107),X111) = hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X106),X110)
| hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114)),X110))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X111))
| ~ hBOOL(hAPP(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool,hAPP(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool),hAPP(fun(X105,fun(X105,X105)),fun(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool)),finite_folding_image(X105,X104),X112),X113),X114)) )
& ( hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114)),X111))
| hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X107),X111) = hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X106),X110)
| ~ hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),hAPP(X104,X104,X109,esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))),X111))
| hAPP(X104,X104,X108,hAPP(X104,X104,X109,esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))) != ti(X104,esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X111))
| ~ hBOOL(hAPP(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool,hAPP(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool),hAPP(fun(X105,fun(X105,X105)),fun(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool)),finite_folding_image(X105,X104),X112),X113),X114)) )
& ( ~ hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),hAPP(X104,X104,X108,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))),X110))
| hAPP(X104,X104,X109,hAPP(X104,X104,X108,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))) != ti(X104,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))
| hAPP(X104,X105,X106,hAPP(X104,X104,X108,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))) != hAPP(X104,X105,X107,esk156_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))
| hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X107),X111) = hAPP(fun(X104,bool),X105,hAPP(fun(X104,X105),fun(fun(X104,bool),X105),X114,X106),X110)
| ~ hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),hAPP(X104,X104,X109,esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))),X111))
| hAPP(X104,X104,X108,hAPP(X104,X104,X109,esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))) != ti(X104,esk155_11(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113,X114))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X111))
| ~ hBOOL(hAPP(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool,hAPP(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool),hAPP(fun(X105,fun(X105,X105)),fun(X105,fun(fun(fun(X104,X105),fun(fun(X104,bool),X105)),bool)),finite_folding_image(X105,X104),X112),X113),X114)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1167])])])]) ).
fof(c_0_2335,plain,
! [X104,X105,X106,X107,X108,X109,X110,X111,X112,X113] :
( ( hBOOL(hAPP(fun(X105,bool),bool,hAPP(X105,fun(fun(X105,bool),bool),member(X105),esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113)),X113))
| hAPP(fun(X105,bool),X106,hAPP(X106,fun(fun(X105,bool),X106),hAPP(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106))),finite_fold_image(X106,X105),times_times(X106)),X109),X107),X113) = hAPP(fun(X104,bool),X106,hAPP(X106,fun(fun(X104,bool),X106),hAPP(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106))),finite_fold_image(X106,X104),times_times(X106)),X108),X107),X112)
| hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113)),X112))
| ~ hBOOL(hAPP(fun(X105,bool),bool,finite_finite_1(X105),X113))
| ~ comm_monoid_mult(X106) )
& ( ~ hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),hAPP(X105,X104,X110,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))),X112))
| hAPP(X104,X105,X111,hAPP(X105,X104,X110,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))) != ti(X105,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))
| hAPP(X104,X106,X108,hAPP(X105,X104,X110,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))) != hAPP(X105,X106,X109,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))
| hAPP(fun(X105,bool),X106,hAPP(X106,fun(fun(X105,bool),X106),hAPP(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106))),finite_fold_image(X106,X105),times_times(X106)),X109),X107),X113) = hAPP(fun(X104,bool),X106,hAPP(X106,fun(fun(X104,bool),X106),hAPP(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106))),finite_fold_image(X106,X104),times_times(X106)),X108),X107),X112)
| hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113)),X112))
| ~ hBOOL(hAPP(fun(X105,bool),bool,finite_finite_1(X105),X113))
| ~ comm_monoid_mult(X106) )
& ( hBOOL(hAPP(fun(X105,bool),bool,hAPP(X105,fun(fun(X105,bool),bool),member(X105),esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113)),X113))
| hAPP(fun(X105,bool),X106,hAPP(X106,fun(fun(X105,bool),X106),hAPP(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106))),finite_fold_image(X106,X105),times_times(X106)),X109),X107),X113) = hAPP(fun(X104,bool),X106,hAPP(X106,fun(fun(X104,bool),X106),hAPP(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106))),finite_fold_image(X106,X104),times_times(X106)),X108),X107),X112)
| ~ hBOOL(hAPP(fun(X105,bool),bool,hAPP(X105,fun(fun(X105,bool),bool),member(X105),hAPP(X104,X105,X111,esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))),X113))
| hAPP(X105,X104,X110,hAPP(X104,X105,X111,esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))) != ti(X104,esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))
| ~ hBOOL(hAPP(fun(X105,bool),bool,finite_finite_1(X105),X113))
| ~ comm_monoid_mult(X106) )
& ( ~ hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),hAPP(X105,X104,X110,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))),X112))
| hAPP(X104,X105,X111,hAPP(X105,X104,X110,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))) != ti(X105,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))
| hAPP(X104,X106,X108,hAPP(X105,X104,X110,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))) != hAPP(X105,X106,X109,esk144_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))
| hAPP(fun(X105,bool),X106,hAPP(X106,fun(fun(X105,bool),X106),hAPP(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X105,X106),fun(X106,fun(fun(X105,bool),X106))),finite_fold_image(X106,X105),times_times(X106)),X109),X107),X113) = hAPP(fun(X104,bool),X106,hAPP(X106,fun(fun(X104,bool),X106),hAPP(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106)),hAPP(fun(X106,fun(X106,X106)),fun(fun(X104,X106),fun(X106,fun(fun(X104,bool),X106))),finite_fold_image(X106,X104),times_times(X106)),X108),X107),X112)
| ~ hBOOL(hAPP(fun(X105,bool),bool,hAPP(X105,fun(fun(X105,bool),bool),member(X105),hAPP(X104,X105,X111,esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))),X113))
| hAPP(X105,X104,X110,hAPP(X104,X105,X111,esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))) != ti(X104,esk143_10(X104,X105,X106,X107,X108,X109,X110,X111,X112,X113))
| ~ hBOOL(hAPP(fun(X105,bool),bool,finite_finite_1(X105),X113))
| ~ comm_monoid_mult(X106) ) ),
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_1168])])])])]) ).
fof(c_0_2336,plain,
! [X103,X104,X105,X106,X107,X108,X109,X110,X111] :
( ( hBOOL(hAPP(fun(X103,bool),bool,hAPP(X103,fun(fun(X103,bool),bool),member(X103),esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X105),X107)),hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X106),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk157_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk159_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X110),X110))
| ~ hBOOL(hAPP(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool,hAPP(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool),hAPP(fun(X104,fun(X104,X104)),fun(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool)),finite_folding_image(X104,X103),X109),X110),X111)) )
& ( ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X103,X104,X105,esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))),hAPP(X103,X104,X106,esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X105),X107)),hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X106),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk157_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk159_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X110),X110))
| ~ hBOOL(hAPP(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool,hAPP(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool),hAPP(fun(X104,fun(X104,X104)),fun(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool)),finite_folding_image(X104,X103),X109),X110),X111)) )
& ( hBOOL(hAPP(fun(X103,bool),bool,hAPP(X103,fun(fun(X103,bool),bool),member(X103),esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X105),X107)),hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X106),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk158_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk160_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X110),X110))
| ~ hBOOL(hAPP(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool,hAPP(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool),hAPP(fun(X104,fun(X104,X104)),fun(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool)),finite_folding_image(X104,X103),X109),X110),X111)) )
& ( ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X103,X104,X105,esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))),hAPP(X103,X104,X106,esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X105),X107)),hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X106),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk158_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk160_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X110),X110))
| ~ hBOOL(hAPP(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool,hAPP(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool),hAPP(fun(X104,fun(X104,X104)),fun(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool)),finite_folding_image(X104,X103),X109),X110),X111)) )
& ( hBOOL(hAPP(fun(X103,bool),bool,hAPP(X103,fun(fun(X103,bool),bool),member(X103),esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X105),X107)),hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X106),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X104,X104,hAPP(X104,fun(X104,X104),X109,esk157_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk158_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))),hAPP(X104,X104,hAPP(X104,fun(X104,X104),X109,esk159_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk160_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X110),X110))
| ~ hBOOL(hAPP(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool,hAPP(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool),hAPP(fun(X104,fun(X104,X104)),fun(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool)),finite_folding_image(X104,X103),X109),X110),X111)) )
& ( ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X103,X104,X105,esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))),hAPP(X103,X104,X106,esk161_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X105),X107)),hAPP(fun(X103,bool),X104,hAPP(fun(X103,X104),fun(fun(X103,bool),X104),X111,X106),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X104,X104,hAPP(X104,fun(X104,X104),X109,esk157_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk158_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))),hAPP(X104,X104,hAPP(X104,fun(X104,X104),X109,esk159_9(X103,X104,X105,X106,X107,X108,X109,X110,X111)),esk160_9(X103,X104,X105,X106,X107,X108,X109,X110,X111))))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X110),X110))
| ~ hBOOL(hAPP(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool,hAPP(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool),hAPP(fun(X104,fun(X104,X104)),fun(X104,fun(fun(fun(X103,X104),fun(fun(X103,bool),X104)),bool)),finite_folding_image(X104,X103),X109),X110),X111)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1169])])])]) ).
fof(c_0_2337,plain,
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ) ),
inference(fof_nnf,[status(thm)],[c_0_1170]) ).
fof(c_0_2338,plain,
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_214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i,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ) ),
inference(fof_nnf,[status(thm)],[c_0_1171]) ).
fof(c_0_2339,plain,
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_214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)
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ) ),
inference(fof_nnf,[status(thm)],[c_0_1172]) ).
fof(c_0_2340,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_1173 ).
fof(c_0_2341,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_1174 ).
fof(c_0_2342,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_1175 ).
fof(c_0_2343,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
c_0_1176 ).
fof(c_0_2344,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(X44,fun(X43,bool),hAPP(fun(X44,fun(X43,bool)),fun(X44,fun(X43,bool)),hAPP(fun(X44,fun(X43,bool)),fun(fun(X44,fun(X43,bool)),fun(X44,fun(X43,bool))),semilattice_inf_inf(fun(X44,fun(X43,bool))),hAPP(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool)),hAPP(fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool))),combc(X44,fun(product_prod(X44,X43),bool),fun(X43,bool)),hAPP(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),hAPP(fun(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool)))),combb(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool)),X44),combc(X43,fun(product_prod(X44,X43),bool),bool)),hAPP(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),hAPP(fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool)))),combb(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),X44),hAPP(fun(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),combb(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),X43),member(product_prod(X44,X43)))),product_Pair(X44,X43)))),X45)),hAPP(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool)),hAPP(fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool))),combc(X44,fun(product_prod(X44,X43),bool),fun(X43,bool)),hAPP(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),hAPP(fun(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool)))),combb(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool)),X44),combc(X43,fun(product_prod(X44,X43),bool),bool)),hAPP(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),hAPP(fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool)))),combb(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),X44),hAPP(fun(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),combb(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),X43),member(product_prod(X44,X43)))),product_Pair(X44,X43)))),X46)),X47),X48))
| hBOOL(hAPP(fun(product_prod(X44,X43),bool),bool,hAPP(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),member(product_prod(X44,X43)),hAPP(X43,product_prod(X44,X43),hAPP(X44,fun(X43,product_prod(X44,X43)),product_Pair(X44,X43),X47),X48)),hAPP(fun(product_prod(X44,X43),bool),fun(product_prod(X44,X43),bool),hAPP(fun(product_prod(X44,X43),bool),fun(fun(product_prod(X44,X43),bool),fun(product_prod(X44,X43),bool)),semilattice_inf_inf(fun(product_prod(X44,X43),bool)),X45),X46))) )
& ( ~ hBOOL(hAPP(fun(product_prod(X50,X49),bool),bool,hAPP(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool),member(product_prod(X50,X49)),hAPP(X49,product_prod(X50,X49),hAPP(X50,fun(X49,product_prod(X50,X49)),product_Pair(X50,X49),X53),X54)),hAPP(fun(product_prod(X50,X49),bool),fun(product_prod(X50,X49),bool),hAPP(fun(product_prod(X50,X49),bool),fun(fun(product_prod(X50,X49),bool),fun(product_prod(X50,X49),bool)),semilattice_inf_inf(fun(product_prod(X50,X49),bool)),X51),X52)))
| hBOOL(hAPP(X49,bool,hAPP(X50,fun(X49,bool),hAPP(fun(X50,fun(X49,bool)),fun(X50,fun(X49,bool)),hAPP(fun(X50,fun(X49,bool)),fun(fun(X50,fun(X49,bool)),fun(X50,fun(X49,bool))),semilattice_inf_inf(fun(X50,fun(X49,bool))),hAPP(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool)),hAPP(fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool))),combc(X50,fun(product_prod(X50,X49),bool),fun(X49,bool)),hAPP(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),hAPP(fun(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool)))),combb(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool)),X50),combc(X49,fun(product_prod(X50,X49),bool),bool)),hAPP(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),hAPP(fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool)))),combb(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),X50),hAPP(fun(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),combb(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool),X49),member(product_prod(X50,X49)))),product_Pair(X50,X49)))),X51)),hAPP(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool)),hAPP(fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool))),combc(X50,fun(product_prod(X50,X49),bool),fun(X49,bool)),hAPP(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),hAPP(fun(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool)))),combb(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool)),X50),combc(X49,fun(product_prod(X50,X49),bool),bool)),hAPP(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),hAPP(fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool)))),combb(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),X50),hAPP(fun(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),combb(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool),X49),member(product_prod(X50,X49)))),product_Pair(X50,X49)))),X52)),X53),X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1177])])])]) ).
fof(c_0_2345,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(X44,fun(X43,bool),hAPP(fun(X44,fun(X43,bool)),fun(X44,fun(X43,bool)),hAPP(fun(X44,fun(X43,bool)),fun(fun(X44,fun(X43,bool)),fun(X44,fun(X43,bool))),semilattice_sup_sup(fun(X44,fun(X43,bool))),hAPP(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool)),hAPP(fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool))),combc(X44,fun(product_prod(X44,X43),bool),fun(X43,bool)),hAPP(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),hAPP(fun(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool)))),combb(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool)),X44),combc(X43,fun(product_prod(X44,X43),bool),bool)),hAPP(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),hAPP(fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool)))),combb(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),X44),hAPP(fun(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),combb(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),X43),member(product_prod(X44,X43)))),product_Pair(X44,X43)))),X45)),hAPP(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool)),hAPP(fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool))),combc(X44,fun(product_prod(X44,X43),bool),fun(X43,bool)),hAPP(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),hAPP(fun(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool))),fun(fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(X44,fun(fun(product_prod(X44,X43),bool),fun(X43,bool)))),combb(fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(product_prod(X44,X43),bool),fun(X43,bool)),X44),combc(X43,fun(product_prod(X44,X43),bool),bool)),hAPP(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),hAPP(fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),fun(fun(X44,fun(X43,product_prod(X44,X43))),fun(X44,fun(X43,fun(fun(product_prod(X44,X43),bool),bool)))),combb(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool)),X44),hAPP(fun(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool)),fun(fun(X43,product_prod(X44,X43)),fun(X43,fun(fun(product_prod(X44,X43),bool),bool))),combb(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),X43),member(product_prod(X44,X43)))),product_Pair(X44,X43)))),X46)),X47),X48))
| hBOOL(hAPP(fun(product_prod(X44,X43),bool),bool,hAPP(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),member(product_prod(X44,X43)),hAPP(X43,product_prod(X44,X43),hAPP(X44,fun(X43,product_prod(X44,X43)),product_Pair(X44,X43),X47),X48)),hAPP(fun(product_prod(X44,X43),bool),fun(product_prod(X44,X43),bool),hAPP(fun(product_prod(X44,X43),bool),fun(fun(product_prod(X44,X43),bool),fun(product_prod(X44,X43),bool)),semilattice_sup_sup(fun(product_prod(X44,X43),bool)),X45),X46))) )
& ( ~ hBOOL(hAPP(fun(product_prod(X50,X49),bool),bool,hAPP(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool),member(product_prod(X50,X49)),hAPP(X49,product_prod(X50,X49),hAPP(X50,fun(X49,product_prod(X50,X49)),product_Pair(X50,X49),X53),X54)),hAPP(fun(product_prod(X50,X49),bool),fun(product_prod(X50,X49),bool),hAPP(fun(product_prod(X50,X49),bool),fun(fun(product_prod(X50,X49),bool),fun(product_prod(X50,X49),bool)),semilattice_sup_sup(fun(product_prod(X50,X49),bool)),X51),X52)))
| hBOOL(hAPP(X49,bool,hAPP(X50,fun(X49,bool),hAPP(fun(X50,fun(X49,bool)),fun(X50,fun(X49,bool)),hAPP(fun(X50,fun(X49,bool)),fun(fun(X50,fun(X49,bool)),fun(X50,fun(X49,bool))),semilattice_sup_sup(fun(X50,fun(X49,bool))),hAPP(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool)),hAPP(fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool))),combc(X50,fun(product_prod(X50,X49),bool),fun(X49,bool)),hAPP(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),hAPP(fun(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool)))),combb(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool)),X50),combc(X49,fun(product_prod(X50,X49),bool),bool)),hAPP(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),hAPP(fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool)))),combb(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),X50),hAPP(fun(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),combb(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool),X49),member(product_prod(X50,X49)))),product_Pair(X50,X49)))),X51)),hAPP(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool)),hAPP(fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(product_prod(X50,X49),bool),fun(X50,fun(X49,bool))),combc(X50,fun(product_prod(X50,X49),bool),fun(X49,bool)),hAPP(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),hAPP(fun(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool))),fun(fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(X50,fun(fun(product_prod(X50,X49),bool),fun(X49,bool)))),combb(fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(product_prod(X50,X49),bool),fun(X49,bool)),X50),combc(X49,fun(product_prod(X50,X49),bool),bool)),hAPP(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),hAPP(fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),fun(fun(X50,fun(X49,product_prod(X50,X49))),fun(X50,fun(X49,fun(fun(product_prod(X50,X49),bool),bool)))),combb(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool)),X50),hAPP(fun(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool)),fun(fun(X49,product_prod(X50,X49)),fun(X49,fun(fun(product_prod(X50,X49),bool),bool))),combb(product_prod(X50,X49),fun(fun(product_prod(X50,X49),bool),bool),X49),member(product_prod(X50,X49)))),product_Pair(X50,X49)))),X52)),X53),X54)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1178])])])]) ).
fof(c_0_2346,plain,
! [X103,X104,X105,X106,X107,X108,X109] :
( ( hBOOL(hAPP(fun(X103,bool),bool,hAPP(X103,fun(fun(X103,bool),bool),member(X103),esk142_7(X103,X104,X105,X106,X107,X108,X109)),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X105),X109),X107)),hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X106),X109),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk138_7(X103,X104,X105,X106,X107,X108,X109)),esk140_7(X103,X104,X105,X106,X107,X108,X109)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X109),X109))
| ~ comm_monoid_mult(X104) )
& ( ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X103,X104,X105,esk142_7(X103,X104,X105,X106,X107,X108,X109))),hAPP(X103,X104,X106,esk142_7(X103,X104,X105,X106,X107,X108,X109))))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X105),X109),X107)),hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X106),X109),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk138_7(X103,X104,X105,X106,X107,X108,X109)),esk140_7(X103,X104,X105,X106,X107,X108,X109)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X109),X109))
| ~ comm_monoid_mult(X104) )
& ( hBOOL(hAPP(fun(X103,bool),bool,hAPP(X103,fun(fun(X103,bool),bool),member(X103),esk142_7(X103,X104,X105,X106,X107,X108,X109)),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X105),X109),X107)),hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X106),X109),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk139_7(X103,X104,X105,X106,X107,X108,X109)),esk141_7(X103,X104,X105,X106,X107,X108,X109)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X109),X109))
| ~ comm_monoid_mult(X104) )
& ( ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X103,X104,X105,esk142_7(X103,X104,X105,X106,X107,X108,X109))),hAPP(X103,X104,X106,esk142_7(X103,X104,X105,X106,X107,X108,X109))))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X105),X109),X107)),hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X106),X109),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,esk139_7(X103,X104,X105,X106,X107,X108,X109)),esk141_7(X103,X104,X105,X106,X107,X108,X109)))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X109),X109))
| ~ comm_monoid_mult(X104) )
& ( hBOOL(hAPP(fun(X103,bool),bool,hAPP(X103,fun(fun(X103,bool),bool),member(X103),esk142_7(X103,X104,X105,X106,X107,X108,X109)),X107))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X105),X109),X107)),hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X106),X109),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X104,X104,hAPP(X104,fun(X104,X104),times_times(X104),esk138_7(X103,X104,X105,X106,X107,X108,X109)),esk139_7(X103,X104,X105,X106,X107,X108,X109))),hAPP(X104,X104,hAPP(X104,fun(X104,X104),times_times(X104),esk140_7(X103,X104,X105,X106,X107,X108,X109)),esk141_7(X103,X104,X105,X106,X107,X108,X109))))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X109),X109))
| ~ comm_monoid_mult(X104) )
& ( ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X103,X104,X105,esk142_7(X103,X104,X105,X106,X107,X108,X109))),hAPP(X103,X104,X106,esk142_7(X103,X104,X105,X106,X107,X108,X109))))
| hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X105),X109),X107)),hAPP(fun(X103,bool),X104,hAPP(X104,fun(fun(X103,bool),X104),hAPP(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104)),hAPP(fun(X104,fun(X104,X104)),fun(fun(X103,X104),fun(X104,fun(fun(X103,bool),X104))),finite_fold_image(X104,X103),times_times(X104)),X106),X109),X107)))
| ~ hBOOL(hAPP(fun(X103,bool),bool,finite_finite_1(X103),X107))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,hAPP(X104,X104,hAPP(X104,fun(X104,X104),times_times(X104),esk138_7(X103,X104,X105,X106,X107,X108,X109)),esk139_7(X103,X104,X105,X106,X107,X108,X109))),hAPP(X104,X104,hAPP(X104,fun(X104,X104),times_times(X104),esk140_7(X103,X104,X105,X106,X107,X108,X109)),esk141_7(X103,X104,X105,X106,X107,X108,X109))))
| ~ hBOOL(hAPP(X104,bool,hAPP(X104,fun(X104,bool),X108,X109),X109))
| ~ comm_monoid_mult(X104) ) ),
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_1179])])])])]) ).
fof(c_0_2347,plain,
! [X46] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk29_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X46),esk29_0))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X46))),lab)),lba)))) )
& hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk29_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_1180])])])]) ).
fof(c_0_2348,plain,
! [X46] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X46),esk28_0))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X46))),lab)),lba)))) )
& hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_1181])])])]) ).
fof(c_0_2349,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
c_0_1182 ).
fof(c_0_2350,plain,
! [X34] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X34))),lab)),lba)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1183])]) ).
fof(c_0_2351,plain,
! [X31] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X31))),lab)),lba)),arrow_301600364e_Prof)),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_2352,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(fun(X43,fun(X44,bool)),bool,hAPP(fun(X43,fun(X44,bool)),fun(fun(X43,fun(X44,bool)),bool),ord_less_eq(fun(X43,fun(X44,bool))),hAPP(fun(product_prod(X43,X44),bool),fun(X43,fun(X44,bool)),hAPP(fun(X43,fun(fun(product_prod(X43,X44),bool),fun(X44,bool))),fun(fun(product_prod(X43,X44),bool),fun(X43,fun(X44,bool))),combc(X43,fun(product_prod(X43,X44),bool),fun(X44,bool)),hAPP(fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),fun(X43,fun(fun(product_prod(X43,X44),bool),fun(X44,bool))),hAPP(fun(fun(X44,fun(fun(product_prod(X43,X44),bool),bool)),fun(fun(product_prod(X43,X44),bool),fun(X44,bool))),fun(fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),fun(X43,fun(fun(product_prod(X43,X44),bool),fun(X44,bool)))),combb(fun(X44,fun(fun(product_prod(X43,X44),bool),bool)),fun(fun(product_prod(X43,X44),bool),fun(X44,bool)),X43),combc(X44,fun(product_prod(X43,X44),bool),bool)),hAPP(fun(X43,fun(X44,product_prod(X43,X44))),fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),hAPP(fun(fun(X44,product_prod(X43,X44)),fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),fun(fun(X43,fun(X44,product_prod(X43,X44))),fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool)))),combb(fun(X44,product_prod(X43,X44)),fun(X44,fun(fun(product_prod(X43,X44),bool),bool)),X43),hAPP(fun(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool)),fun(fun(X44,product_prod(X43,X44)),fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),combb(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool),X44),member(product_prod(X43,X44)))),product_Pair(X43,X44)))),X45)),hAPP(fun(product_prod(X43,X44),bool),fun(X43,fun(X44,bool)),hAPP(fun(X43,fun(fun(product_prod(X43,X44),bool),fun(X44,bool))),fun(fun(product_prod(X43,X44),bool),fun(X43,fun(X44,bool))),combc(X43,fun(product_prod(X43,X44),bool),fun(X44,bool)),hAPP(fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),fun(X43,fun(fun(product_prod(X43,X44),bool),fun(X44,bool))),hAPP(fun(fun(X44,fun(fun(product_prod(X43,X44),bool),bool)),fun(fun(product_prod(X43,X44),bool),fun(X44,bool))),fun(fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),fun(X43,fun(fun(product_prod(X43,X44),bool),fun(X44,bool)))),combb(fun(X44,fun(fun(product_prod(X43,X44),bool),bool)),fun(fun(product_prod(X43,X44),bool),fun(X44,bool)),X43),combc(X44,fun(product_prod(X43,X44),bool),bool)),hAPP(fun(X43,fun(X44,product_prod(X43,X44))),fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),hAPP(fun(fun(X44,product_prod(X43,X44)),fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),fun(fun(X43,fun(X44,product_prod(X43,X44))),fun(X43,fun(X44,fun(fun(product_prod(X43,X44),bool),bool)))),combb(fun(X44,product_prod(X43,X44)),fun(X44,fun(fun(product_prod(X43,X44),bool),bool)),X43),hAPP(fun(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool)),fun(fun(X44,product_prod(X43,X44)),fun(X44,fun(fun(product_prod(X43,X44),bool),bool))),combb(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool),X44),member(product_prod(X43,X44)))),product_Pair(X43,X44)))),X46)))
| hBOOL(hAPP(fun(product_prod(X43,X44),bool),bool,hAPP(fun(product_prod(X43,X44),bool),fun(fun(product_prod(X43,X44),bool),bool),ord_less_eq(fun(product_prod(X43,X44),bool)),X45),X46)) )
& ( ~ hBOOL(hAPP(fun(product_prod(X47,X48),bool),bool,hAPP(fun(product_prod(X47,X48),bool),fun(fun(product_prod(X47,X48),bool),bool),ord_less_eq(fun(product_prod(X47,X48),bool)),X49),X50))
| hBOOL(hAPP(fun(X47,fun(X48,bool)),bool,hAPP(fun(X47,fun(X48,bool)),fun(fun(X47,fun(X48,bool)),bool),ord_less_eq(fun(X47,fun(X48,bool))),hAPP(fun(product_prod(X47,X48),bool),fun(X47,fun(X48,bool)),hAPP(fun(X47,fun(fun(product_prod(X47,X48),bool),fun(X48,bool))),fun(fun(product_prod(X47,X48),bool),fun(X47,fun(X48,bool))),combc(X47,fun(product_prod(X47,X48),bool),fun(X48,bool)),hAPP(fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),fun(X47,fun(fun(product_prod(X47,X48),bool),fun(X48,bool))),hAPP(fun(fun(X48,fun(fun(product_prod(X47,X48),bool),bool)),fun(fun(product_prod(X47,X48),bool),fun(X48,bool))),fun(fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),fun(X47,fun(fun(product_prod(X47,X48),bool),fun(X48,bool)))),combb(fun(X48,fun(fun(product_prod(X47,X48),bool),bool)),fun(fun(product_prod(X47,X48),bool),fun(X48,bool)),X47),combc(X48,fun(product_prod(X47,X48),bool),bool)),hAPP(fun(X47,fun(X48,product_prod(X47,X48))),fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),hAPP(fun(fun(X48,product_prod(X47,X48)),fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),fun(fun(X47,fun(X48,product_prod(X47,X48))),fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool)))),combb(fun(X48,product_prod(X47,X48)),fun(X48,fun(fun(product_prod(X47,X48),bool),bool)),X47),hAPP(fun(product_prod(X47,X48),fun(fun(product_prod(X47,X48),bool),bool)),fun(fun(X48,product_prod(X47,X48)),fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),combb(product_prod(X47,X48),fun(fun(product_prod(X47,X48),bool),bool),X48),member(product_prod(X47,X48)))),product_Pair(X47,X48)))),X49)),hAPP(fun(product_prod(X47,X48),bool),fun(X47,fun(X48,bool)),hAPP(fun(X47,fun(fun(product_prod(X47,X48),bool),fun(X48,bool))),fun(fun(product_prod(X47,X48),bool),fun(X47,fun(X48,bool))),combc(X47,fun(product_prod(X47,X48),bool),fun(X48,bool)),hAPP(fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),fun(X47,fun(fun(product_prod(X47,X48),bool),fun(X48,bool))),hAPP(fun(fun(X48,fun(fun(product_prod(X47,X48),bool),bool)),fun(fun(product_prod(X47,X48),bool),fun(X48,bool))),fun(fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),fun(X47,fun(fun(product_prod(X47,X48),bool),fun(X48,bool)))),combb(fun(X48,fun(fun(product_prod(X47,X48),bool),bool)),fun(fun(product_prod(X47,X48),bool),fun(X48,bool)),X47),combc(X48,fun(product_prod(X47,X48),bool),bool)),hAPP(fun(X47,fun(X48,product_prod(X47,X48))),fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),hAPP(fun(fun(X48,product_prod(X47,X48)),fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),fun(fun(X47,fun(X48,product_prod(X47,X48))),fun(X47,fun(X48,fun(fun(product_prod(X47,X48),bool),bool)))),combb(fun(X48,product_prod(X47,X48)),fun(X48,fun(fun(product_prod(X47,X48),bool),bool)),X47),hAPP(fun(product_prod(X47,X48),fun(fun(product_prod(X47,X48),bool),bool)),fun(fun(X48,product_prod(X47,X48)),fun(X48,fun(fun(product_prod(X47,X48),bool),bool))),combb(product_prod(X47,X48),fun(fun(product_prod(X47,X48),bool),bool),X48),member(product_prod(X47,X48)))),product_Pair(X47,X48)))),X50))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1185])])])]) ).
fof(c_0_2353,plain,
! [X104,X105,X106,X107,X108,X109,X110] :
( ~ comm_monoid_add(X106)
| ~ hBOOL(hAPP(fun(X105,bool),bool,finite_finite_1(X105),X110))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X109))
| hAPP(fun(X105,bool),X106,hAPP(fun(X105,X106),fun(fun(X105,bool),X106),big_co1399186613setsum(X105,X106),hAPP(fun(X105,fun(X104,bool)),fun(X105,X106),hAPP(fun(X105,fun(fun(X104,bool),X106)),fun(fun(X105,fun(X104,bool)),fun(X105,X106)),combs(X105,fun(X104,bool),X106),hAPP(fun(X105,fun(X104,X106)),fun(X105,fun(fun(X104,bool),X106)),hAPP(fun(fun(X104,X106),fun(fun(X104,bool),X106)),fun(fun(X105,fun(X104,X106)),fun(X105,fun(fun(X104,bool),X106))),combb(fun(X104,X106),fun(fun(X104,bool),X106),X105),big_co1399186613setsum(X104,X106)),X107)),hAPP(fun(X105,fun(X104,bool)),fun(X105,fun(X104,bool)),hAPP(fun(fun(X104,bool),fun(X104,bool)),fun(fun(X105,fun(X104,bool)),fun(X105,fun(X104,bool))),combb(fun(X104,bool),fun(X104,bool),X105),collect(X104)),hAPP(fun(X105,fun(X104,bool)),fun(X105,fun(X104,bool)),hAPP(fun(fun(X104,bool),fun(X104,bool)),fun(fun(X105,fun(X104,bool)),fun(X105,fun(X104,bool))),combb(fun(X104,bool),fun(X104,bool),X105),hAPP(fun(X104,fun(bool,bool)),fun(fun(X104,bool),fun(X104,bool)),combs(X104,bool,bool),hAPP(fun(X104,bool),fun(X104,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X104,bool),fun(X104,fun(bool,bool))),combb(bool,fun(bool,bool),X104),fconj),hAPP(fun(X104,bool),fun(X104,bool),hAPP(fun(X104,fun(fun(X104,bool),bool)),fun(fun(X104,bool),fun(X104,bool)),combc(X104,fun(X104,bool),bool),member(X104)),X109)))),X108)))),X110) = hAPP(fun(X104,bool),X106,hAPP(fun(X104,X106),fun(fun(X104,bool),X106),big_co1399186613setsum(X104,X106),hAPP(fun(X104,fun(X105,bool)),fun(X104,X106),hAPP(fun(X104,fun(fun(X105,bool),X106)),fun(fun(X104,fun(X105,bool)),fun(X104,X106)),combs(X104,fun(X105,bool),X106),hAPP(fun(X104,fun(X105,X106)),fun(X104,fun(fun(X105,bool),X106)),hAPP(fun(fun(X105,X106),fun(fun(X105,bool),X106)),fun(fun(X104,fun(X105,X106)),fun(X104,fun(fun(X105,bool),X106))),combb(fun(X105,X106),fun(fun(X105,bool),X106),X104),big_co1399186613setsum(X105,X106)),hAPP(fun(X105,fun(X104,X106)),fun(X104,fun(X105,X106)),combc(X105,X104,X106),X107))),hAPP(fun(X104,fun(X105,bool)),fun(X104,fun(X105,bool)),hAPP(fun(fun(X105,bool),fun(X105,bool)),fun(fun(X104,fun(X105,bool)),fun(X104,fun(X105,bool))),combb(fun(X105,bool),fun(X105,bool),X104),collect(X105)),hAPP(fun(X104,fun(X105,bool)),fun(X104,fun(X105,bool)),hAPP(fun(fun(X105,bool),fun(X105,bool)),fun(fun(X104,fun(X105,bool)),fun(X104,fun(X105,bool))),combb(fun(X105,bool),fun(X105,bool),X104),hAPP(fun(X105,fun(bool,bool)),fun(fun(X105,bool),fun(X105,bool)),combs(X105,bool,bool),hAPP(fun(X105,bool),fun(X105,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X105,bool),fun(X105,fun(bool,bool))),combb(bool,fun(bool,bool),X105),fconj),hAPP(fun(X105,bool),fun(X105,bool),hAPP(fun(X105,fun(fun(X105,bool),bool)),fun(fun(X105,bool),fun(X105,bool)),combc(X105,fun(X105,bool),bool),member(X105)),X110)))),hAPP(fun(X105,fun(X104,bool)),fun(X104,fun(X105,bool)),combc(X105,X104,bool),X108))))),X109) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1186])])]) ).
fof(c_0_2354,plain,
! [X77,X78,X79,X80,X81,X82,X83,X84] :
( ( hBOOL(hAPP(fun(X77,bool),bool,hAPP(X77,fun(fun(X77,bool),bool),member(X77),esk152_8(X77,X78,X79,X80,X81,X82,X83,X84)),X81))
| hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X79),X81) = hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X80),X81)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| ~ hBOOL(hAPP(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool,hAPP(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool),hAPP(fun(X78,fun(X78,X78)),fun(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool)),finite_folding_image(X78,X77),X82),X83),X84)) )
& ( hAPP(X77,X78,X79,esk152_8(X77,X78,X79,X80,X81,X82,X83,X84)) != hAPP(X77,X78,X80,esk152_8(X77,X78,X79,X80,X81,X82,X83,X84))
| hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X79),X81) = hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X80),X81)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| ~ hBOOL(hAPP(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool,hAPP(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool),hAPP(fun(X78,fun(X78,X78)),fun(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool)),finite_folding_image(X78,X77),X82),X83),X84)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1187])])])]) ).
fof(c_0_2355,plain,
! [X44,X45,X46,X47,X48,X49,X50] :
( ~ semiring_0(X46)
| hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),hAPP(fun(X44,bool),X46,hAPP(fun(X44,X46),fun(fun(X44,bool),X46),big_co1399186613setsum(X44,X46),X47),X48)),hAPP(fun(X45,bool),X46,hAPP(fun(X45,X46),fun(fun(X45,bool),X46),big_co1399186613setsum(X45,X46),X49),X50)) = hAPP(fun(X44,bool),X46,hAPP(fun(X44,X46),fun(fun(X44,bool),X46),big_co1399186613setsum(X44,X46),hAPP(fun(X45,bool),fun(X44,X46),hAPP(fun(X44,fun(fun(X45,bool),X46)),fun(fun(X45,bool),fun(X44,X46)),combc(X44,fun(X45,bool),X46),hAPP(fun(X44,fun(X45,X46)),fun(X44,fun(fun(X45,bool),X46)),hAPP(fun(fun(X45,X46),fun(fun(X45,bool),X46)),fun(fun(X44,fun(X45,X46)),fun(X44,fun(fun(X45,bool),X46))),combb(fun(X45,X46),fun(fun(X45,bool),X46),X44),big_co1399186613setsum(X45,X46)),hAPP(fun(X45,X46),fun(X44,fun(X45,X46)),hAPP(fun(X44,fun(fun(X45,X46),fun(X45,X46))),fun(fun(X45,X46),fun(X44,fun(X45,X46))),combc(X44,fun(X45,X46),fun(X45,X46)),hAPP(fun(X44,fun(X46,X46)),fun(X44,fun(fun(X45,X46),fun(X45,X46))),hAPP(fun(fun(X46,X46),fun(fun(X45,X46),fun(X45,X46))),fun(fun(X44,fun(X46,X46)),fun(X44,fun(fun(X45,X46),fun(X45,X46)))),combb(fun(X46,X46),fun(fun(X45,X46),fun(X45,X46)),X44),combb(X46,X46,X45)),hAPP(fun(X44,X46),fun(X44,fun(X46,X46)),hAPP(fun(X46,fun(X46,X46)),fun(fun(X44,X46),fun(X44,fun(X46,X46))),combb(X46,fun(X46,X46),X44),times_times(X46)),X47))),X49))),X50)),X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1188])])]) ).
fof(c_0_2356,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_1189])]) ).
fof(c_0_2357,plain,
! [X42,X43,X44,X45,X46,X47] :
( ~ comm_monoid_add(X44)
| ~ hBOOL(hAPP(fun(X43,bool),bool,finite_finite_1(X43),X47))
| hAPP(fun(X43,bool),X44,hAPP(fun(X43,X44),fun(fun(X43,bool),X44),big_co1399186613setsum(X43,X44),X45),X47) = hAPP(fun(X42,bool),X44,hAPP(fun(X42,X44),fun(fun(X42,bool),X44),big_co1399186613setsum(X42,X44),hAPP(fun(X42,fun(X43,bool)),fun(X42,X44),hAPP(fun(fun(X43,bool),X44),fun(fun(X42,fun(X43,bool)),fun(X42,X44)),combb(fun(X43,bool),X44,X42),hAPP(fun(X43,X44),fun(fun(X43,bool),X44),big_co1399186613setsum(X43,X44),X45)),hAPP(fun(X42,fun(X43,bool)),fun(X42,fun(X43,bool)),hAPP(fun(fun(X43,bool),fun(X43,bool)),fun(fun(X42,fun(X43,bool)),fun(X42,fun(X43,bool))),combb(fun(X43,bool),fun(X43,bool),X42),collect(X43)),hAPP(fun(X42,fun(X43,bool)),fun(X42,fun(X43,bool)),hAPP(fun(fun(X43,bool),fun(X43,bool)),fun(fun(X42,fun(X43,bool)),fun(X42,fun(X43,bool))),combb(fun(X43,bool),fun(X43,bool),X42),hAPP(fun(X43,fun(bool,bool)),fun(fun(X43,bool),fun(X43,bool)),combs(X43,bool,bool),hAPP(fun(X43,bool),fun(X43,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X43,bool),fun(X43,fun(bool,bool))),combb(bool,fun(bool,bool),X43),fconj),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X47)))),hAPP(fun(X43,fun(X42,bool)),fun(X42,fun(X43,bool)),combc(X43,X42,bool),hAPP(fun(X43,X42),fun(X43,fun(X42,bool)),hAPP(fun(X42,fun(X42,bool)),fun(fun(X43,X42),fun(X43,fun(X42,bool))),combb(X42,fun(X42,bool),X43),fequal(X42)),X46)))))),hAPP(fun(X43,bool),fun(X42,bool),hAPP(fun(X43,X42),fun(fun(X43,bool),fun(X42,bool)),image(X43,X42),X46),X47)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1190])])]) ).
fof(c_0_2358,plain,
! [X44,X45,X46,X47,X48] :
( ~ comm_monoid_add(X45)
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X48))
| hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),collect(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(bool,bool)),fun(fun(X44,bool),fun(X44,bool)),combs(X44,bool,bool),hAPP(fun(X44,bool),fun(X44,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X44,bool),fun(X44,fun(bool,bool))),combb(bool,fun(bool,bool),X44),fconj),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X48))),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X47)))) = hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),hAPP(X45,fun(X44,X45),hAPP(fun(X44,fun(X45,X45)),fun(X45,fun(X44,X45)),combc(X44,X45,X45),hAPP(fun(X44,X45),fun(X44,fun(X45,X45)),hAPP(fun(X44,fun(X45,fun(X45,X45))),fun(fun(X44,X45),fun(X44,fun(X45,X45))),combs(X44,X45,fun(X45,X45)),hAPP(fun(X44,bool),fun(X44,fun(X45,fun(X45,X45))),hAPP(fun(bool,fun(X45,fun(X45,X45))),fun(fun(X44,bool),fun(X44,fun(X45,fun(X45,X45)))),combb(bool,fun(X45,fun(X45,X45)),X44),if(X45)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X47))),X46)),zero_zero(X45))),X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1191])])]) ).
fof(c_0_2359,plain,
! [X41,X42,X43,X44] :
( ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk117_4(X41,X42,X43,X44)),X44))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44)))
| hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),hAPP(fun(X42,bool),fun(X42,bool),collect(X42),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,fun(bool,bool)),fun(fun(X42,bool),fun(X42,bool)),combs(X42,bool,bool),hAPP(fun(X42,bool),fun(X42,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X42,bool),fun(X42,fun(bool,bool))),combb(bool,fun(bool,bool),X42),fconj),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))),hAPP(X41,fun(X42,bool),hAPP(fun(X42,fun(X41,bool)),fun(X41,fun(X42,bool)),combc(X42,X41,bool),hAPP(fun(X42,X41),fun(X42,fun(X41,bool)),hAPP(fun(X41,fun(X41,bool)),fun(fun(X42,X41),fun(X42,fun(X41,bool))),combb(X41,fun(X41,bool),X42),fequal(X41)),X43)),hAPP(X42,X41,X43,esk117_4(X41,X42,X43,X44)))))))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44)))
| hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1192])])])]) ).
fof(c_0_2360,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_1193])]) ).
fof(c_0_2361,plain,
! [X44,X45,X46,X47,X48] :
( ~ comm_monoid_add(X45)
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X48))
| hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X48),X47)) = hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),hAPP(X45,fun(X44,X45),hAPP(fun(X44,fun(X45,X45)),fun(X45,fun(X44,X45)),combc(X44,X45,X45),hAPP(fun(X44,X45),fun(X44,fun(X45,X45)),hAPP(fun(X44,fun(X45,fun(X45,X45))),fun(fun(X44,X45),fun(X44,fun(X45,X45))),combs(X44,X45,fun(X45,X45)),hAPP(fun(X44,bool),fun(X44,fun(X45,fun(X45,X45))),hAPP(fun(bool,fun(X45,fun(X45,X45))),fun(fun(X44,bool),fun(X44,fun(X45,fun(X45,X45)))),combb(bool,fun(X45,fun(X45,X45)),X44),if(X45)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X47))),X46)),zero_zero(X45))),X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1194])])]) ).
fof(c_0_2362,plain,
! [X42,X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X45),X46))
| hAPP(fun(X42,bool),X43,hAPP(fun(X42,X43),fun(fun(X42,bool),X43),big_co1399186613setsum(X42,X43),hAPP(X43,fun(X42,X43),hAPP(fun(X42,fun(X43,X43)),fun(X43,fun(X42,X43)),combc(X42,X43,X43),hAPP(fun(X42,X43),fun(X42,fun(X43,X43)),hAPP(fun(X42,fun(X43,fun(X43,X43))),fun(fun(X42,X43),fun(X42,fun(X43,X43))),combs(X42,X43,fun(X43,X43)),hAPP(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43))),hAPP(fun(bool,fun(X43,fun(X43,X43))),fun(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43)))),combb(bool,fun(X43,fun(X43,X43)),X42),if(X43)),hAPP(X42,fun(X42,bool),hAPP(fun(X42,fun(X42,bool)),fun(X42,fun(X42,bool)),combc(X42,X42,bool),fequal(X42)),X45))),X44)),zero_zero(X43))),X46) = hAPP(X42,X43,X44,X45)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X46))
| ~ comm_monoid_add(X43) )
& ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X45),X46))
| hAPP(fun(X42,bool),X43,hAPP(fun(X42,X43),fun(fun(X42,bool),X43),big_co1399186613setsum(X42,X43),hAPP(X43,fun(X42,X43),hAPP(fun(X42,fun(X43,X43)),fun(X43,fun(X42,X43)),combc(X42,X43,X43),hAPP(fun(X42,X43),fun(X42,fun(X43,X43)),hAPP(fun(X42,fun(X43,fun(X43,X43))),fun(fun(X42,X43),fun(X42,fun(X43,X43))),combs(X42,X43,fun(X43,X43)),hAPP(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43))),hAPP(fun(bool,fun(X43,fun(X43,X43))),fun(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43)))),combb(bool,fun(X43,fun(X43,X43)),X42),if(X43)),hAPP(X42,fun(X42,bool),hAPP(fun(X42,fun(X42,bool)),fun(X42,fun(X42,bool)),combc(X42,X42,bool),fequal(X42)),X45))),X44)),zero_zero(X43))),X46) = zero_zero(X43)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X46))
| ~ comm_monoid_add(X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1195])])])]) ).
fof(c_0_2363,plain,
! [X41,X42,X43,X44,X45] :
( ~ comm_monoid_add(X42)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X45))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X43),hAPP(fun(X41,bool),fun(X41,bool),collect(X41),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,fun(bool,bool)),fun(fun(X41,bool),fun(X41,bool)),combs(X41,bool,bool),hAPP(fun(X41,bool),fun(X41,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X41,bool),fun(X41,fun(bool,bool))),combb(bool,fun(bool,bool),X41),fconj),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,fun(fun(X41,bool),bool)),fun(fun(X41,bool),fun(X41,bool)),combc(X41,fun(X41,bool),bool),member(X41)),X45))),X44))) = hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),hAPP(X42,fun(X41,X42),hAPP(fun(X41,fun(X42,X42)),fun(X42,fun(X41,X42)),combc(X41,X42,X42),hAPP(fun(X41,X42),fun(X41,fun(X42,X42)),hAPP(fun(X41,fun(X42,fun(X42,X42))),fun(fun(X41,X42),fun(X41,fun(X42,X42))),combs(X41,X42,fun(X42,X42)),hAPP(fun(X41,bool),fun(X41,fun(X42,fun(X42,X42))),hAPP(fun(bool,fun(X42,fun(X42,X42))),fun(fun(X41,bool),fun(X41,fun(X42,fun(X42,X42)))),combb(bool,fun(X42,fun(X42,X42)),X41),if(X42)),X44)),X43)),zero_zero(X42))),X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1196])])]) ).
fof(c_0_2364,plain,
! [X42,X43,X44,X45,X46,X47] : hAPP(fun(X42,bool),fun(X43,bool),hAPP(fun(X42,X43),fun(fun(X42,bool),fun(X43,bool)),image(X42,X43),hAPP(fun(X42,X43),fun(X42,X43),hAPP(fun(X42,fun(X43,X43)),fun(fun(X42,X43),fun(X42,X43)),combs(X42,X43,X43),hAPP(fun(X42,X43),fun(X42,fun(X43,X43)),hAPP(fun(X42,fun(X43,fun(X43,X43))),fun(fun(X42,X43),fun(X42,fun(X43,X43))),combs(X42,X43,fun(X43,X43)),hAPP(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43))),hAPP(fun(bool,fun(X43,fun(X43,X43))),fun(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43)))),combb(bool,fun(X43,fun(X43,X43)),X42),if(X43)),X44)),X45)),X46)),X47) = hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,bool),fun(fun(X43,bool),fun(X43,bool)),semilattice_sup_sup(fun(X43,bool)),hAPP(fun(X42,bool),fun(X43,bool),hAPP(fun(X42,X43),fun(fun(X42,bool),fun(X43,bool)),image(X42,X43),X45),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,bool),fun(fun(X42,bool),fun(X42,bool)),semilattice_inf_inf(fun(X42,bool)),X47),hAPP(fun(X42,bool),fun(X42,bool),collect(X42),X44)))),hAPP(fun(X42,bool),fun(X43,bool),hAPP(fun(X42,X43),fun(fun(X42,bool),fun(X43,bool)),image(X42,X43),X46),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,bool),fun(fun(X42,bool),fun(X42,bool)),semilattice_inf_inf(fun(X42,bool)),X47),hAPP(fun(X42,bool),fun(X42,bool),collect(X42),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(bool,bool),fun(fun(X42,bool),fun(X42,bool)),combb(bool,bool,X42),fNot),X44))))),
inference(variable_rename,[status(thm)],[c_0_1197]) ).
fof(c_0_2365,plain,
! [X42,X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X45),X46))
| hAPP(fun(X42,bool),X43,hAPP(fun(X42,X43),fun(fun(X42,bool),X43),big_co1399186613setsum(X42,X43),hAPP(X43,fun(X42,X43),hAPP(fun(X42,fun(X43,X43)),fun(X43,fun(X42,X43)),combc(X42,X43,X43),hAPP(fun(X42,X43),fun(X42,fun(X43,X43)),hAPP(fun(X42,fun(X43,fun(X43,X43))),fun(fun(X42,X43),fun(X42,fun(X43,X43))),combs(X42,X43,fun(X43,X43)),hAPP(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43))),hAPP(fun(bool,fun(X43,fun(X43,X43))),fun(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43)))),combb(bool,fun(X43,fun(X43,X43)),X42),if(X43)),hAPP(X42,fun(X42,bool),fequal(X42),X45))),X44)),zero_zero(X43))),X46) = hAPP(X42,X43,X44,X45)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X46))
| ~ comm_monoid_add(X43) )
& ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X45),X46))
| hAPP(fun(X42,bool),X43,hAPP(fun(X42,X43),fun(fun(X42,bool),X43),big_co1399186613setsum(X42,X43),hAPP(X43,fun(X42,X43),hAPP(fun(X42,fun(X43,X43)),fun(X43,fun(X42,X43)),combc(X42,X43,X43),hAPP(fun(X42,X43),fun(X42,fun(X43,X43)),hAPP(fun(X42,fun(X43,fun(X43,X43))),fun(fun(X42,X43),fun(X42,fun(X43,X43))),combs(X42,X43,fun(X43,X43)),hAPP(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43))),hAPP(fun(bool,fun(X43,fun(X43,X43))),fun(fun(X42,bool),fun(X42,fun(X43,fun(X43,X43)))),combb(bool,fun(X43,fun(X43,X43)),X42),if(X43)),hAPP(X42,fun(X42,bool),fequal(X42),X45))),X44)),zero_zero(X43))),X46) = zero_zero(X43)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X46))
| ~ comm_monoid_add(X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1198])])])]) ).
fof(c_0_2366,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),esk54_6(X47,X48,X49,X50,X51,X52)),esk55_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,esk54_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X49,esk55_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_1199])])])])]) ).
fof(c_0_2367,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),esk52_6(X47,X48,X49,X50,X51,X52)),esk53_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,esk52_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X49,esk53_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_1200])])])])]) ).
fof(c_0_2368,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),esk47_6(X47,X48,X49,X50,X51,X52)),esk46_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,esk47_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X50,esk46_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_1201])])])])]) ).
fof(c_0_2369,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),esk45_6(X47,X48,X49,X50,X51,X52)),esk44_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,esk45_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X50,esk44_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_1202])])])])]) ).
fof(c_0_2370,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),esk50_6(X47,X48,X49,X50,X51,X52)),esk51_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,esk50_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X51,esk51_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_1203])])])])]) ).
fof(c_0_2371,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),esk48_6(X47,X48,X49,X50,X51,X52)),esk49_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,esk48_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X51,esk49_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_1204])])])])]) ).
fof(c_0_2372,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),esk42_6(X47,X48,X49,X50,X51,X52)),esk41_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,esk42_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X50,esk41_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_1205])])])])]) ).
fof(c_0_2373,plain,
! [X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),esk40_6(X47,X48,X49,X50,X51,X52)),esk39_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,esk40_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X50,esk39_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_1206])])])])]) ).
fof(c_0_2374,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk2_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk2_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk2_6(X17,X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk2_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1207])])])]) ).
fof(c_0_2375,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1208])])])]) ).
fof(c_0_2376,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1209])])])]) ).
fof(c_0_2377,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_1210])]) ).
fof(c_0_2378,plain,
! [X17,X18] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_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_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1211])])])])]) ).
fof(c_0_2379,plain,
! [X77,X78,X79,X80,X81] :
( ~ comm_monoid_mult(X78)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),hAPP(fun(X77,X78),fun(X77,X78),hAPP(fun(X77,fun(X78,X78)),fun(fun(X77,X78),fun(X77,X78)),combs(X77,X78,X78),hAPP(fun(X77,X78),fun(X77,fun(X78,X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X77,fun(X78,X78))),combb(X78,fun(X78,X78),X77),times_times(X78)),X79)),X80)),one_one(X78)),X81) = hAPP(X78,X78,hAPP(X78,fun(X78,X78),times_times(X78),hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),X79),one_one(X78)),X81)),hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),X80),one_one(X78)),X81)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1212])])]) ).
fof(c_0_2380,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ comm_monoid_add(X46)
| hAPP(fun(X44,bool),X46,hAPP(fun(X44,X46),fun(fun(X44,bool),X46),big_co1399186613setsum(X44,X46),hAPP(fun(X45,bool),fun(X44,X46),hAPP(fun(X44,fun(fun(X45,bool),X46)),fun(fun(X45,bool),fun(X44,X46)),combc(X44,fun(X45,bool),X46),hAPP(fun(X44,fun(X45,X46)),fun(X44,fun(fun(X45,bool),X46)),hAPP(fun(fun(X45,X46),fun(fun(X45,bool),X46)),fun(fun(X44,fun(X45,X46)),fun(X44,fun(fun(X45,bool),X46))),combb(fun(X45,X46),fun(fun(X45,bool),X46),X44),big_co1399186613setsum(X45,X46)),X47)),X48)),X49) = hAPP(fun(X45,bool),X46,hAPP(fun(X45,X46),fun(fun(X45,bool),X46),big_co1399186613setsum(X45,X46),hAPP(fun(X44,bool),fun(X45,X46),hAPP(fun(X45,fun(fun(X44,bool),X46)),fun(fun(X44,bool),fun(X45,X46)),combc(X45,fun(X44,bool),X46),hAPP(fun(X45,fun(X44,X46)),fun(X45,fun(fun(X44,bool),X46)),hAPP(fun(fun(X44,X46),fun(fun(X44,bool),X46)),fun(fun(X45,fun(X44,X46)),fun(X45,fun(fun(X44,bool),X46))),combb(fun(X44,X46),fun(fun(X44,bool),X46),X45),big_co1399186613setsum(X44,X46)),hAPP(fun(X44,fun(X45,X46)),fun(X45,fun(X44,X46)),combc(X44,X45,X46),X47))),X49)),X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1213])])]) ).
fof(c_0_2381,plain,
! [X30,X31] :
( ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk24_2(X30,X31)),arrow_301600364e_Prof))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X31),X30))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X31),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) )
& ( ti(arrow_2142409994le_alt,esk25_2(X30,X31)) != ti(arrow_2142409994le_alt,esk26_2(X30,X31))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X31),X30))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X31),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X30,X31)),esk26_2(X30,X31))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk24_2(X30,X31),X30)))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X31),X30))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X31),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X30,X31)),esk26_2(X30,X31))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X31,esk24_2(X30,X31))))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X31),X30))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X31),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1214])])])]) ).
fof(c_0_2382,plain,
! [X17,X18] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1215])])])])]) ).
fof(c_0_2383,plain,
! [X17,X18] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X17) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X17) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X17)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X17))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X18)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X18) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( hAPP(arrow_1998540521e_indi,nat,h,X18) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X18)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1216])])])])]) ).
fof(c_0_2384,plain,
! [X44,X45,X46,X47,X48] :
( ~ comm_monoid_mult(X45)
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X48))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X47))
| hAPP(X45,X45,hAPP(X45,fun(X45,X45),times_times(X45),hAPP(fun(X44,bool),X45,hAPP(X45,fun(fun(X44,bool),X45),hAPP(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45)),hAPP(fun(X45,fun(X45,X45)),fun(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45))),finite_fold_image(X45,X44),times_times(X45)),X46),one_one(X45)),X48)),hAPP(fun(X44,bool),X45,hAPP(X45,fun(fun(X44,bool),X45),hAPP(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45)),hAPP(fun(X45,fun(X45,X45)),fun(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45))),finite_fold_image(X45,X44),times_times(X45)),X46),one_one(X45)),X47)) = hAPP(X45,X45,hAPP(X45,fun(X45,X45),times_times(X45),hAPP(fun(X44,bool),X45,hAPP(X45,fun(fun(X44,bool),X45),hAPP(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45)),hAPP(fun(X45,fun(X45,X45)),fun(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45))),finite_fold_image(X45,X44),times_times(X45)),X46),one_one(X45)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X48),X47))),hAPP(fun(X44,bool),X45,hAPP(X45,fun(fun(X44,bool),X45),hAPP(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45)),hAPP(fun(X45,fun(X45,X45)),fun(fun(X44,X45),fun(X45,fun(fun(X44,bool),X45))),finite_fold_image(X45,X44),times_times(X45)),X46),one_one(X45)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X48),X47))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1217])])]) ).
fof(c_0_2385,plain,
! [X28,X29,X30,X31,X32,X34,X39,X40] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X29)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X30)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X30),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X29),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X28)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X30)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X29)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X30),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X29),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X28)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X29)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X30)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X30),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X29),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X28)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X30)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,X29)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X31),X32)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X30),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X29),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X28)) )
& ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk10_1(X34)),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X34)) )
& ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk11_1(X34)),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X34)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X34),X39)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X34),X39)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X34)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X34),X40)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X34),X40)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X34)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X34,esk10_1(X34))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X34,esk11_1(X34))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X34)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X34,esk10_1(X34))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X34,esk11_1(X34))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_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_1218])])])])])]) ).
fof(c_0_2386,plain,
! [X18,X19,X20,X21,X22] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X19)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X19),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X19)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X19),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X19)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X19),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X19)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X21),X22)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X22),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X19),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X22) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X21) = ti(arrow_2142409994le_alt,X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1219])])])]) ).
fof(c_0_2387,plain,
! [X54,X55,X56,X57,X58,X59] :
( ( 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),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)))) )
& ( 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)))) )
& ( ~ hBOOL(hAPP(fun(X57,bool),bool,finite_finite_1(X57),hAPP(fun(X57,bool),fun(X57,bool),collect(X57),X58)))
| ~ hBOOL(hAPP(fun(X57,bool),bool,finite_finite_1(X57),hAPP(fun(X57,bool),fun(X57,bool),collect(X57),X59)))
| hBOOL(hAPP(fun(X57,bool),bool,finite_finite_1(X57),hAPP(fun(X57,bool),fun(X57,bool),collect(X57),hAPP(fun(X57,bool),fun(X57,bool),hAPP(fun(X57,fun(bool,bool)),fun(fun(X57,bool),fun(X57,bool)),combs(X57,bool,bool),hAPP(fun(X57,bool),fun(X57,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X57,bool),fun(X57,fun(bool,bool))),combb(bool,fun(bool,bool),X57),fdisj),X58)),X59)))) ) ),
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_1220])])])])]) ).
fof(c_0_2388,plain,
! [X17,X18,X19,X20] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X17)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X18)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X19)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X17),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X18),arrow_301600364e_Prof))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1221])])])]) ).
fof(c_0_2389,plain,
! [X89,X90,X91,X92,X93,X94,X95,X96,X97,X98,X99] :
( ~ hBOOL(hAPP(fun(fun(X91,X92),bool),bool,hAPP(fun(X91,X92),fun(fun(fun(X91,X92),bool),bool),member(fun(X91,X92)),X97),hAPP(fun(X91,fun(X92,bool)),fun(fun(X91,X92),bool),hAPP(fun(X91,bool),fun(fun(X91,fun(X92,bool)),fun(fun(X91,X92),bool)),pi(X91,X92),X98),hAPP(fun(X92,bool),fun(X91,fun(X92,bool)),combk(fun(X92,bool),X91),X99))))
| ~ hBOOL(hAPP(fun(fun(X92,X90),bool),bool,hAPP(fun(X92,X90),fun(fun(fun(X92,X90),bool),bool),member(fun(X92,X90)),X95),hAPP(fun(X92,fun(X90,bool)),fun(fun(X92,X90),bool),hAPP(fun(X92,bool),fun(fun(X92,fun(X90,bool)),fun(fun(X92,X90),bool)),pi(X92,X90),X99),hAPP(fun(X90,bool),fun(X92,fun(X90,bool)),combk(fun(X90,bool),X92),X96))))
| ~ hBOOL(hAPP(fun(fun(X90,X89),bool),bool,hAPP(fun(X90,X89),fun(fun(fun(X90,X89),bool),bool),member(fun(X90,X89)),X93),hAPP(fun(X90,fun(X89,bool)),fun(fun(X90,X89),bool),hAPP(fun(X90,bool),fun(fun(X90,fun(X89,bool)),fun(fun(X90,X89),bool)),pi(X90,X89),X96),hAPP(fun(X89,bool),fun(X90,fun(X89,bool)),combk(fun(X89,bool),X90),X94))))
| hAPP(fun(X91,X90),fun(X91,X89),hAPP(fun(X90,X89),fun(fun(X91,X90),fun(X91,X89)),hAPP(fun(X91,bool),fun(fun(X90,X89),fun(fun(X91,X90),fun(X91,X89))),compose(X91,X90,X89),X98),X93),hAPP(fun(X91,X92),fun(X91,X90),hAPP(fun(X92,X90),fun(fun(X91,X92),fun(X91,X90)),hAPP(fun(X91,bool),fun(fun(X92,X90),fun(fun(X91,X92),fun(X91,X90))),compose(X91,X92,X90),X98),X95),X97)) = hAPP(fun(X91,X92),fun(X91,X89),hAPP(fun(X92,X89),fun(fun(X91,X92),fun(X91,X89)),hAPP(fun(X91,bool),fun(fun(X92,X89),fun(fun(X91,X92),fun(X91,X89))),compose(X91,X92,X89),X98),hAPP(fun(X92,X90),fun(X92,X89),hAPP(fun(X90,X89),fun(fun(X92,X90),fun(X92,X89)),hAPP(fun(X92,bool),fun(fun(X90,X89),fun(fun(X92,X90),fun(X92,X89))),compose(X92,X90,X89),X99),X93),X95)),X97) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1222])]) ).
fof(c_0_2390,plain,
! [X53,X54,X55,X56,X57,X58,X59,X60] :
( ~ hBOOL(hAPP(fun(fun(X54,X55),bool),bool,hAPP(fun(X54,X55),fun(fun(fun(X54,X55),bool),bool),member(fun(X54,X55)),X58),hAPP(fun(X54,fun(X55,bool)),fun(fun(X54,X55),bool),hAPP(fun(X54,bool),fun(fun(X54,fun(X55,bool)),fun(fun(X54,X55),bool)),pi(X54,X55),X59),hAPP(fun(X55,bool),fun(X54,fun(X55,bool)),combk(fun(X55,bool),X54),X60))))
| ~ hBOOL(hAPP(fun(fun(X55,X53),bool),bool,hAPP(fun(X55,X53),fun(fun(fun(X55,X53),bool),bool),member(fun(X55,X53)),X56),hAPP(fun(X55,fun(X53,bool)),fun(fun(X55,X53),bool),hAPP(fun(X55,bool),fun(fun(X55,fun(X53,bool)),fun(fun(X55,X53),bool)),pi(X55,X53),X60),hAPP(fun(X53,bool),fun(X55,fun(X53,bool)),combk(fun(X53,bool),X55),X57))))
| hBOOL(hAPP(fun(fun(X54,X53),bool),bool,hAPP(fun(X54,X53),fun(fun(fun(X54,X53),bool),bool),member(fun(X54,X53)),hAPP(fun(X54,X55),fun(X54,X53),hAPP(fun(X55,X53),fun(fun(X54,X55),fun(X54,X53)),hAPP(fun(X54,bool),fun(fun(X55,X53),fun(fun(X54,X55),fun(X54,X53))),compose(X54,X55,X53),X59),X56),X58)),hAPP(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool),hAPP(fun(X54,bool),fun(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool)),pi(X54,X53),X59),hAPP(fun(X53,bool),fun(X54,fun(X53,bool)),combk(fun(X53,bool),X54),X57)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1223])]) ).
fof(c_0_2391,plain,
! [X104,X105,X106,X107,X108] :
( ( hBOOL(hAPP(fun(X104,bool),bool,hAPP(X104,fun(fun(X104,bool),bool),member(X104),esk173_5(X104,X105,X106,X107,X108)),hAPP(fun(X104,bool),fun(X104,bool),hAPP(fun(X104,bool),fun(fun(X104,bool),fun(X104,bool)),semilattice_inf_inf(fun(X104,bool)),X108),X107)))
| hAPP(fun(X104,bool),X105,hAPP(X105,fun(fun(X104,bool),X105),hAPP(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105)),hAPP(fun(X105,fun(X105,X105)),fun(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105))),finite_fold_image(X105,X104),times_times(X105)),X106),one_one(X105)),hAPP(fun(X104,bool),fun(X104,bool),hAPP(fun(X104,bool),fun(fun(X104,bool),fun(X104,bool)),semilattice_sup_sup(fun(X104,bool)),X108),X107)) = hAPP(X105,X105,hAPP(X105,fun(X105,X105),times_times(X105),hAPP(fun(X104,bool),X105,hAPP(X105,fun(fun(X104,bool),X105),hAPP(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105)),hAPP(fun(X105,fun(X105,X105)),fun(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105))),finite_fold_image(X105,X104),times_times(X105)),X106),one_one(X105)),X108)),hAPP(fun(X104,bool),X105,hAPP(X105,fun(fun(X104,bool),X105),hAPP(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105)),hAPP(fun(X105,fun(X105,X105)),fun(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105))),finite_fold_image(X105,X104),times_times(X105)),X106),one_one(X105)),X107))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X107))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X108))
| ~ comm_monoid_mult(X105) )
& ( hAPP(X104,X105,X106,esk173_5(X104,X105,X106,X107,X108)) != one_one(X105)
| hAPP(fun(X104,bool),X105,hAPP(X105,fun(fun(X104,bool),X105),hAPP(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105)),hAPP(fun(X105,fun(X105,X105)),fun(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105))),finite_fold_image(X105,X104),times_times(X105)),X106),one_one(X105)),hAPP(fun(X104,bool),fun(X104,bool),hAPP(fun(X104,bool),fun(fun(X104,bool),fun(X104,bool)),semilattice_sup_sup(fun(X104,bool)),X108),X107)) = hAPP(X105,X105,hAPP(X105,fun(X105,X105),times_times(X105),hAPP(fun(X104,bool),X105,hAPP(X105,fun(fun(X104,bool),X105),hAPP(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105)),hAPP(fun(X105,fun(X105,X105)),fun(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105))),finite_fold_image(X105,X104),times_times(X105)),X106),one_one(X105)),X108)),hAPP(fun(X104,bool),X105,hAPP(X105,fun(fun(X104,bool),X105),hAPP(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105)),hAPP(fun(X105,fun(X105,X105)),fun(fun(X104,X105),fun(X105,fun(fun(X104,bool),X105))),finite_fold_image(X105,X104),times_times(X105)),X106),one_one(X105)),X107))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X107))
| ~ hBOOL(hAPP(fun(X104,bool),bool,finite_finite_1(X104),X108))
| ~ comm_monoid_mult(X105) ) ),
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_1224])])])])]) ).
fof(c_0_2392,plain,
! [X30,X31] : 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),X30)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X31))))),
inference(variable_rename,[status(thm)],[c_0_1225]) ).
fof(c_0_2393,plain,
! [X41,X42,X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X46),X47)))
| ~ hBOOL(hAPP(fun(X43,bool),bool,hAPP(fun(X43,X41),fun(fun(X43,bool),bool),inj_on(X43,X41),X46),X47))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X44),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X45),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X46),X47))))
| hAPP(X42,X43,hAPP(fun(X43,X42),fun(X42,X43),hAPP(fun(X43,bool),fun(fun(X43,X42),fun(X42,X43)),the_inv_into(X43,X42),X47),hAPP(fun(X43,X41),fun(X43,X42),hAPP(fun(X41,X42),fun(fun(X43,X41),fun(X43,X42)),comp(X41,X42,X43),X45),X46)),X44) = hAPP(X42,X43,hAPP(fun(X42,X41),fun(X42,X43),hAPP(fun(X41,X43),fun(fun(X42,X41),fun(X42,X43)),comp(X41,X43,X42),hAPP(fun(X43,X41),fun(X41,X43),hAPP(fun(X43,bool),fun(fun(X43,X41),fun(X41,X43)),the_inv_into(X43,X41),X47),X46)),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),the_inv_into(X41,X42),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X46),X47)),X45)),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1226])]) ).
fof(c_0_2394,plain,
! [X41,X42,X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X46),X47)))
| ~ hBOOL(hAPP(fun(X43,bool),bool,hAPP(fun(X43,X41),fun(fun(X43,bool),bool),inj_on(X43,X41),X46),X47))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X44),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X45),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X46),X47))))
| hAPP(X42,X43,hAPP(fun(X43,X42),fun(X42,X43),hAPP(fun(X43,bool),fun(fun(X43,X42),fun(X42,X43)),hilbert_inv_into(X43,X42),X47),hAPP(fun(X43,X41),fun(X43,X42),hAPP(fun(X41,X42),fun(fun(X43,X41),fun(X43,X42)),comp(X41,X42,X43),X45),X46)),X44) = hAPP(X42,X43,hAPP(fun(X42,X41),fun(X42,X43),hAPP(fun(X41,X43),fun(fun(X42,X41),fun(X42,X43)),comp(X41,X43,X42),hAPP(fun(X43,X41),fun(X41,X43),hAPP(fun(X43,bool),fun(fun(X43,X41),fun(X41,X43)),hilbert_inv_into(X43,X41),X47),X46)),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),hilbert_inv_into(X41,X42),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X46),X47)),X45)),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1227])]) ).
fof(c_0_2395,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,bool),fun(fun(X43,bool),fun(X43,bool)),semilattice_inf_inf(fun(X43,bool)),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X44)),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X45)),X46))
| hBOOL(hAPP(fun(X43,bool),bool,hAPP(X43,fun(fun(X43,bool),bool),member(X43),X46),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,bool),fun(fun(X43,bool),fun(X43,bool)),semilattice_inf_inf(fun(X43,bool)),X44),X45))) )
& ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),X50),hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,bool),fun(fun(X47,bool),fun(X47,bool)),semilattice_inf_inf(fun(X47,bool)),X48),X49)))
| hBOOL(hAPP(X47,bool,hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,bool),fun(fun(X47,bool),fun(X47,bool)),semilattice_inf_inf(fun(X47,bool)),hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,fun(fun(X47,bool),bool)),fun(fun(X47,bool),fun(X47,bool)),combc(X47,fun(X47,bool),bool),member(X47)),X48)),hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,fun(fun(X47,bool),bool)),fun(fun(X47,bool),fun(X47,bool)),combc(X47,fun(X47,bool),bool),member(X47)),X49)),X50)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1228])])])]) ).
fof(c_0_2396,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,bool),fun(fun(X43,bool),fun(X43,bool)),semilattice_sup_sup(fun(X43,bool)),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X44)),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X45)),X46))
| hBOOL(hAPP(fun(X43,bool),bool,hAPP(X43,fun(fun(X43,bool),bool),member(X43),X46),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,bool),fun(fun(X43,bool),fun(X43,bool)),semilattice_sup_sup(fun(X43,bool)),X44),X45))) )
& ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),X50),hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,bool),fun(fun(X47,bool),fun(X47,bool)),semilattice_sup_sup(fun(X47,bool)),X48),X49)))
| hBOOL(hAPP(X47,bool,hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,bool),fun(fun(X47,bool),fun(X47,bool)),semilattice_sup_sup(fun(X47,bool)),hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,fun(fun(X47,bool),bool)),fun(fun(X47,bool),fun(X47,bool)),combc(X47,fun(X47,bool),bool),member(X47)),X48)),hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,fun(fun(X47,bool),bool)),fun(fun(X47,bool),fun(X47,bool)),combc(X47,fun(X47,bool),bool),member(X47)),X49)),X50)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1229])])])]) ).
fof(c_0_2397,plain,
! [X16,X17,X18,X19,X20] :
( ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X17)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X19)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X20)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X17)),X18))
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X19)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X17)),X18))
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X17)),X18))
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X20),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X20)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1230])])]) ).
fof(c_0_2398,plain,
! [X16,X17,X18,X19,X20] :
( ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X17)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X20)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X19)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X19)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X20)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X19)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X19)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X17) = ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ti(arrow_2142409994le_alt,X16) != ti(arrow_2142409994le_alt,X19)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ti(arrow_2142409994le_alt,X17) != ti(arrow_2142409994le_alt,X20)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X19)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X19)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X17)),X18))
| ti(arrow_2142409994le_alt,X16) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X18),X19),X20)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X19) = ti(arrow_2142409994le_alt,X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1231])])]) ).
fof(c_0_2399,plain,
! [X53,X54,X55,X56,X57] :
( ( hBOOL(hAPP(fun(X54,bool),bool,hAPP(X54,fun(fun(X54,bool),bool),member(X54),esk59_5(X53,X54,X55,X56,X57)),X57))
| hBOOL(hAPP(fun(fun(X54,X53),bool),bool,hAPP(fun(fun(X54,X53),bool),fun(fun(fun(X54,X53),bool),bool),ord_less_eq(fun(fun(X54,X53),bool)),hAPP(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool),hAPP(fun(X54,bool),fun(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool)),pi(X54,X53),X57),X55)),hAPP(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool),hAPP(fun(X54,bool),fun(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool)),pi(X54,X53),X57),X56))) )
& ( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),hAPP(X54,fun(X53,bool),X55,esk59_5(X53,X54,X55,X56,X57))),hAPP(X54,fun(X53,bool),X56,esk59_5(X53,X54,X55,X56,X57))))
| hBOOL(hAPP(fun(fun(X54,X53),bool),bool,hAPP(fun(fun(X54,X53),bool),fun(fun(fun(X54,X53),bool),bool),ord_less_eq(fun(fun(X54,X53),bool)),hAPP(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool),hAPP(fun(X54,bool),fun(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool)),pi(X54,X53),X57),X55)),hAPP(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool),hAPP(fun(X54,bool),fun(fun(X54,fun(X53,bool)),fun(fun(X54,X53),bool)),pi(X54,X53),X57),X56))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1232])])])]) ).
fof(c_0_2400,plain,
! [X8,X9,X10,X11,X12] :
( ( ti(X8,X9) = zero_zero(X8)
| ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X9),X9)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X10),X10))),zero_zero(X8)))
| ~ linord581940658strict(X8) )
& ( ti(X8,X10) = zero_zero(X8)
| ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X9),X9)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X10),X10))),zero_zero(X8)))
| ~ linord581940658strict(X8) )
& ( ti(X8,X11) != zero_zero(X8)
| ti(X8,X12) != zero_zero(X8)
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X11),X11)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X12),X12))),zero_zero(X8)))
| ~ linord581940658strict(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_1233])])])])]) ).
fof(c_0_2401,plain,
! [X36,X37,X38] :
( ~ linordered_ring(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),plus_plus(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),times_times(X36),X37),X37)),hAPP(X36,X36,hAPP(X36,fun(X36,X36),times_times(X36),X38),X38))),zero_zero(X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1234])])]) ).
fof(c_0_2402,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_1235])])])]) ).
fof(c_0_2403,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X55)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X55),X56))),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X56),X54)) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X55)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X56))),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X56),X54)),
inference(variable_rename,[status(thm)],[c_0_1236]) ).
fof(c_0_2404,plain,
! [X44,X45,X46,X47,X48] :
( ( hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),esk132_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)),hAPP(fun(X45,bool),fun(X45,X44),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X45,X44)),restrict(X45,X44),X46),X48)),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,esk132_5(X44,X45,X46,X47,X48))),hAPP(X45,fun(X44,bool),X47,esk132_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)),hAPP(fun(X45,bool),fun(X45,X44),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X45,X44)),restrict(X45,X44),X46),X48)),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_1237])])])]) ).
fof(c_0_2405,plain,
! [X43,X44,X45,X46,X49,X50,X51,X52,X53,X54,X55,X56] :
( ( ~ hBOOL(hAPP(fun(product_prod(X43,X44),bool),bool,hAPP(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool),member(product_prod(X43,X44)),hAPP(X44,product_prod(X43,X44),hAPP(X43,fun(X44,product_prod(X43,X44)),product_Pair(X43,X44),esk22_4(X43,X44,X45,X46)),esk23_4(X43,X44,X45,X46))),X46))
| ~ hBOOL(hAPP(fun(product_prod(X43,X44),bool),bool,hAPP(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool),member(product_prod(X43,X44)),hAPP(X44,product_prod(X43,X44),hAPP(X43,fun(X44,product_prod(X43,X44)),product_Pair(X43,X44),esk22_4(X43,X44,X45,X46)),esk23_4(X43,X44,X45,X46))),X45))
| ti(fun(product_prod(X43,X44),bool),X46) = ti(fun(product_prod(X43,X44),bool),X45) )
& ( hBOOL(hAPP(fun(product_prod(X43,X44),bool),bool,hAPP(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool),member(product_prod(X43,X44)),hAPP(X44,product_prod(X43,X44),hAPP(X43,fun(X44,product_prod(X43,X44)),product_Pair(X43,X44),esk22_4(X43,X44,X45,X46)),esk23_4(X43,X44,X45,X46))),X46))
| hBOOL(hAPP(fun(product_prod(X43,X44),bool),bool,hAPP(product_prod(X43,X44),fun(fun(product_prod(X43,X44),bool),bool),member(product_prod(X43,X44)),hAPP(X44,product_prod(X43,X44),hAPP(X43,fun(X44,product_prod(X43,X44)),product_Pair(X43,X44),esk22_4(X43,X44,X45,X46)),esk23_4(X43,X44,X45,X46))),X45))
| ti(fun(product_prod(X43,X44),bool),X46) = ti(fun(product_prod(X43,X44),bool),X45) )
& ( ~ hBOOL(hAPP(fun(product_prod(X49,X50),bool),bool,hAPP(product_prod(X49,X50),fun(fun(product_prod(X49,X50),bool),bool),member(product_prod(X49,X50)),hAPP(X50,product_prod(X49,X50),hAPP(X49,fun(X50,product_prod(X49,X50)),product_Pair(X49,X50),X53),X54)),X52))
| hBOOL(hAPP(fun(product_prod(X49,X50),bool),bool,hAPP(product_prod(X49,X50),fun(fun(product_prod(X49,X50),bool),bool),member(product_prod(X49,X50)),hAPP(X50,product_prod(X49,X50),hAPP(X49,fun(X50,product_prod(X49,X50)),product_Pair(X49,X50),X53),X54)),X51))
| ti(fun(product_prod(X49,X50),bool),X52) != ti(fun(product_prod(X49,X50),bool),X51) )
& ( ~ hBOOL(hAPP(fun(product_prod(X49,X50),bool),bool,hAPP(product_prod(X49,X50),fun(fun(product_prod(X49,X50),bool),bool),member(product_prod(X49,X50)),hAPP(X50,product_prod(X49,X50),hAPP(X49,fun(X50,product_prod(X49,X50)),product_Pair(X49,X50),X55),X56)),X51))
| hBOOL(hAPP(fun(product_prod(X49,X50),bool),bool,hAPP(product_prod(X49,X50),fun(fun(product_prod(X49,X50),bool),bool),member(product_prod(X49,X50)),hAPP(X50,product_prod(X49,X50),hAPP(X49,fun(X50,product_prod(X49,X50)),product_Pair(X49,X50),X55),X56)),X52))
| ti(fun(product_prod(X49,X50),bool),X52) != ti(fun(product_prod(X49,X50),bool),X51) ) ),
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_1238])])])])])]) ).
fof(c_0_2406,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
c_0_1239 ).
fof(c_0_2407,plain,
! [X77,X78,X79,X80,X81,X82] :
( ( hBOOL(hAPP(fun(X77,bool),bool,hAPP(X77,fun(fun(X77,bool),bool),member(X77),esk137_6(X77,X78,X79,X80,X81,X82)),X82))
| hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),X80),X79),X82) = hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),X81),X79),X82)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X82))
| ~ ab_semigroup_mult(X78) )
& ( hAPP(X77,X78,X80,esk137_6(X77,X78,X79,X80,X81,X82)) != hAPP(X77,X78,X81,esk137_6(X77,X78,X79,X80,X81,X82))
| hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),X80),X79),X82) = hAPP(fun(X77,bool),X78,hAPP(X78,fun(fun(X77,bool),X78),hAPP(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X78,fun(fun(X77,bool),X78))),finite_fold_image(X78,X77),times_times(X78)),X81),X79),X82)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X82))
| ~ ab_semigroup_mult(X78) ) ),
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_1240])])])])]) ).
fof(c_0_2408,plain,
! [X54,X55,X56] :
( ( ~ 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),fconj),X56)),X55)))) )
& ( ~ 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),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),fconj),X56)),X55)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1241])])]) ).
fof(c_0_2409,plain,
! [X67,X68] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk75_2(X67,X68)),hAPP(nat,nat,X68,esk75_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_1242])])]) ).
fof(c_0_2410,plain,
! [X77,X78,X79,X80,X81,X82,X83,X84] :
( ~ hBOOL(hAPP(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool,hAPP(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool),hAPP(fun(X78,fun(X78,X78)),fun(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool)),finite_folding_image(X78,X77),X82),X83),X84))
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,hAPP(fun(X77,X78),fun(X77,X78),hAPP(fun(X77,fun(X78,X78)),fun(fun(X77,X78),fun(X77,X78)),combs(X77,X78,X78),hAPP(fun(X77,X78),fun(X77,fun(X78,X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X77,fun(X78,X78))),combb(X78,fun(X78,X78),X77),X82),X79)),X80)),X81) = hAPP(X78,X78,hAPP(X78,fun(X78,X78),X82,hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X79),X81)),hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X80),X81)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1243])]) ).
fof(c_0_2411,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_1244])])])]) ).
fof(c_0_2412,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_1245])])])]) ).
fof(c_0_2413,plain,
! [X44,X45,X46,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),hAPP(fun(X45,bool),fun(X45,bool),hAPP(fun(X45,bool),fun(fun(X45,bool),fun(X45,bool)),semilattice_inf_inf(fun(X45,bool)),X47),X48))),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(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)],[c_0_1246]) ).
fof(c_0_2414,plain,
! [X44,X45,X46,X47,X48] :
( hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X47) != ti(fun(X45,bool),X48)
| hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),hAPP(fun(X45,bool),fun(X45,X44),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X45,X44)),restrict(X45,X44),hAPP(fun(X44,X45),fun(X45,X44),hAPP(fun(X44,bool),fun(fun(X44,X45),fun(X45,X44)),hilbert_inv_into(X44,X45),X47),X46)),X48)),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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1247])]) ).
fof(c_0_2415,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_1248])])])]) ).
fof(c_0_2416,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ linord1278240602ring_1(X91)
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),X95),X96))
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),X94),X96))
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),zero_zero(X91)),X93))
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),zero_zero(X91)),X92))
| hAPP(X91,X91,hAPP(X91,fun(X91,X91),plus_plus(X91),X93),X92) != one_one(X91)
| hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),hAPP(X91,X91,hAPP(X91,fun(X91,X91),plus_plus(X91),hAPP(X91,X91,hAPP(X91,fun(X91,X91),times_times(X91),X93),X95)),hAPP(X91,X91,hAPP(X91,fun(X91,X91),times_times(X91),X92),X94))),X96)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1249])])]) ).
fof(c_0_2417,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ linord626643107strict(X91)
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less(X91),X95),X96))
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less(X91),X94),X96))
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),zero_zero(X91)),X93))
| ~ hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less_eq(X91),zero_zero(X91)),X92))
| hAPP(X91,X91,hAPP(X91,fun(X91,X91),plus_plus(X91),X93),X92) != one_one(X91)
| hBOOL(hAPP(X91,bool,hAPP(X91,fun(X91,bool),ord_less(X91),hAPP(X91,X91,hAPP(X91,fun(X91,X91),plus_plus(X91),hAPP(X91,X91,hAPP(X91,fun(X91,X91),times_times(X91),X93),X95)),hAPP(X91,X91,hAPP(X91,fun(X91,X91),times_times(X91),X92),X94))),X96)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1250])])]) ).
fof(c_0_2418,plain,
! [X44,X45,X46,X47,X48] :
( ( hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),esk133_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)),hAPP(fun(X45,bool),fun(X45,X44),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X45,X44)),restrict(X45,X44),X46),X48)),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,esk133_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)),hAPP(fun(X45,bool),fun(X45,X44),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X45,X44)),restrict(X45,X44),X46),X48)),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_1251])])])]) ).
fof(c_0_2419,plain,
! [X37,X38,X39,X40] :
( ~ lattice(X37)
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X40))),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1252])])]) ).
fof(c_0_2420,plain,
! [X72,X73,X74,X75,X76,X77] :
( ( hBOOL(hAPP(fun(X73,bool),bool,hAPP(X73,fun(fun(X73,bool),bool),member(X73),esk147_6(X72,X73,X74,X75,X76,X77)),X77))
| hAPP(fun(X73,bool),fun(X72,bool),hAPP(fun(X73,X72),fun(fun(X73,bool),fun(X72,bool)),image(X73,X72),X74),X76) = hAPP(fun(X73,bool),fun(X72,bool),hAPP(fun(X73,X72),fun(fun(X73,bool),fun(X72,bool)),image(X73,X72),X75),X77)
| ti(fun(X73,bool),X76) != ti(fun(X73,bool),X77) )
& ( hAPP(X73,X72,X74,esk147_6(X72,X73,X74,X75,X76,X77)) != hAPP(X73,X72,X75,esk147_6(X72,X73,X74,X75,X76,X77))
| hAPP(fun(X73,bool),fun(X72,bool),hAPP(fun(X73,X72),fun(fun(X73,bool),fun(X72,bool)),image(X73,X72),X74),X76) = hAPP(fun(X73,bool),fun(X72,bool),hAPP(fun(X73,X72),fun(fun(X73,bool),fun(X72,bool)),image(X73,X72),X75),X77)
| ti(fun(X73,bool),X76) != ti(fun(X73,bool),X77) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1253])])])]) ).
fof(c_0_2421,plain,
! [X44,X45,X46] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46) = hAPP(fun(X44,bool),fun(X44,bool),collect(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(bool,bool)),fun(fun(X44,bool),fun(X44,bool)),combs(X44,bool,bool),hAPP(fun(X44,bool),fun(X44,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X44,bool),fun(X44,fun(bool,bool))),combb(bool,fun(bool,bool),X44),fconj),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X45))),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X46))),
inference(variable_rename,[status(thm)],[c_0_1254]) ).
fof(c_0_2422,plain,
! [X44,X45,X46] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46) = hAPP(fun(X44,bool),fun(X44,bool),collect(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(bool,bool)),fun(fun(X44,bool),fun(X44,bool)),combs(X44,bool,bool),hAPP(fun(X44,bool),fun(X44,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X44,bool),fun(X44,fun(bool,bool))),combb(bool,fun(bool,bool),X44),fdisj),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X45))),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,fun(fun(X44,bool),bool)),fun(fun(X44,bool),fun(X44,bool)),combc(X44,fun(X44,bool),bool),member(X44)),X46))),
inference(variable_rename,[status(thm)],[c_0_1255]) ).
fof(c_0_2423,plain,
! [X114,X115,X116,X117,X118] :
( ~ comm_monoid_add(X114)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X117),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X118),one_one(nat))))
| hAPP(fun(nat,bool),X114,hAPP(fun(nat,X114),fun(fun(nat,bool),X114),big_co1399186613setsum(nat,X114),X115),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X117),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X118),X116))) = hAPP(X114,X114,hAPP(X114,fun(X114,X114),plus_plus(X114),hAPP(fun(nat,bool),X114,hAPP(fun(nat,X114),fun(fun(nat,bool),X114),big_co1399186613setsum(nat,X114),X115),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X117),X118))),hAPP(fun(nat,bool),X114,hAPP(fun(nat,X114),fun(fun(nat,bool),X114),big_co1399186613setsum(nat,X114),X115),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X118),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X118),X116)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1256])])]) ).
fof(c_0_2424,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_1257])]) ).
fof(c_0_2425,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,finite_finite_1(X44),X46))
| hAPP(fun(X44,bool),X45,X51,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X47),X46)) = hAPP(X45,X45,hAPP(X45,fun(X45,X45),X48,hAPP(fun(X44,bool),X45,X51,X47)),hAPP(fun(X44,bool),X45,X51,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1258])]) ).
fof(c_0_2426,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_1259])])])]) ).
fof(c_0_2427,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ~ hBOOL(hAPP(fun(fun(X41,bool),X42),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,bool),X42),bool),hAPP(X42,fun(fun(X41,X42),fun(fun(fun(X41,bool),X42),bool)),hAPP(fun(X42,fun(X42,X42)),fun(X42,fun(fun(X41,X42),fun(fun(fun(X41,bool),X42),bool))),finite908156982e_idem(X42,X41),X45),X46),X47),X48))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X44))
| hAPP(X42,X42,hAPP(X42,fun(X42,X42),X45,hAPP(X41,X42,X47,X43)),hAPP(fun(X41,bool),X42,X48,X44)) = hAPP(fun(X41,bool),X42,X48,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1260])]) ).
fof(c_0_2428,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_1261])]) ).
fof(c_0_2429,plain,
! [X44,X45,X46,X47,X48] :
( ( hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),esk131_5(X44,X45,X46,X47,X48)),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),X48)),X47)) )
& ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),hAPP(X45,X44,X46,esk131_5(X44,X45,X46,X47,X48))),X47))
| 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),X48)),X47)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1262])])])]) ).
fof(c_0_2430,plain,
! [X27,X28,X29,X30,X32,X36] :
( ( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X27))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X28),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X29),X30)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X28,esk14_4(X27,X28,X29,X30))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X29),X30)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X27,X28))) )
& ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk15_1(X32)),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X32)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X32)),esk17_1(X32))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk15_1(X32),X36)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X32)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X32)),esk17_1(X32))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X32,esk15_1(X32))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,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_1263])])])])])]) ).
fof(c_0_2431,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X48),X49))
| ~ 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),X49)),X47))
| ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,X44),fun(fun(X45,bool),bool),inj_on(X45,X44),X46),X47))
| ~ 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)),X49))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X49))
| ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X47))
| hAPP(fun(X44,bool),nat,finite_card(X44),X49) = hAPP(fun(X45,bool),nat,finite_card(X45),X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1264])]) ).
fof(c_0_2432,plain,
! [X37,X38,X39,X40] :
( ~ lattice(X37)
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40))),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X40)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1265])])]) ).
fof(c_0_2433,plain,
! [X77,X78,X79,X80,X81] :
( ~ comm_monoid_add(X78)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),big_co1399186613setsum(X77,X78),hAPP(fun(X77,X78),fun(X77,X78),hAPP(fun(X77,fun(X78,X78)),fun(fun(X77,X78),fun(X77,X78)),combs(X77,X78,X78),hAPP(fun(X77,X78),fun(X77,fun(X78,X78)),hAPP(fun(X78,fun(X78,X78)),fun(fun(X77,X78),fun(X77,fun(X78,X78))),combb(X78,fun(X78,X78),X77),plus_plus(X78)),X79)),X80)),X81) = hAPP(X78,X78,hAPP(X78,fun(X78,X78),plus_plus(X78),hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),big_co1399186613setsum(X77,X78),X79),X81)),hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),big_co1399186613setsum(X77,X78),X80),X81)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1266])])]) ).
fof(c_0_2434,plain,
! [X40,X41,X42,X43,X44,X45,X46] :
( ~ 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),X43),X44),X45),X46))
| hAPP(X41,X41,hAPP(X41,fun(X41,X41),X43,X42),X42) = ti(X41,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1267])])])]) ).
fof(c_0_2435,plain,
! [X41,X42,X43,X44,X45] :
( ~ comm_monoid_add(X42)
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),hAPP(fun(X41,X42),fun(X41,X42),hAPP(fun(X41,fun(X42,X42)),fun(fun(X41,X42),fun(X41,X42)),combs(X41,X42,X42),hAPP(fun(X41,X42),fun(X41,fun(X42,X42)),hAPP(fun(X42,fun(X42,X42)),fun(fun(X41,X42),fun(X41,fun(X42,X42))),combb(X42,fun(X42,X42),X41),plus_plus(X42)),X43)),X44)),X45) = hAPP(X42,X42,hAPP(X42,fun(X42,X42),plus_plus(X42),hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X43),X45)),hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1268])])]) ).
fof(c_0_2436,plain,
! [X41,X42,X43,X44,X45] :
( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk124_5(X41,X42,X43,X44,X45)),X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk124_5(X41,X42,X43,X44,X45)),X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk125_5(X41,X42,X43,X44,X45)),X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk125_5(X41,X42,X43,X44,X45)),X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk124_5(X41,X42,X43,X44,X45))) != hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk125_5(X41,X42,X43,X44,X45)))
| hAPP(X42,X41,X43,esk124_5(X41,X42,X43,X44,X45)) != hAPP(X42,X41,X43,esk125_5(X41,X42,X43,X44,X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk124_5(X41,X42,X43,X44,X45))) != hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk125_5(X41,X42,X43,X44,X45)))
| hAPP(X42,X41,X43,esk124_5(X41,X42,X43,X44,X45)) != hAPP(X42,X41,X43,esk125_5(X41,X42,X43,X44,X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk124_5(X41,X42,X43,X44,X45))) = hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk125_5(X41,X42,X43,X44,X45)))
| hAPP(X42,X41,X43,esk124_5(X41,X42,X43,X44,X45)) = hAPP(X42,X41,X43,esk125_5(X41,X42,X43,X44,X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,X42),fun(fun(X42,bool),fun(X42,bool)),image(X42,X42),X44),X45)))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X42),fun(fun(X42,bool),bool),inj_on(X42,X42),X44),X45))
| hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk124_5(X41,X42,X43,X44,X45))) = hAPP(X42,X41,X43,hAPP(X42,X42,X44,esk125_5(X41,X42,X43,X44,X45)))
| hAPP(X42,X41,X43,esk124_5(X41,X42,X43,X44,X45)) = hAPP(X42,X41,X43,esk125_5(X41,X42,X43,X44,X45)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1269])])])]) ).
fof(c_0_2437,plain,
! [X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X43,nat,X45,X46)),hAPP(X43,nat,X45,X47)))
| ~ hBOOL(hAPP(fun(product_prod(X43,X43),bool),bool,hAPP(product_prod(X43,X43),fun(fun(product_prod(X43,X43),bool),bool),member(product_prod(X43,X43)),hAPP(X43,product_prod(X43,X43),hAPP(X43,fun(X43,product_prod(X43,X43)),product_Pair(X43,X43),X46),X47)),X44))
| hBOOL(hAPP(fun(product_prod(X43,X43),bool),bool,hAPP(product_prod(X43,X43),fun(fun(product_prod(X43,X43),bool),bool),member(product_prod(X43,X43)),hAPP(X43,product_prod(X43,X43),hAPP(X43,fun(X43,product_prod(X43,X43)),product_Pair(X43,X43),X46),X47)),hAPP(fun(product_prod(X43,X43),bool),fun(product_prod(X43,X43),bool),hAPP(fun(X43,nat),fun(fun(product_prod(X43,X43),bool),fun(product_prod(X43,X43),bool)),mlex_prod(X43),X45),X44))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1270])]) ).
fof(c_0_2438,plain,
! [X107,X108,X109,X110,X111] :
( ~ semiring_0(X108)
| hAPP(X108,X108,hAPP(X108,fun(X108,X108),times_times(X108),hAPP(fun(X107,bool),X108,hAPP(fun(X107,X108),fun(fun(X107,bool),X108),big_co1399186613setsum(X107,X108),X109),X110)),X111) = hAPP(fun(X107,bool),X108,hAPP(fun(X107,X108),fun(fun(X107,bool),X108),big_co1399186613setsum(X107,X108),hAPP(X108,fun(X107,X108),hAPP(fun(X107,fun(X108,X108)),fun(X108,fun(X107,X108)),combc(X107,X108,X108),hAPP(fun(X107,X108),fun(X107,fun(X108,X108)),hAPP(fun(X108,fun(X108,X108)),fun(fun(X107,X108),fun(X107,fun(X108,X108))),combb(X108,fun(X108,X108),X107),times_times(X108)),X109)),X111)),X110) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1271])])]) ).
fof(c_0_2439,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X41,bool),nat,finite_card(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44))),hAPP(fun(X42,bool),nat,finite_card(X42),X44)))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1272])]) ).
fof(c_0_2440,plain,
! [X9,X10,X11] :
( ti(arrow_2142409994le_alt,X10) = ti(arrow_2142409994le_alt,X11)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X9),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X9),X10),X11)),arrow_1568854078le_Lin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1273])]) ).
fof(c_0_2441,plain,
! [X9,X10,X11] :
( ti(arrow_2142409994le_alt,X10) = ti(arrow_2142409994le_alt,X11)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X9),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X9),X10),X11)),arrow_1568854078le_Lin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1274])]) ).
fof(c_0_2442,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X48),X49))
| ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),X47),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X48),X49)))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X49),X46))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),hAPP(X45,X44,hAPP(fun(X44,X45),fun(X45,X44),hAPP(fun(X44,bool),fun(fun(X44,X45),fun(X45,X44)),the_inv_into(X44,X45),X49),X48),X47)),X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1275])]) ).
fof(c_0_2443,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X9),X9)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X10),X10))))
| ti(X8,X9) != zero_zero(X8)
| ti(X8,X10) != zero_zero(X8)
| ~ linord581940658strict(X8) )
& ( ti(X8,X11) = zero_zero(X8)
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X11),X11)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X12),X12))))
| ~ linord581940658strict(X8) )
& ( ti(X8,X12) = zero_zero(X8)
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X11),X11)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X12),X12))))
| ~ linord581940658strict(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_1276])])])])]) ).
fof(c_0_2444,plain,
! [X47,X48,X49,X50,X51] :
( ( hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),esk108_5(X47,X48,X49,X50,X51)),hAPP(fun(X47,bool),fun(X48,bool),hAPP(fun(X47,X48),fun(fun(X47,bool),fun(X48,bool)),image(X47,X48),X51),top_top(fun(X47,bool)))))
| hBOOL(hAPP(X47,bool,X50,X49))
| ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X51),top_top(fun(X47,bool)))) )
& ( ~ hBOOL(hAPP(X47,bool,X50,hAPP(X48,X47,hAPP(fun(X47,X48),fun(X48,X47),hAPP(fun(X47,bool),fun(fun(X47,X48),fun(X48,X47)),hilbert_inv_into(X47,X48),top_top(fun(X47,bool))),X51),esk108_5(X47,X48,X49,X50,X51))))
| hBOOL(hAPP(X47,bool,X50,X49))
| ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X51),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_1277])])])]) ).
fof(c_0_2445,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),times_times(nat),hAPP(nat,nat,suc,X58)),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,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),times_times(nat),hAPP(nat,nat,suc,X61)),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X61)),X63))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1278])])])]) ).
fof(c_0_2446,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),times_times(nat),hAPP(nat,nat,suc,X58)),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,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),times_times(nat),hAPP(nat,nat,suc,X61)),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X61)),X63))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1279])])])]) ).
fof(c_0_2447,plain,
! [X9,X10,X11] :
( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X9),X10)),X11))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X9)),X11))
| ti(arrow_2142409994le_alt,X9) = ti(arrow_2142409994le_alt,X10)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X11),arrow_1568854078le_Lin)) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X9)),X11))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X9),X10)),X11))
| ti(arrow_2142409994le_alt,X9) = ti(arrow_2142409994le_alt,X10)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X11),arrow_1568854078le_Lin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1280])])]) ).
fof(c_0_2448,plain,
! [X16,X17,X18] :
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X18),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X16),X17)),X18))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X17),X16)),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1281])]) ).
fof(c_0_2449,plain,
! [X43,X44,X45,X46,X47,X48] :
( ( ~ hBOOL(hAPP(fun(X43,bool),bool,hAPP(fun(X43,bool),fun(fun(X43,bool),bool),ord_less_eq(fun(X43,bool)),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X44)),hAPP(fun(X43,bool),fun(X43,bool),hAPP(fun(X43,fun(fun(X43,bool),bool)),fun(fun(X43,bool),fun(X43,bool)),combc(X43,fun(X43,bool),bool),member(X43)),X45)))
| hBOOL(hAPP(fun(X43,bool),bool,hAPP(fun(X43,bool),fun(fun(X43,bool),bool),ord_less_eq(fun(X43,bool)),X44),X45)) )
& ( ~ hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,bool),fun(fun(X46,bool),bool),ord_less_eq(fun(X46,bool)),X47),X48))
| hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,bool),fun(fun(X46,bool),bool),ord_less_eq(fun(X46,bool)),hAPP(fun(X46,bool),fun(X46,bool),hAPP(fun(X46,fun(fun(X46,bool),bool)),fun(fun(X46,bool),fun(X46,bool)),combc(X46,fun(X46,bool),bool),member(X46)),X47)),hAPP(fun(X46,bool),fun(X46,bool),hAPP(fun(X46,fun(fun(X46,bool),bool)),fun(fun(X46,bool),fun(X46,bool)),combc(X46,fun(X46,bool),bool),member(X46)),X48))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1282])])])]) ).
fof(c_0_2450,plain,
! [X77,X78,X79,X80,X81,X82,X83,X84] :
( ~ hBOOL(hAPP(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool,hAPP(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool),hAPP(fun(X78,fun(X78,X78)),fun(X78,fun(fun(fun(X77,X78),fun(fun(X77,bool),X78)),bool)),finite_folding_image(X78,X77),X82),X83),X84))
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| ~ hBOOL(hAPP(fun(X77,bool),bool,hAPP(fun(X77,X77),fun(fun(X77,bool),bool),inj_on(X77,X77),X80),X81))
| hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,X79),hAPP(fun(X77,bool),fun(X77,bool),hAPP(fun(X77,X77),fun(fun(X77,bool),fun(X77,bool)),image(X77,X77),X80),X81)) = hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),X84,hAPP(fun(X77,X77),fun(X77,X78),hAPP(fun(X77,X78),fun(fun(X77,X77),fun(X77,X78)),comp(X77,X78,X77),X79),X80)),X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1283])]) ).
fof(c_0_2451,plain,
! [X41,X42,X43,X44,X45,X46] : hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),hAPP(fun(X41,X43),fun(X41,X42),hAPP(fun(X43,X42),fun(fun(X41,X43),fun(X41,X42)),hAPP(fun(X41,bool),fun(fun(X43,X42),fun(fun(X41,X43),fun(X41,X42))),compose(X41,X43,X42),X44),X45),X46)),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X44))),
inference(variable_rename,[status(thm)],[c_0_1284]) ).
fof(c_0_2452,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(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X46),hAPP(fun(X44,bool),fun(fun(X44,X45),bool),extensional(X44,X45),X47)))
| hAPP(fun(X44,X45),fun(X44,X45),hAPP(fun(X45,X45),fun(fun(X44,X45),fun(X44,X45)),hAPP(fun(X44,bool),fun(fun(X45,X45),fun(fun(X44,X45),fun(X44,X45))),compose(X44,X45,X45),X47),hAPP(fun(X45,bool),fun(X45,X45),hAPP(fun(X45,X45),fun(fun(X45,bool),fun(X45,X45)),restrict(X45,X45),combi(X45)),X48)),X46) = ti(fun(X44,X45),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1285])]) ).
fof(c_0_2453,plain,
! [X40,X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),top_top(fun(X42,bool)))))
| hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),hAPP(fun(X42,bool),fun(X40,bool),hAPP(fun(X42,X40),fun(fun(X42,bool),fun(X40,bool)),image(X42,X40),hAPP(fun(X42,X41),fun(X42,X40),hAPP(fun(X41,X40),fun(fun(X42,X41),fun(X42,X40)),combb(X41,X40,X42),X43),X44)),top_top(fun(X42,bool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1286])]) ).
fof(c_0_2454,plain,
! [X77,X78,X79,X80,X81,X82,X83] :
( ~ ab_semigroup_mult(X79)
| ~ hBOOL(hAPP(fun(X78,bool),bool,finite_finite_1(X78),X83))
| ~ hBOOL(hAPP(fun(X78,bool),bool,hAPP(fun(X78,X77),fun(fun(X78,bool),bool),inj_on(X78,X77),X82),X83))
| hAPP(fun(X77,bool),X79,hAPP(X79,fun(fun(X77,bool),X79),hAPP(fun(X77,X79),fun(X79,fun(fun(X77,bool),X79)),hAPP(fun(X79,fun(X79,X79)),fun(fun(X77,X79),fun(X79,fun(fun(X77,bool),X79))),finite_fold_image(X79,X77),times_times(X79)),X80),X81),hAPP(fun(X78,bool),fun(X77,bool),hAPP(fun(X78,X77),fun(fun(X78,bool),fun(X77,bool)),image(X78,X77),X82),X83)) = hAPP(fun(X78,bool),X79,hAPP(X79,fun(fun(X78,bool),X79),hAPP(fun(X78,X79),fun(X79,fun(fun(X78,bool),X79)),hAPP(fun(X79,fun(X79,X79)),fun(fun(X78,X79),fun(X79,fun(fun(X78,bool),X79))),finite_fold_image(X79,X78),times_times(X79)),hAPP(fun(X78,X77),fun(X78,X79),hAPP(fun(X77,X79),fun(fun(X78,X77),fun(X78,X79)),comp(X77,X79,X78),X80),X82)),X81),X83) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1287])])]) ).
fof(c_0_2455,plain,
! [X44,X45,X46,X47,X48,X49] :
( ( 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(product_prod(fun(X44,bool),fun(X44,bool)),bool),bool,hAPP(product_prod(fun(X44,bool),fun(X44,bool)),fun(fun(product_prod(fun(X44,bool),fun(X44,bool)),bool),bool),member(product_prod(fun(X44,bool),fun(X44,bool))),hAPP(fun(X44,bool),product_prod(fun(X44,bool),fun(X44,bool)),hAPP(fun(X44,bool),fun(fun(X44,bool),product_prod(fun(X44,bool),fun(X44,bool))),product_Pair(fun(X44,bool),fun(X44,bool)),X45),X46)),finite_psubset(X44))) )
& ( hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
| ~ hBOOL(hAPP(fun(product_prod(fun(X44,bool),fun(X44,bool)),bool),bool,hAPP(product_prod(fun(X44,bool),fun(X44,bool)),fun(fun(product_prod(fun(X44,bool),fun(X44,bool)),bool),bool),member(product_prod(fun(X44,bool),fun(X44,bool))),hAPP(fun(X44,bool),product_prod(fun(X44,bool),fun(X44,bool)),hAPP(fun(X44,bool),fun(fun(X44,bool),product_prod(fun(X44,bool),fun(X44,bool))),product_Pair(fun(X44,bool),fun(X44,bool)),X45),X46)),finite_psubset(X44))) )
& ( ~ 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,finite_finite_1(X47),X49))
| hBOOL(hAPP(fun(product_prod(fun(X47,bool),fun(X47,bool)),bool),bool,hAPP(product_prod(fun(X47,bool),fun(X47,bool)),fun(fun(product_prod(fun(X47,bool),fun(X47,bool)),bool),bool),member(product_prod(fun(X47,bool),fun(X47,bool))),hAPP(fun(X47,bool),product_prod(fun(X47,bool),fun(X47,bool)),hAPP(fun(X47,bool),fun(fun(X47,bool),product_prod(fun(X47,bool),fun(X47,bool))),product_Pair(fun(X47,bool),fun(X47,bool)),X48),X49)),finite_psubset(X47))) ) ),
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_1288])])])])]) ).
fof(c_0_2456,plain,
! [X41,X42,X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(fun(X41,X42),fun(fun(X41,bool),X42)),bool,hAPP(X42,fun(fun(fun(X41,X42),fun(fun(X41,bool),X42)),bool),hAPP(fun(X42,fun(X42,X42)),fun(X42,fun(fun(fun(X41,X42),fun(fun(X41,bool),X42)),bool)),finite_folding_image(X42,X41),X45),X46),X47))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),X47,X43),X44) = hAPP(fun(X41,bool),X42,hAPP(X42,fun(fun(X41,bool),X42),hAPP(fun(X41,X42),fun(X42,fun(fun(X41,bool),X42)),hAPP(fun(X42,fun(X42,X42)),fun(fun(X41,X42),fun(X42,fun(fun(X41,bool),X42))),finite_fold_image(X42,X41),X45),X43),X46),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1289])]) ).
fof(c_0_2457,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( ti(arrow_2142409994le_alt,X10) != ti(arrow_2142409994le_alt,X13)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X12),X13))) )
& ( ti(arrow_2142409994le_alt,X11) != ti(arrow_2142409994le_alt,X13)
| ti(arrow_2142409994le_alt,X10) != ti(arrow_2142409994le_alt,X11)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X12),X13))) )
& ( ti(arrow_2142409994le_alt,X11) = ti(arrow_2142409994le_alt,X13)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),X12))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X12),X13))) )
& ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X15) = ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X16),X17))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X16))
| ti(arrow_2142409994le_alt,X15) = ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X16),X17))) )
& ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X15)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X16),X17))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X16))
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X15)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_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_1290])])])])]) ).
fof(c_0_2458,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( ti(arrow_2142409994le_alt,X11) != ti(arrow_2142409994le_alt,X13)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X12),X13))) )
& ( ti(arrow_2142409994le_alt,X10) != ti(arrow_2142409994le_alt,X13)
| ti(arrow_2142409994le_alt,X10) != ti(arrow_2142409994le_alt,X11)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X12),X13))) )
& ( ti(arrow_2142409994le_alt,X10) = ti(arrow_2142409994le_alt,X13)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),X12))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X10),X11)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X12),X13))) )
& ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X15) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X16),X17))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X16))
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X15) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X16),X17))) )
& ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X17)
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X15)
| ti(arrow_2142409994le_alt,X15) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X16),X17))) )
& ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X16))
| ti(arrow_2142409994le_alt,X14) = ti(arrow_2142409994le_alt,X15)
| ti(arrow_2142409994le_alt,X15) = ti(arrow_2142409994le_alt,X17)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_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_1291])])])])]) ).
fof(c_0_2459,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(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X46),hAPP(fun(X44,bool),fun(fun(X44,X45),bool),extensional(X44,X45),X47)))
| hAPP(fun(X44,X44),fun(X44,X45),hAPP(fun(X44,X45),fun(fun(X44,X44),fun(X44,X45)),hAPP(fun(X44,bool),fun(fun(X44,X45),fun(fun(X44,X44),fun(X44,X45))),compose(X44,X44,X45),X47),X46),hAPP(fun(X44,bool),fun(X44,X44),hAPP(fun(X44,X44),fun(fun(X44,bool),fun(X44,X44)),restrict(X44,X44),combi(X44)),X47)) = ti(fun(X44,X45),X46) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1292])])])]) ).
fof(c_0_2460,plain,
! [X41,X42,X43,X44,X45] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X45)))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),hAPP(X41,X42,hAPP(fun(X42,X41),fun(X41,X42),hAPP(fun(X42,bool),fun(fun(X42,X41),fun(X41,X42)),hilbert_inv_into(X42,X41),X45),X44),X43)),X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1293])]) ).
fof(c_0_2461,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_1294])])])]) ).
fof(c_0_2462,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
c_0_1295 ).
fof(c_0_2463,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_1296])])])])]) ).
fof(c_0_2464,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_1297])]) ).
fof(c_0_2465,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_sup_sup(fun(X45,fun(X44,bool))),X46),X47),X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X46,X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1298])]) ).
fof(c_0_2466,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_1299])])]) ).
fof(c_0_2467,plain,
! [X73,X74,X75,X76] :
( ~ order(X73)
| ~ hBOOL(hAPP(X73,bool,hAPP(X73,fun(X73,bool),ord_less(X73),hAPP(nat,X73,X76,esk92_4(X73,X74,X75,X76))),hAPP(nat,X73,X76,hAPP(nat,nat,suc,esk92_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_1300])])])]) ).
fof(c_0_2468,plain,
! [X73,X74,X75,X76] :
( ~ order(X73)
| ~ hBOOL(hAPP(X73,bool,hAPP(X73,fun(X73,bool),ord_less_eq(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_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_1301])])])]) ).
fof(c_0_2469,plain,
! [X58,X59,X60,X61,X62] :
( ~ comm_monoid_add(X58)
| hAPP(fun(nat,bool),X58,hAPP(fun(nat,X58),fun(fun(nat,bool),X58),big_co1399186613setsum(nat,X58),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X61)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X61))) = hAPP(fun(nat,bool),X58,hAPP(fun(nat,X58),fun(fun(nat,bool),X58),big_co1399186613setsum(nat,X58),hAPP(fun(nat,nat),fun(nat,X58),hAPP(fun(nat,X58),fun(fun(nat,nat),fun(nat,X58)),combb(nat,X58,nat),X59),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X61))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X60),X62)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1302])])]) ).
fof(c_0_2470,plain,
! [X58,X59,X60,X61,X62] :
( ~ comm_monoid_add(X58)
| hAPP(fun(nat,bool),X58,hAPP(fun(nat,X58),fun(fun(nat,bool),X58),big_co1399186613setsum(nat,X58),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X61)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X61))) = hAPP(fun(nat,bool),X58,hAPP(fun(nat,X58),fun(fun(nat,bool),X58),big_co1399186613setsum(nat,X58),hAPP(fun(nat,nat),fun(nat,X58),hAPP(fun(nat,X58),fun(fun(nat,nat),fun(nat,X58)),combb(nat,X58,nat),X59),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X61))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X60),X62)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1303])])]) ).
fof(c_0_2471,plain,
! [X44,X45,X46,X47,X48] :
( ~ comm_monoid_add(X45)
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X48))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X47))
| hAPP(X45,X45,hAPP(X45,fun(X45,X45),plus_plus(X45),hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X48),X47))),hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X48),X47))) = hAPP(X45,X45,hAPP(X45,fun(X45,X45),plus_plus(X45),hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),X46),X48)),hAPP(fun(X44,bool),X45,hAPP(fun(X44,X45),fun(fun(X44,bool),X45),big_co1399186613setsum(X44,X45),X46),X47)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1304])])]) ).
fof(c_0_2472,plain,
! [X106,X107,X108,X109,X110,X111] :
( ( ~ hBOOL(hAPP(fun(X108,bool),bool,hAPP(fun(X108,X106),fun(fun(X108,bool),bool),inj_on(X108,X106),X109),hAPP(fun(X107,bool),fun(X108,bool),hAPP(fun(X107,X108),fun(fun(X107,bool),fun(X108,bool)),image(X107,X108),X110),X111)))
| hBOOL(hAPP(fun(X107,bool),bool,hAPP(fun(X107,X106),fun(fun(X107,bool),bool),inj_on(X107,X106),hAPP(fun(X107,X108),fun(X107,X106),hAPP(fun(X108,X106),fun(fun(X107,X108),fun(X107,X106)),comp(X108,X106,X107),X109),X110)),X111))
| ~ hBOOL(hAPP(fun(X107,bool),bool,hAPP(fun(X107,X108),fun(fun(X107,bool),bool),inj_on(X107,X108),X110),X111)) )
& ( ~ hBOOL(hAPP(fun(X107,bool),bool,hAPP(fun(X107,X106),fun(fun(X107,bool),bool),inj_on(X107,X106),hAPP(fun(X107,X108),fun(X107,X106),hAPP(fun(X108,X106),fun(fun(X107,X108),fun(X107,X106)),comp(X108,X106,X107),X109),X110)),X111))
| hBOOL(hAPP(fun(X108,bool),bool,hAPP(fun(X108,X106),fun(fun(X108,bool),bool),inj_on(X108,X106),X109),hAPP(fun(X107,bool),fun(X108,bool),hAPP(fun(X107,X108),fun(fun(X107,bool),fun(X108,bool)),image(X107,X108),X110),X111)))
| ~ hBOOL(hAPP(fun(X107,bool),bool,hAPP(fun(X107,X108),fun(fun(X107,bool),bool),inj_on(X107,X108),X110),X111)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1305])])]) ).
fof(c_0_2473,plain,
! [X97,X98,X99,X100,X101] :
( ~ semiring(X97)
| hAPP(X97,X97,hAPP(X97,fun(X97,X97),plus_plus(X97),hAPP(X97,X97,hAPP(X97,fun(X97,X97),times_times(X97),X98),X99)),hAPP(X97,X97,hAPP(X97,fun(X97,X97),plus_plus(X97),hAPP(X97,X97,hAPP(X97,fun(X97,X97),times_times(X97),X100),X99)),X101)) = hAPP(X97,X97,hAPP(X97,fun(X97,X97),plus_plus(X97),hAPP(X97,X97,hAPP(X97,fun(X97,X97),times_times(X97),hAPP(X97,X97,hAPP(X97,fun(X97,X97),plus_plus(X97),X98),X100)),X99)),X101) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1306])])]) ).
fof(c_0_2474,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_1307])]) ).
fof(c_0_2475,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_inf_inf(fun(X45,fun(X44,bool))),X46),X47),X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X46,X48),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1308])]) ).
fof(c_0_2476,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_inf_inf(fun(X45,fun(X44,bool))),X46),X47),X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1309])]) ).
fof(c_0_2477,plain,
! [X44,X45,X46,X47,X48,X49] :
( ( hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X46,X48),X49))
| ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_inf_inf(fun(X45,fun(X44,bool))),X46),X47),X48),X49)) )
& ( hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49))
| ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_inf_inf(fun(X45,fun(X44,bool))),X46),X47),X48),X49)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1310])])]) ).
fof(c_0_2478,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_1311])]) ).
fof(c_0_2479,plain,
! [X85,X86,X87,X88,X89] :
( ( ~ hBOOL(hAPP(fun(X86,bool),bool,hAPP(fun(X86,X85),fun(fun(X86,bool),bool),inj_on(X86,X85),X89),X88))
| ~ hBOOL(hAPP(fun(X85,bool),bool,hAPP(fun(X85,bool),fun(fun(X85,bool),bool),ord_less_eq(fun(X85,bool)),hAPP(fun(X86,bool),fun(X85,bool),hAPP(fun(X86,X85),fun(fun(X86,bool),fun(X85,bool)),image(X86,X85),X89),X88)),X87))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X86,bool),nat,finite_card(X86),X88)),hAPP(fun(X85,bool),nat,finite_card(X85),X87)))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X87))
| ~ hBOOL(hAPP(fun(X86,bool),bool,finite_finite_1(X86),X88)) )
& ( hBOOL(hAPP(fun(X86,bool),bool,hAPP(fun(X86,X85),fun(fun(X86,bool),bool),inj_on(X86,X85),esk107_4(X85,X86,X87,X88)),X88))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X86,bool),nat,finite_card(X86),X88)),hAPP(fun(X85,bool),nat,finite_card(X85),X87)))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X87))
| ~ hBOOL(hAPP(fun(X86,bool),bool,finite_finite_1(X86),X88)) )
& ( hBOOL(hAPP(fun(X85,bool),bool,hAPP(fun(X85,bool),fun(fun(X85,bool),bool),ord_less_eq(fun(X85,bool)),hAPP(fun(X86,bool),fun(X85,bool),hAPP(fun(X86,X85),fun(fun(X86,bool),fun(X85,bool)),image(X86,X85),esk107_4(X85,X86,X87,X88)),X88)),X87))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X86,bool),nat,finite_card(X86),X88)),hAPP(fun(X85,bool),nat,finite_card(X85),X87)))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X87))
| ~ hBOOL(hAPP(fun(X86,bool),bool,finite_finite_1(X86),X88)) ) ),
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_1312])])])])]) ).
fof(c_0_2480,plain,
! [X91,X92,X93,X94] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X91),X92)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X93),X92)),X94)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X91),X93)),X92)),X94),
inference(variable_rename,[status(thm)],[c_0_1313]) ).
fof(c_0_2481,plain,
! [X41,X42,X43,X44,X45,X46] :
( hAPP(X41,X42,hAPP(fun(X42,X41),fun(X41,X42),hAPP(fun(X42,bool),fun(fun(X42,X41),fun(X41,X42)),hilbert_inv_into(X42,X41),X43),X44),X45) != hAPP(X41,X42,hAPP(fun(X42,X41),fun(X41,X42),hAPP(fun(X42,bool),fun(fun(X42,X41),fun(X41,X42)),hilbert_inv_into(X42,X41),X43),X44),X46)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X45),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X43)))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X43)))
| ti(X41,X45) = ti(X41,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1314])]) ).
fof(c_0_2482,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ order(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ order(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X85),X83))
| hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ order(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X86))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ order(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X87),X88))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ order(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ order(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X88),X90))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ order(X82) ) ),
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_1315])])])])]) ).
fof(c_0_2483,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(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),X47),X48)),X46))
| ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X46))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X48)),hAPP(fun(X45,bool),nat,finite_card(X45),X46))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1316])]) ).
fof(c_0_2484,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_1317])]) ).
fof(c_0_2485,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),hAPP(fun(X41,X43),fun(X41,X42),hAPP(fun(X43,X42),fun(fun(X41,X43),fun(X41,X42)),comp(X43,X42,X41),X44),X45)),X46))
| hBOOL(hAPP(fun(X43,bool),bool,hAPP(fun(X43,X42),fun(fun(X43,bool),bool),inj_on(X43,X42),X44),hAPP(fun(X41,bool),fun(X43,bool),hAPP(fun(X41,X43),fun(fun(X41,bool),fun(X43,bool)),image(X41,X43),X45),X46))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1318])]) ).
fof(c_0_2486,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_1319])]) ).
fof(c_0_2487,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X43),fun(fun(X42,bool),bool),inj_on(X42,X43),X45),X46))
| ~ hBOOL(hAPP(fun(X43,bool),bool,hAPP(fun(X43,X41),fun(fun(X43,bool),bool),inj_on(X43,X41),X44),hAPP(fun(X42,bool),fun(X43,bool),hAPP(fun(X42,X43),fun(fun(X42,bool),fun(X43,bool)),image(X42,X43),X45),X46)))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),hAPP(fun(X42,X43),fun(X42,X41),hAPP(fun(X43,X41),fun(fun(X42,X43),fun(X42,X41)),comp(X43,X41,X42),X44),X45)),X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1320])]) ).
fof(c_0_2488,plain,
! [X114,X115,X116,X117,X118] :
( ~ comm_monoid_add(X114)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X117),X118))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X118),X116))
| hAPP(X114,X114,hAPP(X114,fun(X114,X114),plus_plus(X114),hAPP(fun(nat,bool),X114,hAPP(fun(nat,X114),fun(fun(nat,bool),X114),big_co1399186613setsum(nat,X114),X115),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X117),X118))),hAPP(fun(nat,bool),X114,hAPP(fun(nat,X114),fun(fun(nat,bool),X114),big_co1399186613setsum(nat,X114),X115),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X118),X116))) = hAPP(fun(nat,bool),X114,hAPP(fun(nat,X114),fun(fun(nat,bool),X114),big_co1399186613setsum(nat,X114),X115),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X117),X116)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1321])])]) ).
fof(c_0_2489,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ dense_linorder(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ dense_linorder(X82) ) ),
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_1322])])])])]) ).
fof(c_0_2490,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X89),X90)))
| ~ dense_linorder(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X89),X90)))
| ~ dense_linorder(X82) ) ),
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_1323])])])])]) ).
fof(c_0_2491,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ order(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ order(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ order(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ order(X82) ) ),
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_1324])])])])]) ).
fof(c_0_2492,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ dense_linorder(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ dense_linorder(X82) ) ),
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_1325])])])])]) ).
fof(c_0_2493,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ dense_linorder(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastAtMost(X82),X89),X90)))
| ~ dense_linorder(X82) ) ),
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_1326])])])])]) ).
fof(c_0_2494,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X89),X90)))
| ~ dense_linorder(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr676655987ssThan(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X89),X90)))
| ~ dense_linorder(X82) ) ),
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_1327])])])])]) ).
fof(c_0_2495,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X84),X86))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ dense_linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X87),X88))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X89),X90)))
| ~ dense_linorder(X82) )
& ( ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X89),X87))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X88),X90))
| hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_gr1471790799AtMost(X82),X87),X88)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X89),X90)))
| ~ dense_linorder(X82) ) ),
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_1328])])])])]) ).
fof(c_0_2496,plain,
! [X41,X42,X43,X44,X45] :
( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk145_5(X41,X42,X43,X44,X45)),X45))
| ti(fun(X41,X42),X44) = ti(fun(X41,X42),X43)
| ~ hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),X43),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X45)))
| ~ hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),X44),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X45))) )
& ( hAPP(X41,X42,X44,esk145_5(X41,X42,X43,X44,X45)) != hAPP(X41,X42,X43,esk145_5(X41,X42,X43,X44,X45))
| ti(fun(X41,X42),X44) = ti(fun(X41,X42),X43)
| ~ hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),X43),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X45)))
| ~ hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),X44),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X45))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1329])])])]) ).
fof(c_0_2497,plain,
! [X36,X37,X38] :
( ~ linordered_ring(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),zero_zero(X36)),hAPP(X36,X36,hAPP(X36,fun(X36,X36),plus_plus(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),times_times(X36),X37),X37)),hAPP(X36,X36,hAPP(X36,fun(X36,X36),times_times(X36),X38),X38)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1330])])]) ).
fof(c_0_2498,plain,
! [X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X43,nat,X45,X46)),hAPP(X43,nat,X45,X47)))
| hBOOL(hAPP(fun(product_prod(X43,X43),bool),bool,hAPP(product_prod(X43,X43),fun(fun(product_prod(X43,X43),bool),bool),member(product_prod(X43,X43)),hAPP(X43,product_prod(X43,X43),hAPP(X43,fun(X43,product_prod(X43,X43)),product_Pair(X43,X43),X46),X47)),hAPP(fun(product_prod(X43,X43),bool),fun(product_prod(X43,X43),bool),hAPP(fun(X43,nat),fun(fun(product_prod(X43,X43),bool),fun(product_prod(X43,X43),bool)),mlex_prod(X43),X45),X44))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1331])]) ).
fof(c_0_2499,plain,
! [X82,X83,X84,X85,X86] :
( ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X85),X83))
| hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X83))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ linorder(X82) )
& ( hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X86))
| hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less_eq(X82),X84),X83))
| ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)),hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)))
| ~ linorder(X82) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1332])])])]) ).
fof(c_0_2500,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X41,bool),nat,finite_card(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44))),hAPP(fun(X42,bool),nat,finite_card(X42),X44))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1333])]) ).
fof(c_0_2501,plain,
! [X39,X40,X41,X42,X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(fun(product_prod(X39,X39),bool),bool,hAPP(product_prod(X39,X39),fun(fun(product_prod(X39,X39),bool),bool),member(product_prod(X39,X39)),hAPP(X39,product_prod(X39,X39),hAPP(X39,fun(X39,product_prod(X39,X39)),product_Pair(X39,X39),X40),X41)),hAPP(fun(X39,nat),fun(product_prod(X39,X39),bool),measure(X39),X42)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X39,nat,X42,X40)),hAPP(X39,nat,X42,X41))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X43,nat,X46,X44)),hAPP(X43,nat,X46,X45)))
| hBOOL(hAPP(fun(product_prod(X43,X43),bool),bool,hAPP(product_prod(X43,X43),fun(fun(product_prod(X43,X43),bool),bool),member(product_prod(X43,X43)),hAPP(X43,product_prod(X43,X43),hAPP(X43,fun(X43,product_prod(X43,X43)),product_Pair(X43,X43),X44),X45)),hAPP(fun(X43,nat),fun(product_prod(X43,X43),bool),measure(X43),X46))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1334])])])]) ).
fof(c_0_2502,plain,
! [X86,X87,X88,X89,X90] :
( ( hBOOL(hAPP(fun(X86,bool),bool,hAPP(fun(X86,bool),fun(fun(X86,bool),bool),ord_less_eq(fun(X86,bool)),esk111_5(X86,X87,X88,X89,X90)),X89))
| ~ hBOOL(hAPP(fun(X87,bool),bool,hAPP(fun(X87,bool),fun(fun(X87,bool),bool),ord_less_eq(fun(X87,bool)),X90),hAPP(fun(X86,bool),fun(X87,bool),hAPP(fun(X86,X87),fun(fun(X86,bool),fun(X87,bool)),image(X86,X87),X88),X89)))
| ~ hBOOL(hAPP(fun(X87,bool),bool,finite_finite_1(X87),X90)) )
& ( hBOOL(hAPP(fun(X86,bool),bool,finite_finite_1(X86),esk111_5(X86,X87,X88,X89,X90)))
| ~ hBOOL(hAPP(fun(X87,bool),bool,hAPP(fun(X87,bool),fun(fun(X87,bool),bool),ord_less_eq(fun(X87,bool)),X90),hAPP(fun(X86,bool),fun(X87,bool),hAPP(fun(X86,X87),fun(fun(X86,bool),fun(X87,bool)),image(X86,X87),X88),X89)))
| ~ hBOOL(hAPP(fun(X87,bool),bool,finite_finite_1(X87),X90)) )
& ( ti(fun(X87,bool),X90) = hAPP(fun(X86,bool),fun(X87,bool),hAPP(fun(X86,X87),fun(fun(X86,bool),fun(X87,bool)),image(X86,X87),X88),esk111_5(X86,X87,X88,X89,X90))
| ~ hBOOL(hAPP(fun(X87,bool),bool,hAPP(fun(X87,bool),fun(fun(X87,bool),bool),ord_less_eq(fun(X87,bool)),X90),hAPP(fun(X86,bool),fun(X87,bool),hAPP(fun(X86,X87),fun(fun(X86,bool),fun(X87,bool)),image(X86,X87),X88),X89)))
| ~ hBOOL(hAPP(fun(X87,bool),bool,finite_finite_1(X87),X90)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1335])])])]) ).
fof(c_0_2503,plain,
! [X89,X90,X91,X92,X93] :
( ~ hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),X92),X93))
| ~ hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),X90),X91))
| hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),hAPP(fun(X89,bool),fun(X89,bool),hAPP(fun(X89,bool),fun(fun(X89,bool),fun(X89,bool)),semilattice_inf_inf(fun(X89,bool)),X92),X90)),hAPP(fun(X89,bool),fun(X89,bool),hAPP(fun(X89,bool),fun(fun(X89,bool),fun(X89,bool)),semilattice_inf_inf(fun(X89,bool)),X93),X91))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1336])]) ).
fof(c_0_2504,plain,
! [X89,X90,X91,X92,X93] :
( ~ hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),X92),X93))
| ~ hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),X90),X91))
| hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),hAPP(fun(X89,bool),fun(X89,bool),hAPP(fun(X89,bool),fun(fun(X89,bool),fun(X89,bool)),semilattice_sup_sup(fun(X89,bool)),X92),X90)),hAPP(fun(X89,bool),fun(X89,bool),hAPP(fun(X89,bool),fun(fun(X89,bool),fun(X89,bool)),semilattice_sup_sup(fun(X89,bool)),X93),X91))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1337])]) ).
fof(c_0_2505,plain,
! [X41,X42,X43] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,bool),fun(fun(X41,bool),bool),ord_less_eq(fun(X41,bool)),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,X41),fun(fun(X41,bool),fun(X41,bool)),image(X41,X41),X42),X43)),X43))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X41),fun(fun(X41,bool),bool),inj_on(X41,X41),X42),X43))
| hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,X41),fun(fun(X41,bool),fun(X41,bool)),image(X41,X41),X42),X43) = ti(fun(X41,bool),X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1338])]) ).
fof(c_0_2506,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49))
| ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X46,X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_inf_inf(fun(X45,fun(X44,bool))),X47),X46),X48),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1339])]) ).
fof(c_0_2507,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_1340])]) ).
fof(c_0_2508,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_1341])]) ).
fof(c_0_2509,plain,
! [X80,X81,X82,X83,X84,X86,X87,X88,X89,X90,X91] :
( ( hBOOL(hAPP(fun(X81,bool),bool,hAPP(fun(X81,bool),fun(fun(X81,bool),bool),ord_less_eq(fun(X81,bool)),esk102_5(X80,X81,X82,X83,X84)),X84))
| ~ hBOOL(hAPP(fun(X80,bool),bool,hAPP(fun(X80,bool),fun(fun(X80,bool),bool),ord_less_eq(fun(X80,bool)),X82),hAPP(fun(X81,bool),fun(X80,bool),hAPP(fun(X81,X80),fun(fun(X81,bool),fun(X80,bool)),image(X81,X80),X83),X84))) )
& ( ti(fun(X80,bool),X82) = hAPP(fun(X81,bool),fun(X80,bool),hAPP(fun(X81,X80),fun(fun(X81,bool),fun(X80,bool)),image(X81,X80),X83),esk102_5(X80,X81,X82,X83,X84))
| ~ hBOOL(hAPP(fun(X80,bool),bool,hAPP(fun(X80,bool),fun(fun(X80,bool),bool),ord_less_eq(fun(X80,bool)),X82),hAPP(fun(X81,bool),fun(X80,bool),hAPP(fun(X81,X80),fun(fun(X81,bool),fun(X80,bool)),image(X81,X80),X83),X84))) )
& ( ~ hBOOL(hAPP(fun(X87,bool),bool,hAPP(fun(X87,bool),fun(fun(X87,bool),bool),ord_less_eq(fun(X87,bool)),X91),X90))
| ti(fun(X86,bool),X88) != hAPP(fun(X87,bool),fun(X86,bool),hAPP(fun(X87,X86),fun(fun(X87,bool),fun(X86,bool)),image(X87,X86),X89),X91)
| hBOOL(hAPP(fun(X86,bool),bool,hAPP(fun(X86,bool),fun(fun(X86,bool),bool),ord_less_eq(fun(X86,bool)),X88),hAPP(fun(X87,bool),fun(X86,bool),hAPP(fun(X87,X86),fun(fun(X87,bool),fun(X86,bool)),image(X87,X86),X89),X90))) ) ),
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_1342])])])])])]) ).
fof(c_0_2510,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_1343])]) ).
fof(c_0_2511,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_1344])])]) ).
fof(c_0_2512,plain,
! [X38,X39,X40,X41] :
( ~ linord20386208strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1345])])]) ).
fof(c_0_2513,plain,
! [X38,X39,X40,X41] :
( ~ linord20386208strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X40)))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1346])])]) ).
fof(c_0_2514,plain,
! [X38,X39,X40,X41] :
( ~ linord20386208strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1347])])]) ).
fof(c_0_2515,plain,
! [X38,X39,X40,X41] :
( ~ linordered_semiring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1348])])]) ).
fof(c_0_2516,plain,
! [X38,X39,X40,X41] :
( ~ linord20386208strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X40)))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1349])])]) ).
fof(c_0_2517,plain,
! [X38,X39,X40,X41] :
( ~ linordered_semiring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X40)))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1350])])]) ).
fof(c_0_2518,plain,
! [X18,X19,X20,X21] :
( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X19),X20))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X21))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X19),X20))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X21))
| ~ linord581940658strict(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1351])])])]) ).
fof(c_0_2519,plain,
! [X18,X19,X20,X21] :
( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),X20))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X21))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),X20))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X21))
| ~ linord581940658strict(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1352])])])]) ).
fof(c_0_2520,plain,
! [X18,X19,X20,X21] :
( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X20),X19))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),zero_zero(X18)))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X20),X19))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),zero_zero(X18)))
| ~ linord581940658strict(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1353])])])]) ).
fof(c_0_2521,plain,
! [X18,X19,X20,X21] :
( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),X19))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),zero_zero(X18)))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),X19))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X19)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),zero_zero(X18)))
| ~ linord581940658strict(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1354])])])]) ).
fof(c_0_2522,plain,
! [X106,X107,X108,X109,X110,X111] :
( ~ hBOOL(hAPP(fun(X106,bool),bool,hAPP(fun(X106,X107),fun(fun(X106,bool),bool),inj_on(X106,X107),hAPP(fun(X106,X108),fun(X106,X107),hAPP(fun(X108,X107),fun(fun(X106,X108),fun(X106,X107)),comp(X108,X107,X106),X109),X110)),X111))
| hBOOL(hAPP(fun(X106,bool),bool,hAPP(fun(X106,X108),fun(fun(X106,bool),bool),inj_on(X106,X108),X110),X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1355])]) ).
fof(c_0_2523,plain,
! [X44,X45,X46,X47,X48] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),hAPP(fun(X45,bool),fun(X44,bool),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X44,bool)),image(X45,X44),X47),X48)))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),hAPP(fun(X45,X44),fun(X44,X45),hAPP(fun(X45,bool),fun(fun(X45,X44),fun(X44,X45)),hilbert_inv_into(X45,X44),X48),X47)),X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1356])]) ).
fof(c_0_2524,plain,
! [X41,X42,X43,X44,X45] :
( ( ti(X41,X43) = hAPP(X42,X41,X44,esk109_5(X41,X42,X43,X44,X45))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X45))) )
& ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk109_5(X41,X42,X43,X44,X45)),X45))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X45))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1357])])])]) ).
fof(c_0_2525,plain,
! [X41,X42,X43,X44,X45,X47,X48,X49,X50,X51,X52] :
( ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk103_5(X41,X42,X43,X44,X45)),X45))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X45))) )
& ( ti(X41,X43) = hAPP(X42,X41,X44,esk103_5(X41,X42,X43,X44,X45))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X45))) )
& ( ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X52),X51))
| ti(X47,X49) != hAPP(X48,X47,X50,X52)
| hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),X49),hAPP(fun(X48,bool),fun(X47,bool),hAPP(fun(X48,X47),fun(fun(X48,bool),fun(X47,bool)),image(X48,X47),X50),X51))) ) ),
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_1358])])])])])]) ).
fof(c_0_2526,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(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),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1359])])]) ).
fof(c_0_2527,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(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_eq(X46),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1360])])]) ).
fof(c_0_2528,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(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_eq(X46),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1361])])]) ).
fof(c_0_2529,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(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),zero_zero(X46)),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1362])])]) ).
fof(c_0_2530,plain,
! [X46,X47,X48,X49,X50] :
( ~ ordered_semiring(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),zero_zero(X46)),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1363])])]) ).
fof(c_0_2531,plain,
! [X46,X47,X48,X49,X50] :
( ~ ordered_semiring(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),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1364])])]) ).
fof(c_0_2532,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50,X51,X52] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(X44,fun(X43,bool),hAPP(fun(product_prod(X44,X43),bool),fun(X44,fun(X43,bool)),in_rel(X44,X43),X45),X46),X47))
| hBOOL(hAPP(fun(product_prod(X44,X43),bool),bool,hAPP(product_prod(X44,X43),fun(fun(product_prod(X44,X43),bool),bool),member(product_prod(X44,X43)),hAPP(X43,product_prod(X44,X43),hAPP(X44,fun(X43,product_prod(X44,X43)),product_Pair(X44,X43),X46),X47)),X45)) )
& ( ~ hBOOL(hAPP(fun(product_prod(X49,X48),bool),bool,hAPP(product_prod(X49,X48),fun(fun(product_prod(X49,X48),bool),bool),member(product_prod(X49,X48)),hAPP(X48,product_prod(X49,X48),hAPP(X49,fun(X48,product_prod(X49,X48)),product_Pair(X49,X48),X51),X52)),X50))
| hBOOL(hAPP(X48,bool,hAPP(X49,fun(X48,bool),hAPP(fun(product_prod(X49,X48),bool),fun(X49,fun(X48,bool)),in_rel(X49,X48),X50),X51),X52)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1365])])])]) ).
fof(c_0_2533,plain,
! [X58,X59,X60] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),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),zero_zero(nat)),X60)) )
& ( ~ 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),times_times(nat),X60),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X60)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1366])])]) ).
fof(c_0_2534,plain,
! [X58,X59,X60] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),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(nat),zero_zero(nat)),X60)) )
& ( ~ 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),times_times(nat),X60),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X60)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1367])])]) ).
fof(c_0_2535,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),times_times(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X60)))
| ~ 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_eq(nat),X59),X60)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X61))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63))) )
& ( ~ 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),times_times(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63))) ) ),
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_1368])])])])]) ).
fof(c_0_2536,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),times_times(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X59))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X60)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X62))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X63),X62))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),X63))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X63),X62))) ) ),
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_1369])])])])]) ).
fof(c_0_2537,plain,
! [X53,X54,X55,X56,X57,X58] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,X54),fun(fun(X53,bool),bool),inj_on(X53,X54),X57),X58))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X56),X58))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X58))
| hAPP(fun(X53,bool),fun(X54,bool),hAPP(fun(X53,X54),fun(fun(X53,bool),fun(X54,bool)),image(X53,X54),X57),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X56),X55)) = hAPP(fun(X54,bool),fun(X54,bool),hAPP(fun(X54,bool),fun(fun(X54,bool),fun(X54,bool)),semilattice_inf_inf(fun(X54,bool)),hAPP(fun(X53,bool),fun(X54,bool),hAPP(fun(X53,X54),fun(fun(X53,bool),fun(X54,bool)),image(X53,X54),X57),X56)),hAPP(fun(X53,bool),fun(X54,bool),hAPP(fun(X53,X54),fun(fun(X53,bool),fun(X54,bool)),image(X53,X54),X57),X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1370])]) ).
fof(c_0_2538,plain,
! [X18,X19,X20,X21,X22,X23,X24] :
( ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),zero_zero(X18)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X19))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X21)))
| ~ linord581940658strict(X18) )
& ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),X20))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X19))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X21)))
| ~ linord581940658strict(X18) )
& ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),zero_zero(X18)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),X21))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X21)))
| ~ linord581940658strict(X18) )
& ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),X20))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),X21))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X21)))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X22))
| ~ 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),times_times(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X22),X24)))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X22),zero_zero(X18)))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X24),X23))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X22),X24)))
| ~ linord581940658strict(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_1371])])])])]) ).
fof(c_0_2539,plain,
! [X18,X19,X20,X21,X22,X23,X24] :
( ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),zero_zero(X18)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X20))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ linord581940658strict(X18) )
& ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),X19))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X20))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ linord581940658strict(X18) )
& ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),zero_zero(X18)))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),X21))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ linord581940658strict(X18) )
& ( hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X21),X19))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),X21))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X21),X20)))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),X23))
| ~ 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),times_times(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X24),X23)))
| ~ linord581940658strict(X18) )
& ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X23),zero_zero(X18)))
| ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X24),X22))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),times_times(X18),X24),X23)))
| ~ linord581940658strict(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_1372])])])])]) ).
fof(c_0_2540,plain,
! [X41,X42] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42))
| hBOOL(hAPP(fun(fun(X41,bool),bool),bool,finite_finite_1(fun(X41,bool)),hAPP(fun(fun(X41,bool),bool),fun(fun(X41,bool),bool),collect(fun(X41,bool)),hAPP(fun(X41,bool),fun(fun(X41,bool),bool),hAPP(fun(fun(X41,bool),fun(fun(X41,bool),bool)),fun(fun(X41,bool),fun(fun(X41,bool),bool)),combc(fun(X41,bool),fun(X41,bool),bool),ord_less_eq(fun(X41,bool))),X42)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1373])]) ).
fof(c_0_2541,plain,
! [X53,X54,X55,X56,X57,X58,X59,X60] :
( hAPP(fun(X54,bool),fun(X55,bool),hAPP(fun(X54,X55),fun(fun(X54,bool),fun(X55,bool)),image(X54,X55),X58),X59) != ti(fun(X55,bool),X60)
| hAPP(fun(X55,bool),fun(X53,bool),hAPP(fun(X55,X53),fun(fun(X55,bool),fun(X53,bool)),image(X55,X53),X56),X60) != ti(fun(X53,bool),X57)
| hAPP(fun(X54,bool),fun(X53,bool),hAPP(fun(X54,X53),fun(fun(X54,bool),fun(X53,bool)),image(X54,X53),hAPP(fun(X54,X55),fun(X54,X53),hAPP(fun(X55,X53),fun(fun(X54,X55),fun(X54,X53)),hAPP(fun(X54,bool),fun(fun(X55,X53),fun(fun(X54,X55),fun(X54,X53))),compose(X54,X55,X53),X59),X56),X58)),X59) = ti(fun(X53,bool),X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1374])]) ).
fof(c_0_2542,plain,
! [X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X45))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X44,bool),nat,finite_card(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45))),hAPP(fun(X44,bool),nat,finite_card(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X45))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X46)),hAPP(fun(X44,bool),nat,finite_card(X44),X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1375])]) ).
fof(c_0_2543,plain,
! [X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X45))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X46)),hAPP(fun(X44,bool),nat,finite_card(X44),X45)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X44,bool),nat,finite_card(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45))),hAPP(fun(X44,bool),nat,finite_card(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X45))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1376])]) ).
fof(c_0_2544,plain,
! [X39,X40,X41,X42] :
( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X42),top_top(fun(X40,bool))))
| hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,fun(X39,X41)),fun(fun(X40,bool),bool),inj_on(X40,fun(X39,X41)),hAPP(fun(X40,X41),fun(X40,fun(X39,X41)),hAPP(fun(X41,fun(X39,X41)),fun(fun(X40,X41),fun(X40,fun(X39,X41))),combb(X41,fun(X39,X41),X40),combk(X41,X39)),X42)),top_top(fun(X40,bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1377])]) ).
fof(c_0_2545,plain,
! [X55,X56,X57,X58,X59,X60,X61] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X57)),X58))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X58),hAPP(nat,nat,suc,X57))) = zero_zero(X55)
| ~ comm_monoid_add(X55) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X60)),X61))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X61),hAPP(nat,nat,suc,X60))) = hAPP(X55,X55,hAPP(X55,fun(X55,X55),plus_plus(X55),hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X61),X60))),hAPP(nat,X55,X59,hAPP(nat,nat,suc,X60)))
| ~ comm_monoid_add(X55) ) ),
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_1378])])])])]) ).
fof(c_0_2546,plain,
! [X40,X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X44),top_top(fun(X41,bool))))
| hAPP(fun(X41,X42),fun(X41,X40),hAPP(fun(X42,X40),fun(fun(X41,X42),fun(X41,X40)),comp(X42,X40,X41),hAPP(fun(X42,X41),fun(X42,X40),hAPP(fun(X41,X40),fun(fun(X42,X41),fun(X42,X40)),comp(X41,X40,X42),X43),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),hilbert_inv_into(X41,X42),top_top(fun(X41,bool))),X44))),X44) = ti(fun(X41,X40),X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1379])]) ).
fof(c_0_2547,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_sup_sup(fun(X45,fun(X44,bool))),X46),X47),X48),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1380])]) ).
fof(c_0_2548,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_sup_sup(fun(X45,fun(X44,bool))),X47),X46),X48),X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1381])]) ).
fof(c_0_2549,plain,
! [X44,X45,X46,X47,X48,X49] :
( ( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X47,X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_sup_sup(fun(X45,fun(X44,bool))),X46),X47),X48),X49)) )
& ( ~ hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),X46,X48),X49))
| hBOOL(hAPP(X44,bool,hAPP(X45,fun(X44,bool),hAPP(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool)),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,fun(X44,bool)),fun(X45,fun(X44,bool))),semilattice_sup_sup(fun(X45,fun(X44,bool))),X46),X47),X48),X49)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1382])])]) ).
fof(c_0_2550,plain,
! [X9,X10] :
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X10),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X10),X9)),arrow_1568854078le_Lin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1383])]) ).
fof(c_0_2551,plain,
! [X9,X10] :
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X10),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X10),X9)),arrow_1568854078le_Lin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1384])]) ).
fof(c_0_2552,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),hAPP(fun(X41,bool),fun(X41,X42),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X41,X42)),restrict(X41,X42),X43),X44)),X44))
| hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X43),X44)) )
& ( ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,X46),fun(fun(X45,bool),bool),inj_on(X45,X46),X47),X48))
| hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,X46),fun(fun(X45,bool),bool),inj_on(X45,X46),hAPP(fun(X45,bool),fun(X45,X46),hAPP(fun(X45,X46),fun(fun(X45,bool),fun(X45,X46)),restrict(X45,X46),X47),X48)),X48)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1385])])])]) ).
fof(c_0_2553,plain,
! [X40,X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X44),top_top(fun(X41,bool))))
| ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X43),top_top(fun(X40,bool))))
| hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X42),fun(fun(X40,bool),bool),inj_on(X40,X42),hAPP(fun(X40,X41),fun(X40,X42),hAPP(fun(X41,X42),fun(fun(X40,X41),fun(X40,X42)),comp(X41,X42,X40),X44),X43)),top_top(fun(X40,bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1386])]) ).
fof(c_0_2554,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_1387])])])])]) ).
fof(c_0_2555,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_1388])])])])]) ).
fof(c_0_2556,plain,
! [X38,X39,X40,X41] :
( ~ ordere236663937imp_le(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1389])])]) ).
fof(c_0_2557,plain,
! [X38,X39,X40,X41] :
( ~ ordere236663937imp_le(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1390])])]) ).
fof(c_0_2558,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_1391])])])])]) ).
fof(c_0_2559,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_1392])])])])]) ).
fof(c_0_2560,plain,
! [X38,X39,X40,X41] :
( ~ ordere236663937imp_le(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1393])])]) ).
fof(c_0_2561,plain,
! [X38,X39,X40,X41] :
( ~ ordere236663937imp_le(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1394])])]) ).
fof(c_0_2562,plain,
! [X54,X55,X56] : 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),fconj),X55)),X56)) = hAPP(fun(X54,bool),fun(X54,bool),hAPP(fun(X54,bool),fun(fun(X54,bool),fun(X54,bool)),semilattice_inf_inf(fun(X54,bool)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X55)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X56)),
inference(variable_rename,[status(thm)],[c_0_1395]) ).
fof(c_0_2563,plain,
! [X54,X55,X56] : 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)) = hAPP(fun(X54,bool),fun(X54,bool),hAPP(fun(X54,bool),fun(fun(X54,bool),fun(X54,bool)),semilattice_sup_sup(fun(X54,bool)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X55)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X56)),
inference(variable_rename,[status(thm)],[c_0_1396]) ).
fof(c_0_2564,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_1397])]) ).
fof(c_0_2565,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X43),X44))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),the_inv_into(X41,X42),X44),X43)),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X43),X44))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1398])]) ).
fof(c_0_2566,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X60))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X61))
| ~ 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),times_times(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63))) ) ),
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_1399])])])])]) ).
fof(c_0_2567,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X59))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X60))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X62))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),X63))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X63),X62))) ) ),
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_1400])])])])]) ).
fof(c_0_2568,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_1401])])])]) ).
fof(c_0_2569,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_1402])])])]) ).
fof(c_0_2570,plain,
! [X40,X41,X42,X43] :
( ~ ord(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(X40,X41,X42,esk43_4(X40,X41,X42,X43))),hAPP(X40,X41,X43,esk43_4(X40,X41,X42,X43))))
| hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X42),X43)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1403])])])]) ).
fof(c_0_2571,plain,
! [X40,X41,X42,X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X42),X43))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(X40,X41,X42,X44)),hAPP(X40,X41,X43,X44)))
| ~ ord(X41) )
& ( ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(X40,X41,X45,esk30_4(X40,X41,X45,X46))),hAPP(X40,X41,X46,esk30_4(X40,X41,X45,X46))))
| hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X45),X46))
| ~ ord(X41) ) ),
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_1404])])])])])]) ).
fof(c_0_2572,plain,
! [X44,X45,X46,X47,X48,X51,X52,X53,X54,X55,X56] :
( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk167_4(X44,X45,X46,X47)),X47))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk166_4(X44,X45,X46,X47)),X46))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X48),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X47)))
| ~ hBOOL(hAPP(X44,bool,X45,X48)) )
& ( hBOOL(hAPP(X44,bool,X45,esk167_4(X44,X45,X46,X47)))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk166_4(X44,X45,X46,X47)),X46))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X48),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X47)))
| ~ hBOOL(hAPP(X44,bool,X45,X48)) )
& ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk167_4(X44,X45,X46,X47)),X47))
| hBOOL(hAPP(X44,bool,X45,esk166_4(X44,X45,X46,X47)))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X48),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X47)))
| ~ hBOOL(hAPP(X44,bool,X45,X48)) )
& ( hBOOL(hAPP(X44,bool,X45,esk167_4(X44,X45,X46,X47)))
| hBOOL(hAPP(X44,bool,X45,esk166_4(X44,X45,X46,X47)))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X48),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X47)))
| ~ hBOOL(hAPP(X44,bool,X45,X48)) )
& ( hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk168_4(X51,X52,X53,X54)),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,bool),fun(fun(X51,bool),fun(X51,bool)),semilattice_sup_sup(fun(X51,bool)),X53),X54)))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X55),X53))
| ~ hBOOL(hAPP(X51,bool,X52,X55)) )
& ( hBOOL(hAPP(X51,bool,X52,esk168_4(X51,X52,X53,X54)))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X55),X53))
| ~ hBOOL(hAPP(X51,bool,X52,X55)) )
& ( hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk168_4(X51,X52,X53,X54)),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,bool),fun(fun(X51,bool),fun(X51,bool)),semilattice_sup_sup(fun(X51,bool)),X53),X54)))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X56),X54))
| ~ hBOOL(hAPP(X51,bool,X52,X56)) )
& ( hBOOL(hAPP(X51,bool,X52,esk168_4(X51,X52,X53,X54)))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X56),X54))
| ~ hBOOL(hAPP(X51,bool,X52,X56)) ) ),
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_1405])])])])])]) ).
fof(c_0_2573,plain,
! [X41,X42,X43,X44,X45] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X44),X45))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X43),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X44),X45)))
| hAPP(X41,X42,X44,hAPP(X42,X41,hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),the_inv_into(X41,X42),X45),X44),X43)) = ti(X42,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1406])]) ).
fof(c_0_2574,plain,
! [X44,X45,X46,X47,X48] :
( hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X47) != ti(fun(X45,bool),X48)
| hAPP(fun(X45,X44),fun(X45,X45),hAPP(fun(X44,X45),fun(fun(X45,X44),fun(X45,X45)),hAPP(fun(X45,bool),fun(fun(X44,X45),fun(fun(X45,X44),fun(X45,X45))),compose(X45,X44,X45),X48),X46),hAPP(fun(X45,bool),fun(X45,X44),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X45,X44)),restrict(X45,X44),hAPP(fun(X44,X45),fun(X45,X44),hAPP(fun(X44,bool),fun(fun(X44,X45),fun(X45,X44)),hilbert_inv_into(X44,X45),X47),X46)),X48)) = hAPP(fun(X45,bool),fun(X45,X45),hAPP(fun(X45,X45),fun(fun(X45,bool),fun(X45,X45)),restrict(X45,X45),combi(X45)),X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1407])]) ).
fof(c_0_2575,plain,
! [X44,X45,X46,X47,X49,X50,X51,X52,X53,X54,X57] :
( ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X49),X46))
| hBOOL(hAPP(X44,bool,X45,X49))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk169_4(X44,X45,X46,X47)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X47))) )
& ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X50),X47))
| hBOOL(hAPP(X44,bool,X45,X50))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk169_4(X44,X45,X46,X47)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X47))) )
& ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X49),X46))
| hBOOL(hAPP(X44,bool,X45,X49))
| ~ hBOOL(hAPP(X44,bool,X45,esk169_4(X44,X45,X46,X47))) )
& ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X50),X47))
| hBOOL(hAPP(X44,bool,X45,X50))
| ~ hBOOL(hAPP(X44,bool,X45,esk169_4(X44,X45,X46,X47))) )
& ( hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk171_4(X51,X52,X53,X54)),X54))
| hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk170_4(X51,X52,X53,X54)),X53))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X57),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,bool),fun(fun(X51,bool),fun(X51,bool)),semilattice_sup_sup(fun(X51,bool)),X53),X54)))
| hBOOL(hAPP(X51,bool,X52,X57)) )
& ( ~ hBOOL(hAPP(X51,bool,X52,esk171_4(X51,X52,X53,X54)))
| hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk170_4(X51,X52,X53,X54)),X53))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X57),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,bool),fun(fun(X51,bool),fun(X51,bool)),semilattice_sup_sup(fun(X51,bool)),X53),X54)))
| hBOOL(hAPP(X51,bool,X52,X57)) )
& ( hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk171_4(X51,X52,X53,X54)),X54))
| ~ hBOOL(hAPP(X51,bool,X52,esk170_4(X51,X52,X53,X54)))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X57),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,bool),fun(fun(X51,bool),fun(X51,bool)),semilattice_sup_sup(fun(X51,bool)),X53),X54)))
| hBOOL(hAPP(X51,bool,X52,X57)) )
& ( ~ hBOOL(hAPP(X51,bool,X52,esk171_4(X51,X52,X53,X54)))
| ~ hBOOL(hAPP(X51,bool,X52,esk170_4(X51,X52,X53,X54)))
| ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),X57),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,bool),fun(fun(X51,bool),fun(X51,bool)),semilattice_sup_sup(fun(X51,bool)),X53),X54)))
| hBOOL(hAPP(X51,bool,X52,X57)) ) ),
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_1408])])])])])]) ).
fof(c_0_2576,plain,
! [X41,X42,X43,X44,X45] :
( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),hAPP(X41,X42,X45,X43)),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X45),X44)))
| hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X44))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),top_top(fun(X41,bool)))) )
& ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X44))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),hAPP(X41,X42,X45,X43)),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X45),X44)))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),top_top(fun(X41,bool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1409])])]) ).
fof(c_0_2577,plain,
! [X53,X54,X55,X56] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X56))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X54),X56))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X54)),X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1410])]) ).
fof(c_0_2578,plain,
! [X82,X83,X84,X85,X86,X87,X88,X89,X90] :
( ( ti(X82,X85) = ti(X82,X86)
| ti(X82,X83) = ti(X82,X84)
| hAPP(X82,X82,hAPP(X82,fun(X82,X82),plus_plus(X82),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X85),X83)),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X86),X84)) != hAPP(X82,X82,hAPP(X82,fun(X82,X82),plus_plus(X82),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X85),X84)),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X86),X83))
| ~ semiri456707255roduct(X82) )
& ( ti(X82,X89) != ti(X82,X90)
| hAPP(X82,X82,hAPP(X82,fun(X82,X82),plus_plus(X82),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X89),X87)),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X90),X88)) = hAPP(X82,X82,hAPP(X82,fun(X82,X82),plus_plus(X82),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X89),X88)),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X90),X87))
| ~ semiri456707255roduct(X82) )
& ( ti(X82,X87) != ti(X82,X88)
| hAPP(X82,X82,hAPP(X82,fun(X82,X82),plus_plus(X82),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X89),X87)),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X90),X88)) = hAPP(X82,X82,hAPP(X82,fun(X82,X82),plus_plus(X82),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X89),X88)),hAPP(X82,X82,hAPP(X82,fun(X82,X82),times_times(X82),X90),X87))
| ~ semiri456707255roduct(X82) ) ),
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_1411])])])])]) ).
fof(c_0_2579,plain,
! [X92,X93,X94,X95,X96,X97,X98,X99,X100] :
( ( hAPP(X92,X92,hAPP(X92,fun(X92,X92),plus_plus(X92),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X93),X94)),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X95),X96)) != hAPP(X92,X92,hAPP(X92,fun(X92,X92),plus_plus(X92),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X93),X96)),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X95),X94))
| ti(X92,X93) = ti(X92,X95)
| ti(X92,X94) = ti(X92,X96)
| ~ semiri456707255roduct(X92) )
& ( ti(X92,X97) != ti(X92,X99)
| hAPP(X92,X92,hAPP(X92,fun(X92,X92),plus_plus(X92),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X97),X98)),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X99),X100)) = hAPP(X92,X92,hAPP(X92,fun(X92,X92),plus_plus(X92),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X97),X100)),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X99),X98))
| ~ semiri456707255roduct(X92) )
& ( ti(X92,X98) != ti(X92,X100)
| hAPP(X92,X92,hAPP(X92,fun(X92,X92),plus_plus(X92),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X97),X98)),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X99),X100)) = hAPP(X92,X92,hAPP(X92,fun(X92,X92),plus_plus(X92),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X97),X100)),hAPP(X92,X92,hAPP(X92,fun(X92,X92),times_times(X92),X99),X98))
| ~ semiri456707255roduct(X92) ) ),
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_1412])])])])]) ).
fof(c_0_2580,plain,
! [X83,X84,X85,X86,X87,X88] :
( hAPP(fun(X83,bool),fun(X84,bool),hAPP(fun(X83,X84),fun(fun(X83,bool),fun(X84,bool)),image(X83,X84),X86),X87) != ti(fun(X84,bool),X88)
| ~ hBOOL(hAPP(fun(X84,bool),bool,hAPP(fun(X84,bool),fun(fun(X84,bool),bool),ord_less_eq(fun(X84,bool)),X85),X88))
| hAPP(fun(X83,bool),fun(X84,bool),hAPP(fun(X83,X84),fun(fun(X83,bool),fun(X84,bool)),image(X83,X84),X86),hAPP(fun(X84,bool),fun(X83,bool),hAPP(fun(X84,X83),fun(fun(X84,bool),fun(X83,bool)),image(X84,X83),hAPP(fun(X83,X84),fun(X84,X83),hAPP(fun(X83,bool),fun(fun(X83,X84),fun(X84,X83)),hilbert_inv_into(X83,X84),X87),X86)),X85)) = ti(fun(X84,bool),X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1413])]) ).
fof(c_0_2581,plain,
! [X55,X56,X57,X58] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X55))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X56))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X58))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1414])])])])]) ).
fof(c_0_2582,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X53))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X52))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1415])]) ).
fof(c_0_2583,plain,
! [X55,X56,X57,X58,X59,X60,X61] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X58),hAPP(nat,nat,suc,X57))) = zero_zero(X55)
| ~ comm_monoid_add(X55) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X60),X61))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X61),hAPP(nat,nat,suc,X60))) = hAPP(X55,X55,hAPP(X55,fun(X55,X55),plus_plus(X55),hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X61),X60))),hAPP(nat,X55,X59,X60))
| ~ comm_monoid_add(X55) ) ),
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_1416])])])])]) ).
fof(c_0_2584,plain,
! [X9] :
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X9),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X9)),arrow_301600364e_Prof)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1417])]) ).
fof(c_0_2585,plain,
! [X99,X100,X101] :
( ( hBOOL(hAPP(X99,bool,hAPP(X99,fun(X99,bool),ord_less(X99),zero_zero(X99)),esk135_3(X99,X100,X101)))
| hBOOL(hAPP(X99,bool,hAPP(X99,fun(X99,bool),ord_less_eq(X99),X100),X101))
| ~ linord1117847801e_zero(X99) )
& ( hBOOL(hAPP(X99,bool,hAPP(X99,fun(X99,bool),ord_less(X99),esk135_3(X99,X100,X101)),one_one(X99)))
| hBOOL(hAPP(X99,bool,hAPP(X99,fun(X99,bool),ord_less_eq(X99),X100),X101))
| ~ linord1117847801e_zero(X99) )
& ( ~ hBOOL(hAPP(X99,bool,hAPP(X99,fun(X99,bool),ord_less_eq(X99),hAPP(X99,X99,hAPP(X99,fun(X99,X99),times_times(X99),esk135_3(X99,X100,X101)),X100)),X101))
| hBOOL(hAPP(X99,bool,hAPP(X99,fun(X99,bool),ord_less_eq(X99),X100),X101))
| ~ linord1117847801e_zero(X99) ) ),
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_1418])])])])]) ).
fof(c_0_2586,plain,
! [X53,X54,X55,X56,X57,X58,X59,X60] :
( ( hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X55)),X56) != hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X56))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X56),X54)) )
& ( ~ hBOOL(hAPP(fun(X57,bool),bool,hAPP(fun(X57,bool),fun(fun(X57,bool),bool),ord_less_eq(fun(X57,bool)),X60),X58))
| hAPP(fun(X57,bool),fun(X57,bool),hAPP(fun(X57,bool),fun(fun(X57,bool),fun(X57,bool)),semilattice_sup_sup(fun(X57,bool)),hAPP(fun(X57,bool),fun(X57,bool),hAPP(fun(X57,bool),fun(fun(X57,bool),fun(X57,bool)),semilattice_inf_inf(fun(X57,bool)),X58),X59)),X60) = hAPP(fun(X57,bool),fun(X57,bool),hAPP(fun(X57,bool),fun(fun(X57,bool),fun(X57,bool)),semilattice_inf_inf(fun(X57,bool)),X58),hAPP(fun(X57,bool),fun(X57,bool),hAPP(fun(X57,bool),fun(fun(X57,bool),fun(X57,bool)),semilattice_sup_sup(fun(X57,bool)),X59),X60)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1419])])])]) ).
fof(c_0_2587,plain,
! [X41,X42,X43,X44,X45] :
( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk79_5(X41,X42,X43,X44,X45)),X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk79_5(X41,X42,X43,X44,X45)),X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X44),X45))
| hAPP(X42,X41,X43,esk79_5(X41,X42,X43,X44,X45)) != hAPP(X42,X41,X44,esk79_5(X41,X42,X43,X44,X45)) )
& ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X44),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X45))
| hAPP(X42,X41,X43,esk79_5(X41,X42,X43,X44,X45)) != hAPP(X42,X41,X44,esk79_5(X41,X42,X43,X44,X45)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1420])])])]) ).
fof(c_0_2588,plain,
! [X55,X56,X57,X58] :
( ~ comm_monoid_add(X55)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X57),X58)) = hAPP(X55,X55,hAPP(X55,fun(X55,X55),plus_plus(X55),hAPP(nat,X55,X56,X57)),hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X57)),X58))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1421])])]) ).
fof(c_0_2589,plain,
! [X55,X56,X57,X58] :
( ~ comm_monoid_add(X55)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),X58)) = hAPP(X55,X55,hAPP(X55,fun(X55,X55),plus_plus(X55),hAPP(nat,X55,X56,X57)),hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X57)),X58))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1422])])]) ).
fof(c_0_2590,plain,
! [X30,X31,X32,X33,X34] :
( ( ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X30),X31))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X32),arrow_301600364e_Prof))
| hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X30,X32) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X32,X31) )
& ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk18_2(X33,X34)),arrow_301600364e_Prof))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X33),X34)) )
& ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X33,esk18_2(X33,X34)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk18_2(X33,X34),X34)
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X33),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_1423])])])])])]) ).
fof(c_0_2591,plain,
! [X38,X39,X40,X41] :
( ~ linord893533164strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1424])])]) ).
fof(c_0_2592,plain,
! [X38,X39,X40,X41] :
( ~ linord20386208strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1425])])]) ).
fof(c_0_2593,plain,
! [X38,X39,X40,X41] :
( ~ linord20386208strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X39)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1426])])]) ).
fof(c_0_2594,plain,
! [X38,X39,X40,X41] :
( ~ ordere1490568538miring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1427])])]) ).
fof(c_0_2595,plain,
! [X38,X39,X40,X41] :
( ~ ordered_semiring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1428])])]) ).
fof(c_0_2596,plain,
! [X38,X39,X40,X41] :
( ~ ordered_semiring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X39)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1429])])]) ).
fof(c_0_2597,plain,
! [X38,X39,X40,X41] :
( ~ linord581940658strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),zero_zero(X38)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1430])])]) ).
fof(c_0_2598,plain,
! [X38,X39,X40,X41] :
( ~ linord581940658strict(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),zero_zero(X38)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X39)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1431])])]) ).
fof(c_0_2599,plain,
! [X38,X39,X40,X41] :
( ~ ordered_ring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),zero_zero(X38)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1432])])]) ).
fof(c_0_2600,plain,
! [X38,X39,X40,X41] :
( ~ ordered_ring(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),zero_zero(X38)))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X41),X39)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1433])])]) ).
fof(c_0_2601,plain,
! [X46,X47,X48,X49,X50] :
( ~ semilattice_inf(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),semilattice_inf_inf(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),semilattice_inf_inf(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1434])])]) ).
fof(c_0_2602,plain,
! [X46,X47,X48,X49,X50] :
( ~ semilattice_sup(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),semilattice_sup_sup(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),semilattice_sup_sup(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1435])])]) ).
fof(c_0_2603,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_1436])])]) ).
fof(c_0_2604,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_1437])])]) ).
fof(c_0_2605,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_1438])])]) ).
fof(c_0_2606,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_1439])])]) ).
fof(c_0_2607,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_1440])])])]) ).
fof(c_0_2608,plain,
! [X16,X17,X18,X19,X20] :
( ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X17),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X17))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)),zero_zero(X16)))
| ~ linord581940658strict(X16) )
& ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X18))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X17))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)),zero_zero(X16)))
| ~ linord581940658strict(X16) )
& ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X17),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X18),zero_zero(X16)))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)),zero_zero(X16)))
| ~ linord581940658strict(X16) )
& ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X18))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X18),zero_zero(X16)))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)),zero_zero(X16)))
| ~ linord581940658strict(X16) )
& ( ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X19))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X20),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X19),X20)),zero_zero(X16)))
| ~ linord581940658strict(X16) )
& ( ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X19),zero_zero(X16)))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X20))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X19),X20)),zero_zero(X16)))
| ~ linord581940658strict(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_1441])])])])]) ).
fof(c_0_2609,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),zero_zero(nat)),X60))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X60)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X62),X60))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1442])]) ).
fof(c_0_2610,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),zero_zero(nat)),X60))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X61)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X62))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1443])]) ).
fof(c_0_2611,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),times_times(nat),X64),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X65),X63))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1444])]) ).
fof(c_0_2612,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_1445])]) ).
fof(c_0_2613,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_1446])]) ).
fof(c_0_2614,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X42),X43))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X42),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,bool),fun(fun(X41,bool),fun(X41,bool)),semilattice_inf_inf(fun(X41,bool)),X43),hAPP(fun(X41,bool),fun(X41,bool),collect(X41),X44)))) )
& ( hBOOL(hAPP(X41,bool,X44,X42))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X42),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,bool),fun(fun(X41,bool),fun(X41,bool)),semilattice_inf_inf(fun(X41,bool)),X43),hAPP(fun(X41,bool),fun(X41,bool),collect(X41),X44)))) )
& ( ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),X46),X47))
| ~ hBOOL(hAPP(X45,bool,X48,X46))
| hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),X46),hAPP(fun(X45,bool),fun(X45,bool),hAPP(fun(X45,bool),fun(fun(X45,bool),fun(X45,bool)),semilattice_inf_inf(fun(X45,bool)),X47),hAPP(fun(X45,bool),fun(X45,bool),collect(X45),X48)))) ) ),
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_1447])])])])]) ).
fof(c_0_2615,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X53))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X52))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X53),X52))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1448])]) ).
fof(c_0_2616,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X53))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X52))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1449])]) ).
fof(c_0_2617,plain,
! [X36,X37,X38] :
( ~ linordered_idom(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),zero_zero(X36)),X38))
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),zero_zero(X36)),X37))
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),one_one(X36)))
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),times_times(X36),X38),X37)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1450])])]) ).
fof(c_0_2618,plain,
! [X36,X37,X38] :
( ~ linordered_idom(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),zero_zero(X36)),X38))
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),zero_zero(X36)),X37))
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),one_one(X36)))
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),times_times(X36),X37),X38)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1451])])]) ).
fof(c_0_2619,plain,
! [X63,X66] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X63,hAPP(nat,nat,suc,esk153_1(X63)))),hAPP(nat,nat,X63,esk153_1(X63))))
| hAPP(nat,nat,X63,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk154_1(X63)),X66)) = hAPP(nat,nat,X63,esk154_1(X63)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1452])])])]) ).
fof(c_0_2620,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
c_0_1453 ).
fof(c_0_2621,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
c_0_1454 ).
fof(c_0_2622,plain,
! [X41,X42,X43,X44] :
( hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X44),top_top(fun(X41,bool))) != top_top(fun(X42,bool))
| hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X44),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),hilbert_inv_into(X41,X42),top_top(fun(X41,bool))),X44)),X43)) = ti(fun(X42,bool),X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1455])]) ).
fof(c_0_2623,plain,
! [X41,X42,X43,X44,X45] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X45)))
| hAPP(X42,X41,X44,hAPP(X41,X42,hAPP(fun(X42,X41),fun(X41,X42),hAPP(fun(X42,bool),fun(fun(X42,X41),fun(X41,X42)),hilbert_inv_into(X42,X41),X45),X44),X43)) = ti(X41,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1456])]) ).
fof(c_0_2624,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),X48),top_top(fun(X44,bool))))
| hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X48),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47)) = hAPP(fun(X45,bool),fun(X45,bool),hAPP(fun(X45,bool),fun(fun(X45,bool),fun(X45,bool)),semilattice_inf_inf(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)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1457])]) ).
fof(c_0_2625,plain,
! [X40,X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(fun(X41,bool),fun(X42,X42)),bool,hAPP(fun(X41,fun(X42,X42)),fun(fun(fun(X41,bool),fun(X42,X42)),bool),finite_folding_idem(X41,X42),X45),X46))
| hAPP(fun(X40,X42),fun(X40,X42),hAPP(fun(X42,X42),fun(fun(X40,X42),fun(X40,X42)),comp(X42,X42,X40),hAPP(X41,fun(X42,X42),X45,X43)),hAPP(fun(X40,X42),fun(X40,X42),hAPP(fun(X42,X42),fun(fun(X40,X42),fun(X40,X42)),comp(X42,X42,X40),hAPP(X41,fun(X42,X42),X45,X43)),X44)) = hAPP(fun(X40,X42),fun(X40,X42),hAPP(fun(X42,X42),fun(fun(X40,X42),fun(X40,X42)),comp(X42,X42,X40),hAPP(X41,fun(X42,X42),X45,X43)),X44) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1458])])])]) ).
fof(c_0_2626,plain,
! [X41,X42,X43,X44,X45] :
( ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk69_5(X41,X42,X43,X44,X45)),X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X44),X45)) )
& ( hAPP(X41,X42,X43,hAPP(X42,X41,X44,esk69_5(X41,X42,X43,X44,X45))) != ti(X42,esk69_5(X41,X42,X43,X44,X45))
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X44),X45)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1459])])])]) ).
fof(c_0_2627,plain,
! [X47,X48,X49,X50,X52,X53] :
( ( ti(X48,X49) = hAPP(X47,X48,X50,esk104_4(X47,X48,X49,X50))
| ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X47,bool),fun(X48,bool),hAPP(fun(X47,X48),fun(fun(X47,bool),fun(X48,bool)),image(X47,X48),X50),top_top(fun(X47,bool)))))
| ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X50),top_top(fun(X47,bool)))) )
& ( ti(X48,X49) != hAPP(X47,X48,X50,X52)
| ti(X47,X52) = ti(X47,esk104_4(X47,X48,X49,X50))
| ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X47,bool),fun(X48,bool),hAPP(fun(X47,X48),fun(fun(X47,bool),fun(X48,bool)),image(X47,X48),X50),top_top(fun(X47,bool)))))
| ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X50),top_top(fun(X47,bool)))) )
& ( ti(X48,X49) = hAPP(X47,X48,X50,esk105_5(X47,X48,X49,X50,X53))
| ti(X48,X49) != hAPP(X47,X48,X50,X53)
| hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X47,bool),fun(X48,bool),hAPP(fun(X47,X48),fun(fun(X47,bool),fun(X48,bool)),image(X47,X48),X50),top_top(fun(X47,bool)))))
| ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X50),top_top(fun(X47,bool)))) )
& ( ti(X47,esk105_5(X47,X48,X49,X50,X53)) != ti(X47,X53)
| ti(X48,X49) != hAPP(X47,X48,X50,X53)
| hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X47,bool),fun(X48,bool),hAPP(fun(X47,X48),fun(fun(X47,bool),fun(X48,bool)),image(X47,X48),X50),top_top(fun(X47,bool)))))
| ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X50),top_top(fun(X47,bool)))) ) ),
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_1460])])])])]) ).
fof(c_0_2628,plain,
! [X96,X97,X98,X99,X100] :
( ~ comm_semiring_1(X96)
| hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X98)),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X99),X100)) = hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X99),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X98)),X100)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1461])])]) ).
fof(c_0_2629,plain,
! [X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X43),fun(fun(X42,bool),bool),inj_on(X42,X43),X45),X46))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,bool),fun(fun(X42,bool),bool),ord_less_eq(fun(X42,bool)),X44),X46))
| hAPP(fun(X43,bool),fun(X42,bool),hAPP(fun(X43,X42),fun(fun(X43,bool),fun(X42,bool)),image(X43,X42),hAPP(fun(X42,X43),fun(X43,X42),hAPP(fun(X42,bool),fun(fun(X42,X43),fun(X43,X42)),hilbert_inv_into(X42,X43),X46),X45)),hAPP(fun(X42,bool),fun(X43,bool),hAPP(fun(X42,X43),fun(fun(X42,bool),fun(X43,bool)),image(X42,X43),X45),X44)) = ti(fun(X42,bool),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1462])]) ).
fof(c_0_2630,plain,
! [X64,X65,X66] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X66))
| hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X65),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X66),X64)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X65),X66)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X66),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X66),X64))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1463])]) ).
fof(c_0_2631,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_1464])])])])]) ).
fof(c_0_2632,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_1465])])])])]) ).
fof(c_0_2633,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_1466])])])])]) ).
fof(c_0_2634,plain,
! [X35,X36,X37,X38] :
( ( hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X38))
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),X37)),X38))
| ~ semilattice_sup(X35) )
& ( hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),X37)),X38))
| ~ semilattice_sup(X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1467])])])]) ).
fof(c_0_2635,plain,
! [X10,X11,X12,X13,X14,X15,X16] :
( ( hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X11),X13))
| ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),hAPP(X10,X10,hAPP(X10,fun(X10,X10),semilattice_sup_sup(X10),X11),X12)),X13))
| ~ semilattice_sup(X10) )
& ( hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X12),X13))
| ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),hAPP(X10,X10,hAPP(X10,fun(X10,X10),semilattice_sup_sup(X10),X11),X12)),X13))
| ~ semilattice_sup(X10) )
& ( ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X14),X16))
| ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X15),X16))
| hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),hAPP(X10,X10,hAPP(X10,fun(X10,X10),semilattice_sup_sup(X10),X14),X15)),X16))
| ~ semilattice_sup(X10) ) ),
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_1468])])])])]) ).
fof(c_0_2636,plain,
! [X44,X45,X46,X47,X48] :
( ( hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X47) != hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X48)
| ti(fun(X44,bool),X47) = ti(fun(X44,bool),X48)
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X47),X48))) )
& ( ti(fun(X44,bool),X47) != ti(fun(X44,bool),X48)
| hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X47) = hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X48)
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X47),X48))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1469])])]) ).
fof(c_0_2637,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),times_times(X16),X18),X17)),ring_1_Ints(X16))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1470])])]) ).
fof(c_0_2638,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_1471])])]) ).
fof(c_0_2639,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X55)),X56) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X56)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X56)),
inference(variable_rename,[status(thm)],[c_0_1472]) ).
fof(c_0_2640,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X55)),X56) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X56)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X55),X56)),
inference(variable_rename,[status(thm)],[c_0_1473]) ).
fof(c_0_2641,plain,
! [X39,X40,X41] :
( hAPP(fun(X39,bool),fun(X40,bool),hAPP(fun(X39,X40),fun(fun(X39,bool),fun(X40,bool)),image(X39,X40),X41),top_top(fun(X39,bool))) != top_top(fun(X40,bool))
| hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X39),fun(fun(X40,bool),bool),inj_on(X40,X39),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))),X41)),top_top(fun(X40,bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1474])]) ).
fof(c_0_2642,plain,
! [X85,X86] :
( ( ti(fun(X85,bool),X86) = hAPP(fun(nat,bool),fun(X85,bool),hAPP(fun(nat,X85),fun(fun(nat,bool),fun(X85,bool)),image(nat,X85),esk121_2(X85,X86)),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)),esk120_2(X85,X86))))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X86)) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X85),fun(fun(nat,bool),bool),inj_on(nat,X85),esk121_2(X85,X86)),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)),esk120_2(X85,X86)))))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X86)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1475])])])]) ).
fof(c_0_2643,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)),X47),hAPP(fun(X44,bool),fun(fun(X44,X45),bool),extensional(X44,X45),X48)))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X48),X46))
| 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,bool),fun(fun(X44,X45),bool),extensional(X44,X45),X46))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1476])]) ).
fof(c_0_2644,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_1477])]) ).
fof(c_0_2645,plain,
! [X44,X45,X46,X47,X48,X49,X50,X51] :
( ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(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)) )
& ( ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),X50))
| hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X48,bool),fun(X48,bool),hAPP(fun(X48,bool),fun(fun(X48,bool),fun(X48,bool)),semilattice_sup_sup(fun(X48,bool)),X50),X51))) )
& ( ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),X51))
| hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X48,bool),fun(X48,bool),hAPP(fun(X48,bool),fun(fun(X48,bool),fun(X48,bool)),semilattice_sup_sup(fun(X48,bool)),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_1478])])])])]) ).
fof(c_0_2646,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(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_1479])]) ).
fof(c_0_2647,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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55)),X56)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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)),X58)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1480])])])]) ).
fof(c_0_2648,plain,
! [X52,X53,X54] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),X54))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1481])]) ).
fof(c_0_2649,plain,
! [X52,X53,X54] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),X54))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1482])]) ).
fof(c_0_2650,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_1483])]) ).
fof(c_0_2651,plain,
! [X52,X53,X54] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X54))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),X54)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X54))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),X54)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1484])])]) ).
fof(c_0_2652,plain,
! [X38,X39,X40,X41] :
( ~ ordere223160158up_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X40),X39)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1485])])]) ).
fof(c_0_2653,plain,
! [X38,X39,X40,X41] :
( ~ ordere223160158up_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1486])])]) ).
fof(c_0_2654,plain,
! [X38,X39,X40,X41] :
( ~ ordere779506340up_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X40),X39)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1487])])]) ).
fof(c_0_2655,plain,
! [X38,X39,X40,X41] :
( ~ ordere779506340up_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1488])])]) ).
fof(c_0_2656,plain,
! [X41,X42,X43,X44,X45] :
( ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk134_5(X41,X42,X43,X44,X45)),X45))
| hAPP(fun(X42,bool),fun(X42,X41),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X42,X41)),restrict(X42,X41),X43),X45) = hAPP(fun(X42,bool),fun(X42,X41),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X42,X41)),restrict(X42,X41),X44),X45) )
& ( hAPP(X42,X41,X43,esk134_5(X41,X42,X43,X44,X45)) != hAPP(X42,X41,X44,esk134_5(X41,X42,X43,X44,X45))
| hAPP(fun(X42,bool),fun(X42,X41),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X42,X41)),restrict(X42,X41),X43),X45) = hAPP(fun(X42,bool),fun(X42,X41),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X42,X41)),restrict(X42,X41),X44),X45) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1489])])])]) ).
fof(c_0_2657,plain,
! [X44,X45,X46] :
( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk172_3(X44,X45,X46)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X45)))
| hAPP(fun(X44,bool),nat,finite_card(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X46)),hAPP(fun(X44,bool),nat,finite_card(X44),X45))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X45))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46)) )
& ( one_one(nat) != zero_zero(nat)
| hAPP(fun(X44,bool),nat,finite_card(X44),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X46)),hAPP(fun(X44,bool),nat,finite_card(X44),X45))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X45))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1490])])])]) ).
fof(c_0_2658,plain,
! [X77,X78,X79,X80,X81] :
( ~ comm_monoid_add(X78)
| ~ hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),X81))
| ~ hBOOL(hAPP(fun(X77,bool),bool,hAPP(fun(X77,X77),fun(fun(X77,bool),bool),inj_on(X77,X77),X80),X81))
| hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),big_co1399186613setsum(X77,X78),X79),hAPP(fun(X77,bool),fun(X77,bool),hAPP(fun(X77,X77),fun(fun(X77,bool),fun(X77,bool)),image(X77,X77),X80),X81)) = hAPP(fun(X77,bool),X78,hAPP(fun(X77,X78),fun(fun(X77,bool),X78),big_co1399186613setsum(X77,X78),hAPP(fun(X77,X77),fun(X77,X78),hAPP(fun(X77,X78),fun(fun(X77,X77),fun(X77,X78)),comp(X77,X78,X77),X79),X80)),X81) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1491])])]) ).
fof(c_0_2659,plain,
! [X107,X108,X109,X110,X111] :
( ~ semiring_0(X108)
| hAPP(X108,X108,hAPP(X108,fun(X108,X108),times_times(X108),X109),hAPP(fun(X107,bool),X108,hAPP(fun(X107,X108),fun(fun(X107,bool),X108),big_co1399186613setsum(X107,X108),X110),X111)) = hAPP(fun(X107,bool),X108,hAPP(fun(X107,X108),fun(fun(X107,bool),X108),big_co1399186613setsum(X107,X108),hAPP(fun(X107,X108),fun(X107,X108),hAPP(fun(X108,X108),fun(fun(X107,X108),fun(X107,X108)),combb(X108,X108,X107),hAPP(X108,fun(X108,X108),times_times(X108),X109)),X110)),X111) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1492])])]) ).
fof(c_0_2660,plain,
! [X42,X43,X44,X45] :
( ( hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),esk136_4(X42,X43,X44,X45)),X45))
| hAPP(fun(X42,bool),X43,hAPP(X43,fun(fun(X42,bool),X43),hAPP(fun(X42,X43),fun(X43,fun(fun(X42,bool),X43)),hAPP(fun(X43,fun(X43,X43)),fun(fun(X42,X43),fun(X43,fun(fun(X42,bool),X43))),finite_fold_image(X43,X42),times_times(X43)),X44),one_one(X43)),X45) = one_one(X43)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X45))
| ~ comm_monoid_mult(X43) )
& ( hAPP(X42,X43,X44,esk136_4(X42,X43,X44,X45)) != one_one(X43)
| hAPP(fun(X42,bool),X43,hAPP(X43,fun(fun(X42,bool),X43),hAPP(fun(X42,X43),fun(X43,fun(fun(X42,bool),X43)),hAPP(fun(X43,fun(X43,X43)),fun(fun(X42,X43),fun(X43,fun(fun(X42,bool),X43))),finite_fold_image(X43,X42),times_times(X43)),X44),one_one(X43)),X45) = one_one(X43)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X45))
| ~ comm_monoid_mult(X43) ) ),
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_1493])])])])]) ).
fof(c_0_2661,plain,
! [X55,X56,X57,X58] :
( ~ comm_monoid_add(X55)
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X57)),hAPP(nat,nat,suc,X58))) = hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),hAPP(fun(nat,nat),fun(nat,X55),hAPP(fun(nat,X55),fun(fun(nat,nat),fun(nat,X55)),combb(nat,X55,nat),X56),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),X58)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1494])])]) ).
fof(c_0_2662,plain,
! [X55,X56,X57,X58] :
( ~ comm_monoid_add(X55)
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X57)),hAPP(nat,nat,suc,X58))) = hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),hAPP(fun(nat,nat),fun(nat,X55),hAPP(fun(nat,X55),fun(fun(nat,nat),fun(nat,X55)),combb(nat,X55,nat),X56),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X57),X58)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1495])])]) ).
fof(c_0_2663,plain,
! [X53,X54,X55,X56] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X56))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X54))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X56),X54))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1496])]) ).
fof(c_0_2664,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),times_times(nat),X60),X61)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X62))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1497])]) ).
fof(c_0_2665,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),times_times(nat),X61),X60)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X62),X60))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1498])]) ).
fof(c_0_2666,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_1499])]) ).
fof(c_0_2667,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_1500])]) ).
fof(c_0_2668,plain,
! [X41,X42,X43,X44] : hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),hAPP(fun(X41,bool),fun(X41,X42),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X41,X42)),restrict(X41,X42),X43),X44)),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X44))),
inference(variable_rename,[status(thm)],[c_0_1501]) ).
fof(c_0_2669,plain,
! [X41,X42,X43] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,bool),fun(fun(X41,bool),bool),ord_less_eq(fun(X41,bool)),X43),hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,X41),fun(fun(X41,bool),fun(X41,bool)),image(X41,X41),X42),X43)))
| hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X41),fun(fun(X41,bool),bool),inj_on(X41,X41),X42),X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1502])]) ).
fof(c_0_2670,plain,
! [X64,X65,X66] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),X64)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X65),X66)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X65),X64)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X66),X64)),
inference(variable_rename,[status(thm)],[c_0_1503]) ).
fof(c_0_2671,plain,
! [X64,X65,X66] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),X64)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X65),X66)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X65),X64)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X66),X64)),
inference(variable_rename,[status(thm)],[c_0_1504]) ).
fof(c_0_2672,plain,
! [X23,X24,X25] :
( ~ linord20386208strict(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),zero_zero(X23)),X24))
| hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24)),zero_zero(X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1505])])]) ).
fof(c_0_2673,plain,
! [X23,X24,X25] :
( ~ linord20386208strict(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),X24),zero_zero(X23)))
| hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),X25)),zero_zero(X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1506])])]) ).
fof(c_0_2674,plain,
! [X23,X24,X25] :
( ~ linord20386208strict(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),X24),zero_zero(X23)))
| hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24)),zero_zero(X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1507])])]) ).
fof(c_0_2675,plain,
! [X23,X24,X25] :
( ( ~ 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),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),times_times(X23),X25),X24)),zero_zero(X23)))
| ~ ordere453448008miring(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),zero_zero(X23)),X24))
| hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24)),zero_zero(X23)))
| ~ ordere453448008miring(X23) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1508])])])]) ).
fof(c_0_2676,plain,
! [X23,X24,X25] :
( ~ ordere453448008miring(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),zero_zero(X23)),X24))
| hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24)),zero_zero(X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1509])])]) ).
fof(c_0_2677,plain,
! [X23,X24,X25] :
( ~ ordere453448008miring(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),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),times_times(X23),X24),X25)),zero_zero(X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1510])])]) ).
fof(c_0_2678,plain,
! [X23,X24,X25] :
( ~ ordere453448008miring(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),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),times_times(X23),X25),X24)),zero_zero(X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1511])])]) ).
fof(c_0_2679,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_1512])])]) ).
fof(c_0_2680,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_1513])])]) ).
fof(c_0_2681,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_1514])])]) ).
fof(c_0_2682,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_1515])])]) ).
fof(c_0_2683,plain,
! [X37,X38,X39,X40] :
( ~ semilattice_sup(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),X38),X40))
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X38)),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1516])])]) ).
fof(c_0_2684,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_sup(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X37),X36)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1517])])]) ).
fof(c_0_2685,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,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X47),X46))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X47),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X48),X46))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1518])]) ).
fof(c_0_2686,plain,
! [X77,X78,X79,X80,X81,X82] :
( ~ comm_monoid_add(X79)
| ~ hBOOL(hAPP(fun(X77,bool),bool,hAPP(fun(X77,X78),fun(fun(X77,bool),bool),inj_on(X77,X78),X81),X82))
| hAPP(fun(X78,bool),X79,hAPP(fun(X78,X79),fun(fun(X78,bool),X79),big_co1399186613setsum(X78,X79),X80),hAPP(fun(X77,bool),fun(X78,bool),hAPP(fun(X77,X78),fun(fun(X77,bool),fun(X78,bool)),image(X77,X78),X81),X82)) = hAPP(fun(X77,bool),X79,hAPP(fun(X77,X79),fun(fun(X77,bool),X79),big_co1399186613setsum(X77,X79),hAPP(fun(X77,X78),fun(X77,X79),hAPP(fun(X78,X79),fun(fun(X77,X78),fun(X77,X79)),comp(X78,X79,X77),X80),X81)),X82) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1519])])]) ).
fof(c_0_2687,plain,
! [X22,X23] :
( ~ linordered_ring(X22)
| ~ hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less(X22),hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),X23)),zero_zero(X22))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1520])])]) ).
fof(c_0_2688,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1521])])]) ).
fof(c_0_2689,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1522])])]) ).
fof(c_0_2690,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1523])])]) ).
fof(c_0_2691,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1524])])]) ).
fof(c_0_2692,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1525])])]) ).
fof(c_0_2693,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1526])])]) ).
fof(c_0_2694,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1527])])]) ).
fof(c_0_2695,plain,
! [X78,X79,X80,X81] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less(X78),X80),X81))
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X81),X79))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X80),X81)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X81),X79)) = hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X80),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1528])])]) ).
fof(c_0_2696,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(fun(fun(X44,bool),fun(X45,X45)),bool,hAPP(fun(X44,fun(X45,X45)),fun(fun(fun(X44,bool),fun(X45,X45)),bool),finite_folding_idem(X44,X45),X48),X49))
| ~ 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(fun(X45,X45),fun(X45,X45),hAPP(fun(X45,X45),fun(fun(X45,X45),fun(X45,X45)),comp(X45,X45,X45),hAPP(fun(X44,bool),fun(X45,X45),X49,X47)),hAPP(fun(X44,bool),fun(X45,X45),X49,X46)) = hAPP(fun(X44,bool),fun(X45,X45),X49,X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1529])]) ).
fof(c_0_2697,plain,
! [X44,X45,X46,X47,X48,X49] :
( ~ hBOOL(hAPP(fun(fun(X44,bool),fun(X45,X45)),bool,hAPP(fun(X44,fun(X45,X45)),fun(fun(fun(X44,bool),fun(X45,X45)),bool),finite_folding_idem(X44,X45),X48),X49))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X47))
| ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
| hAPP(fun(X44,bool),fun(X45,X45),X49,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X47),X46)) = hAPP(fun(X45,X45),fun(X45,X45),hAPP(fun(X45,X45),fun(fun(X45,X45),fun(X45,X45)),comp(X45,X45,X45),hAPP(fun(X44,bool),fun(X45,X45),X49,X47)),hAPP(fun(X44,bool),fun(X45,X45),X49,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1530])]) ).
fof(c_0_2698,plain,
! [X55,X56,X57,X58] :
( ~ comm_monoid_add(X55)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
| hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X57),X58)) = hAPP(X55,X55,hAPP(X55,fun(X55,X55),plus_plus(X55),hAPP(nat,X55,X56,X57)),hAPP(fun(nat,bool),X55,hAPP(fun(nat,X55),fun(fun(nat,bool),X55),big_co1399186613setsum(nat,X55),X56),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X57),X58))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1531])])]) ).
fof(c_0_2699,plain,
! [X41,X42] : hBOOL(hAPP(fun(fun(X41,X41),bool),bool,hAPP(fun(X41,X41),fun(fun(fun(X41,X41),bool),bool),member(fun(X41,X41)),combi(X41)),hAPP(fun(X41,fun(X41,bool)),fun(fun(X41,X41),bool),hAPP(fun(X41,bool),fun(fun(X41,fun(X41,bool)),fun(fun(X41,X41),bool)),pi(X41,X41),X42),hAPP(fun(X41,bool),fun(X41,fun(X41,bool)),combk(fun(X41,bool),X41),X42)))),
inference(variable_rename,[status(thm)],[c_0_1532]) ).
fof(c_0_2700,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_1533]) ).
fof(c_0_2701,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_1534]) ).
fof(c_0_2702,plain,
! [X44,X45,X46,X47,X48,X49,X50,X51] :
( ( 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),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47))) )
& ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X47))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47))) )
& ( ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),X50))
| ~ hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),X51))
| hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),X49),hAPP(fun(X48,bool),fun(X48,bool),hAPP(fun(X48,bool),fun(fun(X48,bool),fun(X48,bool)),semilattice_inf_inf(fun(X48,bool)),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_1535])])])])]) ).
fof(c_0_2703,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(X44,fun(fun(X44,bool),bool),member(X44),X46),X45))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X47),X45))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1536])]) ).
fof(c_0_2704,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(fun(X41,bool),fun(X42,X42)),bool,hAPP(fun(X41,fun(X42,X42)),fun(fun(fun(X41,bool),fun(X42,X42)),bool),finite_folding_idem(X41,X42),X45),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X44))
| hAPP(fun(X42,X42),fun(X42,X42),hAPP(fun(X42,X42),fun(fun(X42,X42),fun(X42,X42)),comp(X42,X42,X42),hAPP(fun(X41,bool),fun(X42,X42),X46,X44)),hAPP(X41,fun(X42,X42),X45,X43)) = hAPP(fun(X41,bool),fun(X42,X42),X46,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1537])]) ).
fof(c_0_2705,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47)))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X46)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1538])])])]) ).
fof(c_0_2706,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47)))
| 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_1539])]) ).
fof(c_0_2707,plain,
! [X44,X45,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),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47))) )
& ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X47))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X47))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1540])])]) ).
fof(c_0_2708,plain,
! [X41,X42] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42))
| hAPP(fun(X41,bool),nat,finite_card(X41),X42) = hAPP(fun(X41,bool),nat,hAPP(nat,fun(fun(X41,bool),nat),hAPP(fun(X41,nat),fun(nat,fun(fun(X41,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X41,nat),fun(nat,fun(fun(X41,bool),nat))),finite_fold_image(nat,X41),plus_plus(nat)),hAPP(nat,fun(X41,nat),combk(nat,X41),one_one(nat))),zero_zero(nat)),X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1541])]) ).
fof(c_0_2709,plain,
! [X41,X42,X43,X44] :
( ( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42))
| hAPP(fun(X41,bool),nat,finite_card(X41),X42) = hAPP(fun(X41,bool),nat,hAPP(nat,fun(fun(X41,bool),nat),hAPP(fun(X41,nat),fun(nat,fun(fun(X41,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X41,nat),fun(nat,fun(fun(X41,bool),nat))),finite_fold_image(nat,X41),plus_plus(nat)),hAPP(nat,fun(X41,nat),combk(nat,X41),one_one(nat))),zero_zero(nat)),X42) )
& ( hBOOL(hAPP(fun(X43,bool),bool,finite_finite_1(X43),X44))
| hAPP(fun(X43,bool),nat,finite_card(X43),X44) = 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_1542])])])]) ).
fof(c_0_2710,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_1543])]) ).
fof(c_0_2711,plain,
! [X44,X45,X46,X47,X48] :
( ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X48))
| ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),hAPP(fun(X45,bool),fun(X44,bool),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X44,bool)),image(X45,X44),X47),X48)))
| hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1544])]) ).
fof(c_0_2712,plain,
! [X23,X24,X25] :
( ~ linord20386208strict(X23)
| ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),X25)))
| ~ 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)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1545])])]) ).
fof(c_0_2713,plain,
! [X23,X24,X25] :
( ~ linord20386208strict(X23)
| ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),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)),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1546])])]) ).
fof(c_0_2714,plain,
! [X41,X42,X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(fun(X43,bool),bool,hAPP(X43,fun(fun(X43,bool),bool),member(X43),X46),X47))
| hAPP(X43,X41,hAPP(fun(X43,X42),fun(X43,X41),hAPP(fun(X42,X41),fun(fun(X43,X42),fun(X43,X41)),hAPP(fun(X43,bool),fun(fun(X42,X41),fun(fun(X43,X42),fun(X43,X41))),compose(X43,X42,X41),X47),X44),X45),X46) = hAPP(X42,X41,X44,hAPP(X43,X42,X45,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1547])]) ).
fof(c_0_2715,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X44),top_top(fun(X41,bool))))
| hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),hilbert_inv_into(X41,X42),top_top(fun(X41,bool))),X44)),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X44),X43)) = ti(fun(X41,bool),X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1548])]) ).
fof(c_0_2716,plain,
! [X84,X85,X86,X87] :
( ~ hBOOL(hAPP(fun(X84,bool),bool,hAPP(fun(X84,X85),fun(fun(X84,bool),bool),inj_on(X84,X85),X87),top_top(fun(X84,bool))))
| hAPP(fun(X85,bool),fun(X84,bool),hAPP(fun(X85,X84),fun(fun(X85,bool),fun(X84,bool)),image(X85,X84),hAPP(fun(X84,X85),fun(X85,X84),hAPP(fun(X84,bool),fun(fun(X84,X85),fun(X85,X84)),hilbert_inv_into(X84,X85),top_top(fun(X84,bool))),X87)),hAPP(fun(X84,bool),fun(X85,bool),hAPP(fun(X84,X85),fun(fun(X84,bool),fun(X85,bool)),image(X84,X85),X87),X86)) = ti(fun(X84,bool),X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1549])]) ).
fof(c_0_2717,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X55),X56)) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X55)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X56)),
inference(variable_rename,[status(thm)],[c_0_1550]) ).
fof(c_0_2718,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X56)) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X55)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X56)),
inference(variable_rename,[status(thm)],[c_0_1551]) ).
fof(c_0_2719,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44)))
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X44))
| hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1552])]) ).
fof(c_0_2720,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_1553]) ).
fof(c_0_2721,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)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46)),X45)),
inference(variable_rename,[status(thm)],[c_0_1554]) ).
fof(c_0_2722,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)),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46)),X46)),
inference(variable_rename,[status(thm)],[c_0_1555]) ).
fof(c_0_2723,plain,
! [X44,X45,X46,X47,X48] : hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X47),X48)) = hAPP(fun(X45,bool),fun(X45,bool),hAPP(fun(X45,bool),fun(fun(X45,bool),fun(X45,bool)),semilattice_sup_sup(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)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X48)),
inference(variable_rename,[status(thm)],[c_0_1556]) ).
fof(c_0_2724,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_1557]) ).
fof(c_0_2725,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_1558]) ).
fof(c_0_2726,plain,
! [X96,X97,X98,X99,X100] :
( ~ comm_semiring_1(X96)
| hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X98)),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X99),X100)) = hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X99)),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X98),X100)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1559])])]) ).
fof(c_0_2727,plain,
! [X96,X97,X98,X99,X100] :
( ~ comm_semiring_1(X96)
| hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X98)),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X99),X100)) = hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X98),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X99),X100))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1560])])]) ).
fof(c_0_2728,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_1561])])]) ).
fof(c_0_2729,plain,
! [X41,X42,X43,X44,X45] :
( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X44),X45))
| hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),hAPP(X42,X41,X43,X44)),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X45))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1562])]) ).
fof(c_0_2730,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X43),X44))
| hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),the_inv_into(X41,X42),X44),X43)),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X43),X44)) = ti(fun(X41,bool),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1563])]) ).
fof(c_0_2731,plain,
! [X39,X40,X41,X42] :
( ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),X41),hAPP(fun(X40,bool),fun(X39,bool),hAPP(fun(X40,X39),fun(fun(X40,bool),fun(X39,bool)),image(X40,X39),X42),top_top(fun(X40,bool)))))
| ti(X39,X41) = hAPP(X40,X39,X42,esk116_4(X39,X40,X41,X42)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1564])])]) ).
fof(c_0_2732,plain,
! [X50] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X50)))),
inference(variable_rename,[status(thm)],[c_0_1565]) ).
fof(c_0_2733,plain,
! [X85,X86,X89,X90,X91,X92] :
( ( ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X86))
| ti(fun(X85,bool),X86) = hAPP(fun(nat,bool),fun(X85,bool),hAPP(fun(nat,X85),fun(fun(nat,bool),fun(X85,bool)),image(nat,X85),esk119_2(X85,X86)),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)),esk118_2(X85,X86)))) )
& ( ti(fun(X89,bool),X90) != hAPP(fun(nat,bool),fun(X89,bool),hAPP(fun(nat,X89),fun(fun(nat,bool),fun(X89,bool)),image(nat,X89),X92),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)),X91)))
| hBOOL(hAPP(fun(X89,bool),bool,finite_finite_1(X89),X90)) ) ),
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_1566])])])])]) ).
fof(c_0_2734,plain,
! [X41,X42,X43,X44] :
( ti(fun(X41,bool),X42) != hAPP(fun(nat,bool),fun(X41,bool),hAPP(fun(nat,X41),fun(fun(nat,bool),fun(X41,bool)),image(nat,X41),X43),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)),X44)))
| hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1567])])])]) ).
fof(c_0_2735,plain,
! [X34,X35,X36,X38,X39,X40] :
( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk162_2(X34,X35)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X35)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X35))
| ~ hBOOL(hAPP(nat,bool,X34,X36)) )
& ( hBOOL(hAPP(nat,bool,X34,esk162_2(X34,X35)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X35))
| ~ hBOOL(hAPP(nat,bool,X34,X36)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk163_2(X38,X39)),X39))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X40),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X39)))
| ~ hBOOL(hAPP(nat,bool,X38,X40)) )
& ( hBOOL(hAPP(nat,bool,X38,esk163_2(X38,X39)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X40),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X39)))
| ~ hBOOL(hAPP(nat,bool,X38,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_1568])])])])])]) ).
fof(c_0_2736,plain,
! [X34,X35,X36,X38,X39,X40] :
( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk114_2(X34,X35)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X35)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35))
| ~ hBOOL(hAPP(nat,bool,X34,X36)) )
& ( hBOOL(hAPP(nat,bool,X34,esk114_2(X34,X35)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35))
| ~ hBOOL(hAPP(nat,bool,X34,X36)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk115_2(X38,X39)),X39))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X40),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X39)))
| ~ hBOOL(hAPP(nat,bool,X38,X40)) )
& ( hBOOL(hAPP(nat,bool,X38,esk115_2(X38,X39)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X40),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X39)))
| ~ hBOOL(hAPP(nat,bool,X38,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_1569])])])])])]) ).
fof(c_0_2737,plain,
! [X16,X17,X18,X19,X20] :
( ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X17),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X17))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)))
| ~ linord581940658strict(X16) )
& ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X18),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X17))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)))
| ~ linord581940658strict(X16) )
& ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X17),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X18))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)))
| ~ linord581940658strict(X16) )
& ( hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X18),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X18))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18)))
| ~ linord581940658strict(X16) )
& ( ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X19))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),X20))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X19),X20)))
| ~ linord581940658strict(X16) )
& ( ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X19),zero_zero(X16)))
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),X20),zero_zero(X16)))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X19),X20)))
| ~ linord581940658strict(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_1570])])])])]) ).
fof(c_0_2738,plain,
! [X39,X40,X41,X42,X43,X44,X45] :
( ( hAPP(fun(X39,bool),fun(X40,bool),hAPP(fun(X39,X40),fun(fun(X39,bool),fun(X40,bool)),image(X39,X40),X41),top_top(fun(X39,bool))) != top_top(fun(X40,bool))
| hAPP(X39,X40,X41,hAPP(X40,X39,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))),X41),X42)) = ti(X40,X42) )
& ( hAPP(X43,X44,X45,hAPP(X44,X43,hAPP(fun(X43,X44),fun(X44,X43),hAPP(fun(X43,bool),fun(fun(X43,X44),fun(X44,X43)),hilbert_inv_into(X43,X44),top_top(fun(X43,bool))),X45),esk106_3(X43,X44,X45))) != ti(X44,esk106_3(X43,X44,X45))
| hAPP(fun(X43,bool),fun(X44,bool),hAPP(fun(X43,X44),fun(fun(X43,bool),fun(X44,bool)),image(X43,X44),X45),top_top(fun(X43,bool))) = top_top(fun(X44,bool)) ) ),
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_1571])])])])]) ).
fof(c_0_2739,plain,
! [X41,X42,X43,X44] :
( ~ comm_monoid_add(X42)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X43),X44) = hAPP(fun(X41,bool),X42,hAPP(X42,fun(fun(X41,bool),X42),hAPP(fun(X41,X42),fun(X42,fun(fun(X41,bool),X42)),hAPP(fun(X42,fun(X42,X42)),fun(fun(X41,X42),fun(X42,fun(fun(X41,bool),X42))),finite_fold_image(X42,X41),plus_plus(X42)),X43),zero_zero(X42)),X44) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1572])])]) ).
fof(c_0_2740,plain,
! [X41,X42,X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X43),X44) = hAPP(fun(X41,bool),X42,hAPP(X42,fun(fun(X41,bool),X42),hAPP(fun(X41,X42),fun(X42,fun(fun(X41,bool),X42)),hAPP(fun(X42,fun(X42,X42)),fun(fun(X41,X42),fun(X42,fun(fun(X41,bool),X42))),finite_fold_image(X42,X41),plus_plus(X42)),X43),zero_zero(X42)),X44)
| ~ comm_monoid_add(X42) )
& ( hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X46))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X45),X46) = zero_zero(X42)
| ~ comm_monoid_add(X42) ) ),
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_1573])])])])]) ).
fof(c_0_2741,plain,
! [X34,X35,X37,X38,X39,X41] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk164_2(X34,X35)),X35))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X37),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X35)))
| hBOOL(hAPP(nat,bool,X34,X37)) )
& ( ~ hBOOL(hAPP(nat,bool,X34,esk164_2(X34,X35)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X37),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X35)))
| hBOOL(hAPP(nat,bool,X34,X37)) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk165_2(X38,X39)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X39)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X41),X39))
| hBOOL(hAPP(nat,bool,X38,X41)) )
& ( ~ hBOOL(hAPP(nat,bool,X38,esk165_2(X38,X39)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X41),X39))
| hBOOL(hAPP(nat,bool,X38,X41)) ) ),
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_1574])])])])])]) ).
fof(c_0_2742,plain,
! [X34,X35,X37,X38,X39,X41] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk112_2(X34,X35)),X35))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X37),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X35)))
| hBOOL(hAPP(nat,bool,X34,X37)) )
& ( ~ hBOOL(hAPP(nat,bool,X34,esk112_2(X34,X35)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X37),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X35)))
| hBOOL(hAPP(nat,bool,X34,X37)) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk113_2(X38,X39)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X39)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X41),X39))
| hBOOL(hAPP(nat,bool,X38,X41)) )
& ( ~ hBOOL(hAPP(nat,bool,X38,esk113_2(X38,X39)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X41),X39))
| hBOOL(hAPP(nat,bool,X38,X41)) ) ),
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_1575])])])])])]) ).
fof(c_0_2743,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_inf(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X36),X37)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1576])])]) ).
fof(c_0_2744,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_inf(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X37),X36)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1577])])]) ).
fof(c_0_2745,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_inf(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X37),X36)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1578])])]) ).
fof(c_0_2746,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_inf(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X36),X37)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1579])])]) ).
fof(c_0_2747,plain,
! [X88,X89,X90,X91,X92,X93,X94] : hAPP(fun(X88,X89),fun(X88,X90),hAPP(fun(X89,X90),fun(fun(X88,X89),fun(X88,X90)),comp(X89,X90,X88),X92),hAPP(fun(X88,X91),fun(X88,X89),hAPP(fun(X91,X89),fun(fun(X88,X91),fun(X88,X89)),comp(X91,X89,X88),X93),X94)) = hAPP(fun(X88,X91),fun(X88,X90),hAPP(fun(X91,X90),fun(fun(X88,X91),fun(X88,X90)),comp(X91,X90,X88),hAPP(fun(X91,X89),fun(X91,X90),hAPP(fun(X89,X90),fun(fun(X91,X89),fun(X91,X90)),comp(X89,X90,X91),X92),X93)),X94),
inference(variable_rename,[status(thm)],[c_0_1580]) ).
fof(c_0_2748,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_1581])])])])]) ).
fof(c_0_2749,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_1582])])])])]) ).
fof(c_0_2750,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_1583])])])]) ).
fof(c_0_2751,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_1584])]) ).
fof(c_0_2752,plain,
! [X41,X42,X43,X44,X45,X46] : hAPP(fun(X41,X42),fun(X41,X43),hAPP(fun(X42,X43),fun(fun(X41,X42),fun(X41,X43)),hAPP(fun(X41,bool),fun(fun(X42,X43),fun(fun(X41,X42),fun(X41,X43))),compose(X41,X42,X43),X44),X45),X46) = hAPP(fun(X41,bool),fun(X41,X43),hAPP(fun(X41,X43),fun(fun(X41,bool),fun(X41,X43)),restrict(X41,X43),hAPP(fun(X41,X42),fun(X41,X43),hAPP(fun(X42,X43),fun(fun(X41,X42),fun(X41,X43)),combb(X42,X43,X41),X45),X46)),X44),
inference(variable_rename,[status(thm)],[c_0_1585]) ).
fof(c_0_2753,plain,
! [X54,X55,X56,X57] :
( ( hBOOL(hAPP(X54,bool,hAPP(X55,fun(X54,bool),X57,esk57_4(X54,X55,X56,X57)),esk58_4(X54,X55,X56,X57)))
| hBOOL(hAPP(fun(X55,fun(X54,bool)),bool,hAPP(fun(X55,fun(X54,bool)),fun(fun(X55,fun(X54,bool)),bool),ord_less_eq(fun(X55,fun(X54,bool))),X57),X56)) )
& ( ~ hBOOL(hAPP(X54,bool,hAPP(X55,fun(X54,bool),X56,esk57_4(X54,X55,X56,X57)),esk58_4(X54,X55,X56,X57)))
| hBOOL(hAPP(fun(X55,fun(X54,bool)),bool,hAPP(fun(X55,fun(X54,bool)),fun(fun(X55,fun(X54,bool)),bool),ord_less_eq(fun(X55,fun(X54,bool))),X57),X56)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1586])])])]) ).
fof(c_0_2754,plain,
! [X40,X41,X42,X43,X44] :
( hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X44),top_top(fun(X41,bool))) != top_top(fun(X42,bool))
| hAPP(fun(X42,bool),fun(X40,bool),hAPP(fun(X42,X40),fun(fun(X42,bool),fun(X40,bool)),image(X42,X40),X43),top_top(fun(X42,bool))) != top_top(fun(X40,bool))
| hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),hAPP(fun(X41,X42),fun(X41,X40),hAPP(fun(X42,X40),fun(fun(X41,X42),fun(X41,X40)),comp(X42,X40,X41),X43),X44)),top_top(fun(X41,bool))) = top_top(fun(X40,bool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1587])]) ).
fof(c_0_2755,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP(fun(X8,bool),bool,hAPP(fun(X8,bool),fun(fun(X8,bool),bool),ord_less_eq(fun(X8,bool)),hAPP(X8,fun(X8,bool),ord_atLeast(X8),X9)),hAPP(X8,fun(X8,bool),ord_atLeast(X8),X10)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),X9))
| ~ order(X8) )
& ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X12),X11))
| hBOOL(hAPP(fun(X8,bool),bool,hAPP(fun(X8,bool),fun(fun(X8,bool),bool),ord_less_eq(fun(X8,bool)),hAPP(X8,fun(X8,bool),ord_atLeast(X8),X11)),hAPP(X8,fun(X8,bool),ord_atLeast(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_1588])])])])]) ).
fof(c_0_2756,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP(fun(X8,bool),bool,hAPP(fun(X8,bool),fun(fun(X8,bool),bool),ord_less_eq(fun(X8,bool)),hAPP(X8,fun(X8,bool),ord_greaterThan(X8),X9)),hAPP(X8,fun(X8,bool),ord_greaterThan(X8),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(fun(X8,bool),bool,hAPP(fun(X8,bool),fun(fun(X8,bool),bool),ord_less_eq(fun(X8,bool)),hAPP(X8,fun(X8,bool),ord_greaterThan(X8),X11)),hAPP(X8,fun(X8,bool),ord_greaterThan(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_1589])])])])]) ).
fof(c_0_2757,plain,
! [X52,X53,X54] :
( ~ linordered_semidom(X52)
| ~ hBOOL(hAPP(X52,bool,hAPP(X52,fun(X52,bool),ord_less(X52),one_one(X52)),X54))
| ~ hBOOL(hAPP(X52,bool,hAPP(X52,fun(X52,bool),ord_less(X52),one_one(X52)),X53))
| hBOOL(hAPP(X52,bool,hAPP(X52,fun(X52,bool),ord_less(X52),one_one(X52)),hAPP(X52,X52,hAPP(X52,fun(X52,X52),times_times(X52),X54),X53))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1590])])]) ).
fof(c_0_2758,plain,
! [X23,X24,X25] :
( ~ linord20386208strict(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),times_times(X23),X25),X24))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1591])])]) ).
fof(c_0_2759,plain,
! [X23,X24,X25] :
( ( ~ 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),times_times(X23),X25),X24)))
| ~ ordered_ring(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),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24)))
| ~ ordered_ring(X23) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1592])])])]) ).
fof(c_0_2760,plain,
! [X23,X24,X25] :
( ~ ordere453448008miring(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),times_times(X23),X25),X24))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1593])])]) ).
fof(c_0_2761,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_1594])])]) ).
fof(c_0_2762,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_1595])])]) ).
fof(c_0_2763,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_1596])])]) ).
fof(c_0_2764,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_1597])])]) ).
fof(c_0_2765,plain,
! [X40,X41,X42,X43,X44] : hAPP(fun(X40,bool),fun(X41,bool),hAPP(fun(X40,X41),fun(fun(X40,bool),fun(X41,bool)),image(X40,X41),hAPP(fun(X40,X42),fun(X40,X41),hAPP(fun(X42,X41),fun(fun(X40,X42),fun(X40,X41)),combb(X42,X41,X40),X43),X44)),top_top(fun(X40,bool))) = hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),hAPP(fun(X40,bool),fun(X42,bool),hAPP(fun(X40,X42),fun(fun(X40,bool),fun(X42,bool)),image(X40,X42),X44),top_top(fun(X40,bool)))),
inference(variable_rename,[status(thm)],[c_0_1598]) ).
fof(c_0_2766,plain,
! [X23,X24,X25] :
( ~ linord581940658strict(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),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1599])])]) ).
fof(c_0_2767,plain,
! [X23,X24,X25] :
( ~ ordered_ring(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),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1600])])]) ).
fof(c_0_2768,plain,
! [X27,X28] :
( ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk27_2(X27,X28)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X27) = ti(arrow_2142409994le_alt,X28) )
& ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X27),X28)),esk27_2(X27,X28)))
| ti(arrow_2142409994le_alt,X27) = ti(arrow_2142409994le_alt,X28) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1601])])])]) ).
fof(c_0_2769,plain,
! [X38,X39,X40,X41] :
( ~ ordere216010020id_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1602])])]) ).
fof(c_0_2770,plain,
! [X38,X39,X40,X41] :
( ~ ordere216010020id_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1603])])]) ).
fof(c_0_2771,plain,
! [X38,X39,X40,X41] :
( ~ linordered_semidom(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),zero_zero(X38)),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1604])])]) ).
fof(c_0_2772,plain,
! [X38,X39,X40,X41] :
( ~ ordere216010020id_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1605])])]) ).
fof(c_0_2773,plain,
! [X38,X39,X40,X41] :
( ~ ordere216010020id_add(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),zero_zero(X38)),X41))
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X40))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X40),X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1606])])]) ).
fof(c_0_2774,plain,
! [X10,X11,X12,X13,X14,X15,X16] :
( ( hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X11),X12))
| ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X11),hAPP(X10,X10,hAPP(X10,fun(X10,X10),semilattice_inf_inf(X10),X12),X13)))
| ~ semilattice_inf(X10) )
& ( hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X11),X13))
| ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X11),hAPP(X10,X10,hAPP(X10,fun(X10,X10),semilattice_inf_inf(X10),X12),X13)))
| ~ semilattice_inf(X10) )
& ( ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X14),X15))
| ~ hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X14),X16))
| hBOOL(hAPP(X10,bool,hAPP(X10,fun(X10,bool),ord_less_eq(X10),X14),hAPP(X10,X10,hAPP(X10,fun(X10,X10),semilattice_inf_inf(X10),X15),X16)))
| ~ semilattice_inf(X10) ) ),
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_1607])])])])]) ).
fof(c_0_2775,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_inf(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X36))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X38),X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1608])])]) ).
fof(c_0_2776,plain,
! [X37,X38,X39,X40] :
( ~ semilattice_inf(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),X39),X38))
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X40),X38))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1609])])]) ).
fof(c_0_2777,plain,
! [X76,X77,X78] :
( ( hBOOL(hAPP(X76,bool,hAPP(X76,fun(X76,bool),ord_less(X76),zero_zero(X76)),esk100_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),esk100_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_1610])])])])]) ).
fof(c_0_2778,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),esk20_0))
& hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk20_0),arrow_1568854078le_Lin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1611])])]) ).
fof(c_0_2779,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),esk19_0))
& hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk19_0),arrow_1568854078le_Lin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1612])])]) ).
fof(c_0_2780,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
c_0_1613 ).
fof(c_0_2781,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
c_0_1614 ).
fof(c_0_2782,plain,
! [X107,X108,X109,X110,X111,X112] : hAPP(fun(X107,bool),fun(X108,bool),hAPP(fun(X107,X108),fun(fun(X107,bool),fun(X108,bool)),image(X107,X108),hAPP(fun(X107,X109),fun(X107,X108),hAPP(fun(X109,X108),fun(fun(X107,X109),fun(X107,X108)),comp(X109,X108,X107),X110),X111)),X112) = hAPP(fun(X109,bool),fun(X108,bool),hAPP(fun(X109,X108),fun(fun(X109,bool),fun(X108,bool)),image(X109,X108),X110),hAPP(fun(X107,bool),fun(X109,bool),hAPP(fun(X107,X109),fun(fun(X107,bool),fun(X109,bool)),image(X107,X109),X111),X112)),
inference(variable_rename,[status(thm)],[c_0_1615]) ).
fof(c_0_2783,plain,
! [X41,X42,X43,X44,X45,X46] : hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X44),hAPP(fun(X43,bool),fun(X41,bool),hAPP(fun(X43,X41),fun(fun(X43,bool),fun(X41,bool)),image(X43,X41),X45),X46)) = hAPP(fun(X43,bool),fun(X42,bool),hAPP(fun(X43,X42),fun(fun(X43,bool),fun(X42,bool)),image(X43,X42),hAPP(fun(X43,X41),fun(X43,X42),hAPP(fun(X41,X42),fun(fun(X43,X41),fun(X43,X42)),combb(X41,X42,X43),X44),X45)),X46),
inference(variable_rename,[status(thm)],[c_0_1616]) ).
fof(c_0_2784,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_1617])])])])]) ).
fof(c_0_2785,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),X46))
| hAPP(X41,X42,X45,X43) != hAPP(X41,X42,X45,X44)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),X46))
| ti(X41,X43) = ti(X41,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1618])]) ).
fof(c_0_2786,plain,
! [X41,X42,X43,X44,X45,X46] :
( ( hAPP(X41,X42,X45,X44) != hAPP(X41,X42,X45,X43)
| ti(X41,X44) = ti(X41,X43)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),X46)) )
& ( ti(X41,X44) != ti(X41,X43)
| hAPP(X41,X42,X45,X44) = hAPP(X41,X42,X45,X43)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),X46)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1619])])]) ).
fof(c_0_2787,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),X46))
| ti(X41,X43) = ti(X41,X44)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),X46))
| hAPP(X41,X42,X45,X43) != hAPP(X41,X42,X45,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1620])]) ).
fof(c_0_2788,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X43),X44))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X45),X44))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X44))
| hAPP(X41,X42,X43,X45) != hAPP(X41,X42,X43,X46)
| ti(X41,X45) = ti(X41,X46) )
& ( hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),esk31_4(X47,X48,X49,X50)),X50))
| hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X49),X50)) )
& ( hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),esk32_4(X47,X48,X49,X50)),X50))
| hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X49),X50)) )
& ( hAPP(X47,X48,X49,esk31_4(X47,X48,X49,X50)) = hAPP(X47,X48,X49,esk32_4(X47,X48,X49,X50))
| hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X49),X50)) )
& ( ti(X47,esk31_4(X47,X48,X49,X50)) != ti(X47,esk32_4(X47,X48,X49,X50))
| hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),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_1621])])])])])]) ).
fof(c_0_2789,plain,
! [X37,X38,X39,X40] :
( ~ distrib_lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X40)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1622])])]) ).
fof(c_0_2790,plain,
! [X37,X38,X39,X40] :
( ~ distrib_lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X40)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1623])])]) ).
fof(c_0_2791,plain,
! [X38,X39,X40,X41] :
( ~ comm_semiring(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1624])])]) ).
fof(c_0_2792,plain,
! [X38,X39,X40,X41] :
( ~ comm_semiring_1(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X41)),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1625])])]) ).
fof(c_0_2793,plain,
! [X50,X51,X52,X53] :
( ~ comm_semiring_1(X50)
| hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),X51),X52)),hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),X53),X52)) = hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),X51),X53)),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1626])])]) ).
fof(c_0_2794,plain,
! [X55,X56,X57,X58] :
( ( 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56))) )
& ( 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),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)),X58))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1627])])])])]) ).
fof(c_0_2795,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X45),X46))
| ti(X41,X43) != hAPP(X42,X41,X44,X45)
| hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X44),X46))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1628])]) ).
fof(c_0_2796,plain,
! [X41,X42,X43,X44,X45,X46] :
( ti(X41,X44) != hAPP(X42,X41,X45,X46)
| ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(X42,fun(fun(X42,bool),bool),member(X42),X46),X43))
| hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X45),X43))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1629])]) ).
fof(c_0_2797,plain,
! [X41,X42,X43,X45,X46] :
( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk175_3(X41,X42,X43)),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( hAPP(X41,nat,X42,esk175_3(X41,X42,X43)) = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X45),X43))
| ti(X41,esk175_3(X41,X42,X43)) = ti(X41,X45)
| hAPP(X41,nat,X42,X45) = zero_zero(nat)
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk176_4(X41,X42,X43,X46)),X43))
| hAPP(X41,nat,X42,X46) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( ti(X41,X46) != ti(X41,esk176_4(X41,X42,X43,X46))
| hAPP(X41,nat,X42,X46) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( hAPP(X41,nat,X42,esk176_4(X41,X42,X43,X46)) != zero_zero(nat)
| hAPP(X41,nat,X42,X46) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) ) ),
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_1630])])])])]) ).
fof(c_0_2798,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_1631])])])])]) ).
fof(c_0_2799,plain,
! [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))))
| hAPP(fun(X40,bool),fun(X39,bool),hAPP(fun(X40,X39),fun(fun(X40,bool),fun(X39,bool)),image(X40,X39),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))),X41)),top_top(fun(X40,bool))) = top_top(fun(X39,bool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1632])]) ).
fof(c_0_2800,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(X44,fun(fun(X44,bool),bool),member(X44),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X47))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1633])]) ).
fof(c_0_2801,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(X44,fun(fun(X44,bool),bool),member(X44),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X47),X45))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1634])]) ).
fof(c_0_2802,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(X44,fun(fun(X44,bool),bool),member(X44),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X47))) )
& ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),X45))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X47))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1635])])]) ).
fof(c_0_2803,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X55)),X56) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X55),X56)),
inference(variable_rename,[status(thm)],[c_0_1636]) ).
fof(c_0_2804,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X55)),X56) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X56)),
inference(variable_rename,[status(thm)],[c_0_1637]) ).
fof(c_0_2805,plain,
! [X52,X53,X54] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X53),X54)),
inference(variable_rename,[status(thm)],[c_0_1638]) ).
fof(c_0_2806,plain,
! [X15,X16] :
( ~ ring_char_0(X15)
| ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),ring_1_Ints(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) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1639])])]) ).
fof(c_0_2807,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_1640])])])])]) ).
fof(c_0_2808,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_1641])])])])]) ).
fof(c_0_2809,plain,
! [X35,X36,X37,X38] :
( ( 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),X36),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X37),X38)))
| ~ semilattice_inf(X35) )
& ( hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X38))
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X37),X38)))
| ~ semilattice_inf(X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1642])])])]) ).
fof(c_0_2810,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46),X47))
| hBOOL(hAPP(X44,bool,X45,X47))
| hBOOL(hAPP(X44,bool,X46,X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1643])]) ).
fof(c_0_2811,plain,
! [X41,X42,X43,X44,X45] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X44),X45))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X45))
| hAPP(X42,X41,hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),the_inv_into(X41,X42),X45),X44),hAPP(X41,X42,X44,X43)) = ti(X41,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1644])]) ).
fof(c_0_2812,plain,
! [X41,X42,X43,X44,X45] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X44),X45))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X45))
| hAPP(X42,X41,hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),hilbert_inv_into(X41,X42),X45),X44),hAPP(X41,X42,X44,X43)) = ti(X41,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1645])]) ).
fof(c_0_2813,plain,
! [X54,X55,X56,X57,X58,X59] :
( ~ hBOOL(hAPP(fun(X54,fun(X55,bool)),bool,hAPP(fun(X54,fun(X55,bool)),fun(fun(X54,fun(X55,bool)),bool),ord_less_eq(fun(X54,fun(X55,bool))),X58),X59))
| ~ hBOOL(hAPP(X55,bool,hAPP(X54,fun(X55,bool),X58,X56),X57))
| hBOOL(hAPP(X55,bool,hAPP(X54,fun(X55,bool),X59,X56),X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1646])]) ).
fof(c_0_2814,plain,
! [X54,X55,X56,X57,X58,X59] :
( ~ hBOOL(hAPP(X54,bool,hAPP(X55,fun(X54,bool),X57,X58),X59))
| ~ hBOOL(hAPP(fun(X55,fun(X54,bool)),bool,hAPP(fun(X55,fun(X54,bool)),fun(fun(X55,fun(X54,bool)),bool),ord_less_eq(fun(X55,fun(X54,bool))),X57),X56))
| hBOOL(hAPP(X54,bool,hAPP(X55,fun(X54,bool),X56,X58),X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1647])]) ).
fof(c_0_2815,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_1648])]) ).
fof(c_0_2816,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_1649])]) ).
fof(c_0_2817,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),X46))
| hAPP(X41,X42,X45,X43) != ti(X42,X44)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X46))
| hAPP(X42,X41,hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),the_inv_into(X41,X42),X46),X45),X44) = ti(X41,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1650])]) ).
fof(c_0_2818,plain,
! [X41,X42,X43,X44,X45,X46] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X45),X46))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),X46))
| hAPP(X41,X42,X45,X44) != ti(X42,X43)
| hAPP(X42,X41,hAPP(fun(X41,X42),fun(X42,X41),hAPP(fun(X41,bool),fun(fun(X41,X42),fun(X42,X41)),hilbert_inv_into(X41,X42),X46),X45),X43) = ti(X41,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1651])]) ).
fof(c_0_2819,plain,
! [X41,X42,X43,X45,X46] :
( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk177_3(X41,X42,X43)),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) != one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( hAPP(X41,nat,X42,esk177_3(X41,X42,X43)) = one_one(nat)
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) != one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X45),X43))
| ti(X41,esk177_3(X41,X42,X43)) = ti(X41,X45)
| hAPP(X41,nat,X42,X45) = zero_zero(nat)
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) != one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk178_4(X41,X42,X43,X46)),X43))
| hAPP(X41,nat,X42,X46) != one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) = one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( ti(X41,X46) != ti(X41,esk178_4(X41,X42,X43,X46))
| hAPP(X41,nat,X42,X46) != one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) = one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
& ( hAPP(X41,nat,X42,esk178_4(X41,X42,X43,X46)) != zero_zero(nat)
| hAPP(X41,nat,X42,X46) != one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X46),X43))
| hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),X42),X43) = one_one(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) ) ),
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_1652])])])])]) ).
fof(c_0_2820,plain,
! [X8,X9,X10,X11,X12] :
( ( ti(X8,X9) = zero_zero(X8)
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X9),X9)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X10),X10)) != zero_zero(X8)
| ~ linord581940658strict(X8) )
& ( ti(X8,X10) = zero_zero(X8)
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X9),X9)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X10),X10)) != zero_zero(X8)
| ~ linord581940658strict(X8) )
& ( ti(X8,X11) != zero_zero(X8)
| ti(X8,X12) != zero_zero(X8)
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X11),X11)),hAPP(X8,X8,hAPP(X8,fun(X8,X8),times_times(X8),X12),X12)) = zero_zero(X8)
| ~ linord581940658strict(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_1653])])])])]) ).
fof(c_0_2821,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_1654])])]) ).
fof(c_0_2822,plain,
! [X113,X114,X115,X116,X117,X118] :
( ( hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),X114))
| ~ hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),hAPP(fun(X113,bool),fun(X113,bool),hAPP(fun(X113,bool),fun(fun(X113,bool),fun(X113,bool)),semilattice_sup_sup(fun(X113,bool)),X114),X115))) )
& ( hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),X115))
| ~ hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),hAPP(fun(X113,bool),fun(X113,bool),hAPP(fun(X113,bool),fun(fun(X113,bool),fun(X113,bool)),semilattice_sup_sup(fun(X113,bool)),X114),X115))) )
& ( ~ hBOOL(hAPP(fun(X116,bool),bool,finite_finite_1(X116),X117))
| ~ hBOOL(hAPP(fun(X116,bool),bool,finite_finite_1(X116),X118))
| hBOOL(hAPP(fun(X116,bool),bool,finite_finite_1(X116),hAPP(fun(X116,bool),fun(X116,bool),hAPP(fun(X116,bool),fun(fun(X116,bool),fun(X116,bool)),semilattice_sup_sup(fun(X116,bool)),X117),X118))) ) ),
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_1655])])])])]) ).
fof(c_0_2823,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_1656]) ).
fof(c_0_2824,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_1657]) ).
fof(c_0_2825,plain,
! [X53,X54,X55,X56] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X55),X56))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X56),X54))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X55),X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1658])]) ).
fof(c_0_2826,plain,
! [X53,X54,X55,X56] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X56))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X56),X54))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1659])]) ).
fof(c_0_2827,plain,
! [X53,X54,X55,X56] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X55),X56))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X56),X54))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X55),X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1660])]) ).
fof(c_0_2828,plain,
! [X53,X54,X55,X56] :
( ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X55),X56))
| ~ hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less_eq(fun(X53,bool)),X56),X54))
| hBOOL(hAPP(fun(X53,bool),bool,hAPP(fun(X53,bool),fun(fun(X53,bool),bool),ord_less(fun(X53,bool)),X55),X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1661])]) ).
fof(c_0_2829,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46),X47))
| hBOOL(hAPP(X44,bool,X45,X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1662])]) ).
fof(c_0_2830,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46),X47))
| hBOOL(hAPP(X44,bool,X46,X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1663])]) ).
fof(c_0_2831,plain,
! [X44,X45,X46,X47] :
( ( hBOOL(hAPP(X44,bool,X45,X47))
| ~ hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46),X47)) )
& ( hBOOL(hAPP(X44,bool,X46,X47))
| ~ hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46),X47)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1664])])]) ).
fof(c_0_2832,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_1665])])])]) ).
fof(c_0_2833,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_1666])])])]) ).
fof(c_0_2834,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X52)),hAPP(nat,nat,suc,X53)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1667])]) ).
fof(c_0_2835,plain,
! [X39,X40,X41,X42] : hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),hAPP(X40,X39,X41,X42)),hAPP(fun(X40,bool),fun(X39,bool),hAPP(fun(X40,X39),fun(fun(X40,bool),fun(X39,bool)),image(X40,X39),X41),top_top(fun(X40,bool))))),
inference(variable_rename,[status(thm)],[c_0_1668]) ).
fof(c_0_2836,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_1669])]) ).
fof(c_0_2837,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_1670])]) ).
fof(c_0_2838,plain,
! [X39,X40,X41,X42,X43] :
( ~ hBOOL(hAPP(fun(fun(X39,bool),fun(X40,X40)),bool,hAPP(fun(X39,fun(X40,X40)),fun(fun(fun(X39,bool),fun(X40,X40)),bool),finite_folding_idem(X39,X40),X42),X43))
| hAPP(fun(X40,X40),fun(X40,X40),hAPP(fun(X40,X40),fun(fun(X40,X40),fun(X40,X40)),comp(X40,X40,X40),hAPP(X39,fun(X40,X40),X42,X41)),hAPP(X39,fun(X40,X40),X42,X41)) = hAPP(X39,fun(X40,X40),X42,X41) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1671])])])]) ).
fof(c_0_2839,plain,
! [X78,X79,X80] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X79),X80))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastLessThan(X78),X79),X80)),hAPP(X78,fun(X78,bool),ord_atLeast(X78),X80)) = hAPP(X78,fun(X78,bool),ord_atLeast(X78),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1672])])]) ).
fof(c_0_2840,plain,
! [X78,X79,X80] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X79),X80))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_atLeastAtMost(X78),X79),X80)),hAPP(X78,fun(X78,bool),ord_greaterThan(X78),X80)) = hAPP(X78,fun(X78,bool),ord_atLeast(X78),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1673])])]) ).
fof(c_0_2841,plain,
! [X78,X79,X80] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less(X78),X79),X80))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr676655987ssThan(X78),X79),X80)),hAPP(X78,fun(X78,bool),ord_atLeast(X78),X80)) = hAPP(X78,fun(X78,bool),ord_greaterThan(X78),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1674])])]) ).
fof(c_0_2842,plain,
! [X78,X79,X80] :
( ~ linorder(X78)
| ~ hBOOL(hAPP(X78,bool,hAPP(X78,fun(X78,bool),ord_less_eq(X78),X79),X80))
| hAPP(fun(X78,bool),fun(X78,bool),hAPP(fun(X78,bool),fun(fun(X78,bool),fun(X78,bool)),semilattice_sup_sup(fun(X78,bool)),hAPP(X78,fun(X78,bool),hAPP(X78,fun(X78,fun(X78,bool)),ord_gr1471790799AtMost(X78),X79),X80)),hAPP(X78,fun(X78,bool),ord_greaterThan(X78),X80)) = hAPP(X78,fun(X78,bool),ord_greaterThan(X78),X79) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1675])])]) ).
fof(c_0_2843,plain,
! [X40,X41,X42,X43] :
( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X43),top_top(fun(X40,bool))))
| hAPP(X40,X41,X43,hAPP(X41,X40,X42,esk34_4(X40,X41,X42,X43))) != ti(X41,esk34_4(X40,X41,X42,X43))
| 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) = ti(fun(X41,X40),X42) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1676])])]) ).
fof(c_0_2844,plain,
! [X112,X113,X114,X115,X116,X117,X118,X119,X120,X121,X122] :
( hAPP(X112,X113,X117,hAPP(X114,X112,X118,X119)) != hAPP(X115,X113,X120,hAPP(X116,X115,X121,X122))
| hAPP(X114,X113,hAPP(fun(X114,X112),fun(X114,X113),hAPP(fun(X112,X113),fun(fun(X114,X112),fun(X114,X113)),comp(X112,X113,X114),X117),X118),X119) = hAPP(X116,X113,hAPP(fun(X116,X115),fun(X116,X113),hAPP(fun(X115,X113),fun(fun(X116,X115),fun(X116,X113)),comp(X115,X113,X116),X120),X121),X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1677])]) ).
fof(c_0_2845,plain,
! [X50,X51,X52] :
( ~ comm_semiring_1(X50)
| hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),X51),X52)),X52) = hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),X51),one_one(X50))),X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1678])])]) ).
fof(c_0_2846,plain,
! [X37,X38,X39,X40] :
( ~ distrib_lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1679])])]) ).
fof(c_0_2847,plain,
! [X37,X38,X39,X40] :
( ~ distrib_lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1680])])]) ).
fof(c_0_2848,plain,
! [X96,X97,X98,X99] :
( ~ comm_semiring_1(X96)
| hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X98)),X99) = hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X99)),X98) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1681])])]) ).
fof(c_0_2849,plain,
! [X37,X38,X39,X40] :
( ~ comm_semiring_1(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),times_times(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),times_times(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),times_times(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1682])])]) ).
fof(c_0_2850,plain,
! [X38,X39,X40,X41] :
( ~ comm_semiring_1(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41)),X40) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1683])])]) ).
fof(c_0_2851,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1684])])]) ).
fof(c_0_2852,plain,
! [X36,X37,X38] :
( ~ semilattice_inf(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1685])])]) ).
fof(c_0_2853,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1686])])]) ).
fof(c_0_2854,plain,
! [X36,X37,X38] :
( ~ semilattice_inf(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1687])])]) ).
fof(c_0_2855,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_1688])]) ).
fof(c_0_2856,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_1689])]) ).
fof(c_0_2857,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_1690])]) ).
fof(c_0_2858,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_1691])]) ).
fof(c_0_2859,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_1692])]) ).
fof(c_0_2860,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_1693])]) ).
fof(c_0_2861,plain,
! [X40,X41,X42,X43,X44] :
( ~ ord(X41)
| ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X43),X44))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(X40,X41,X43,X42)),hAPP(X40,X41,X44,X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1694])])]) ).
fof(c_0_2862,plain,
! [X40,X41,X42,X43,X44] :
( ~ ord(X41)
| ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X43),X44))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(X40,X41,X43,X42)),hAPP(X40,X41,X44,X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1695])])]) ).
fof(c_0_2863,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_1696])])])]) ).
fof(c_0_2864,plain,
! [X82,X83,X84,X85,X86] :
( ( ti(X82,X85) = ti(X82,X83)
| hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86) != hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X85),X86))
| ~ linorder(X82) )
& ( ti(X82,X86) = ti(X82,X84)
| hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86) != hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X85),X86))
| ~ linorder(X82) )
& ( ti(X82,X85) != ti(X82,X83)
| ti(X82,X86) != ti(X82,X84)
| hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86) = hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84)
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X85),X86))
| ~ linorder(X82) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1697])])])]) ).
fof(c_0_2865,plain,
! [X82,X83,X84,X85,X86] :
( ~ linorder(X82)
| hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84) != hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X85),X86))
| ti(X82,X83) = ti(X82,X85) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1698])])]) ).
fof(c_0_2866,plain,
! [X82,X83,X84,X85,X86] :
( ~ linorder(X82)
| hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X83),X84) != hAPP(X82,fun(X82,bool),hAPP(X82,fun(X82,fun(X82,bool)),ord_atLeastLessThan(X82),X85),X86)
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X83),X84))
| ~ hBOOL(hAPP(X82,bool,hAPP(X82,fun(X82,bool),ord_less(X82),X85),X86))
| ti(X82,X84) = ti(X82,X86) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1699])])]) ).
fof(c_0_2867,plain,
! [X58,X59,X60] :
( ~ comm_monoid_add(X58)
| hAPP(nat,X58,X60,zero_zero(nat)) != zero_zero(X58)
| hAPP(fun(nat,bool),X58,hAPP(fun(nat,X58),fun(fun(nat,bool),X58),big_co1399186613setsum(nat,X58),X60),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X59)) = hAPP(fun(nat,bool),X58,hAPP(fun(nat,X58),fun(fun(nat,bool),X58),big_co1399186613setsum(nat,X58),X60),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X59)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1700])])]) ).
fof(c_0_2868,plain,
! [X58,X59] :
( hAPP(nat,nat,X59,zero_zero(nat)) != zero_zero(nat)
| hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X58)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X59),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1701])]) ).
fof(c_0_2869,plain,
! [X52,X53,X54] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X54)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X54)),
inference(variable_rename,[status(thm)],[c_0_1702]) ).
fof(c_0_2870,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X42),X43))
| ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less(fun(X40,X41)),X42),X43))
| ~ ord(X41) )
& ( ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X43),X42))
| ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less(fun(X40,X41)),X42),X43))
| ~ ord(X41) )
& ( ~ hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X44),X45))
| hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less_eq(fun(X40,X41)),X45),X44))
| hBOOL(hAPP(fun(X40,X41),bool,hAPP(fun(X40,X41),fun(fun(X40,X41),bool),ord_less(fun(X40,X41)),X44),X45))
| ~ ord(X41) ) ),
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_1703])])])])]) ).
fof(c_0_2871,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(fun(X41,X42),bool),bool,hAPP(fun(X41,X42),fun(fun(fun(X41,X42),bool),bool),member(fun(X41,X42)),X43),hAPP(fun(X41,bool),fun(fun(X41,X42),bool),extensional(X41,X42),X44)))
| hAPP(fun(X41,bool),fun(X41,X42),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X41,X42)),restrict(X41,X42),X43),X44) = ti(fun(X41,X42),X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1704])]) ).
fof(c_0_2872,plain,
! [X98,X99,X100,X101,X102,X103] :
( ~ semiri456707255roduct(X98)
| ti(X98,X103) = zero_zero(X98)
| ti(X98,X101) != ti(X98,X102)
| ti(X98,X99) = ti(X98,X100)
| hAPP(X98,X98,hAPP(X98,fun(X98,X98),plus_plus(X98),X101),hAPP(X98,X98,hAPP(X98,fun(X98,X98),times_times(X98),X103),X99)) != hAPP(X98,X98,hAPP(X98,fun(X98,X98),plus_plus(X98),X102),hAPP(X98,X98,hAPP(X98,fun(X98,X98),times_times(X98),X103),X100)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1705])])]) ).
fof(c_0_2873,plain,
! [X39,X40,X41,X42] :
( hAPP(fun(X39,bool),fun(X40,bool),hAPP(fun(X39,X40),fun(fun(X39,bool),fun(X40,bool)),image(X39,X40),X42),top_top(fun(X39,bool))) != top_top(fun(X40,bool))
| hAPP(X39,X40,X42,hAPP(X40,X39,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),X41)) = ti(X40,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1706])]) ).
fof(c_0_2874,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_sup(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X38),X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1707])])]) ).
fof(c_0_2875,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_sup(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),X38))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1708])])]) ).
fof(c_0_2876,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_sup(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),X38))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1709])])]) ).
fof(c_0_2877,plain,
! [X35,X36,X37,X38] :
( ~ semilattice_sup(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X38))
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X38),X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1710])])]) ).
fof(c_0_2878,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_1711])])])])]) ).
fof(c_0_2879,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_1712])]) ).
fof(c_0_2880,plain,
! [X41,X42,X43,X44] :
( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X44))
| hAPP(fun(X41,bool),nat,finite_card(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44)) = hAPP(fun(X42,bool),nat,finite_card(X42),X44)
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44)) )
& ( hAPP(fun(X41,bool),nat,finite_card(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44)) != hAPP(fun(X42,bool),nat,finite_card(X42),X44)
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X44))
| ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1713])])]) ).
fof(c_0_2881,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X44))
| hAPP(fun(X41,bool),nat,finite_card(X41),hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),X43),X44)) != hAPP(fun(X42,bool),nat,finite_card(X42),X44)
| hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,X41),fun(fun(X42,bool),bool),inj_on(X42,X41),X43),X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1714])]) ).
fof(c_0_2882,plain,
! [X37,X38,X39] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X38),X39))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X38),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X39),X37))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1715])]) ).
fof(c_0_2883,plain,
! [X37,X38,X39] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X38),X39))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X38),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X37),X39))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1716])]) ).
fof(c_0_2884,plain,
! [X37,X38,X39] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X38),X39))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X38),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X37),X39))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1717])]) ).
fof(c_0_2885,plain,
! [X37,X38,X39] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X38),X39))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X38),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X39),X37))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1718])]) ).
fof(c_0_2886,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_1719])]) ).
fof(c_0_2887,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_1720])]) ).
fof(c_0_2888,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_1721])]) ).
fof(c_0_2889,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_1722])]) ).
fof(c_0_2890,plain,
! [X65,X66] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),esk95_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,esk95_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_1723])])])]) ).
fof(c_0_2891,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X52)),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1724])]) ).
fof(c_0_2892,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_1725])])])]) ).
fof(c_0_2893,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_1726])])])]) ).
fof(c_0_2894,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X52)),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1727])]) ).
fof(c_0_2895,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X52)),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1728])]) ).
fof(c_0_2896,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X55),X56)) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X55),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_inf_inf(fun(X53,bool)),X54),X56)),
inference(variable_rename,[status(thm)],[c_0_1729]) ).
fof(c_0_2897,plain,
! [X53,X54,X55,X56] : hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),X56)) = hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X55),hAPP(fun(X53,bool),fun(X53,bool),hAPP(fun(X53,bool),fun(fun(X53,bool),fun(X53,bool)),semilattice_sup_sup(fun(X53,bool)),X54),X56)),
inference(variable_rename,[status(thm)],[c_0_1730]) ).
fof(c_0_2898,plain,
! [X113,X114,X115] :
( ~ hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),X115))
| ~ hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),X114))
| hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),hAPP(fun(X113,bool),fun(X113,bool),hAPP(fun(X113,bool),fun(fun(X113,bool),fun(X113,bool)),semilattice_sup_sup(fun(X113,bool)),X115),X114))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1731])]) ).
fof(c_0_2899,plain,
! [X39,X40,X41,X42,X43] :
( ti(X39,X41) != hAPP(X40,X39,X42,X43)
| hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),X41),hAPP(fun(X40,bool),fun(X39,bool),hAPP(fun(X40,X39),fun(fun(X40,bool),fun(X39,bool)),image(X40,X39),X42),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_1732])])])]) ).
fof(c_0_2900,plain,
! [X44,X45,X46,X47,X48] :
( ( 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)
| ti(fun(X44,bool),X46) = ti(fun(X44,bool),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)))) )
& ( ti(fun(X44,bool),X46) != ti(fun(X44,bool),X47)
| 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_1733])])]) ).
fof(c_0_2901,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X52)),hAPP(nat,nat,suc,X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1734])]) ).
fof(c_0_2902,plain,
! [X58,X59,X60,X61,X63] :
( ( hBOOL(hAPP(X58,bool,X60,esk146_3(X58,X59,X60)))
| ~ hBOOL(hAPP(X58,bool,X60,X61)) )
& ( ~ hBOOL(hAPP(X58,bool,X60,X63))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X58,nat,X59,esk146_3(X58,X59,X60))),hAPP(X58,nat,X59,X63)))
| ~ hBOOL(hAPP(X58,bool,X60,X61)) ) ),
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_1735])])])])])]) ).
fof(c_0_2903,plain,
! [X41,X42,X43,X44] : hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),hAPP(fun(X41,bool),fun(X41,X42),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X41,X42)),restrict(X41,X42),X43),X44)),X44) = hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X43),X44),
inference(variable_rename,[status(thm)],[c_0_1736]) ).
fof(c_0_2904,plain,
! [X54,X55,X56] :
( ( hBOOL(hAPP(X54,bool,X56,esk150_3(X54,X55,X56)))
| hBOOL(hAPP(fun(X54,bool),bool,hAPP(fun(X54,bool),fun(fun(X54,bool),bool),ord_less_eq(fun(X54,bool)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X56)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X55))) )
& ( ~ hBOOL(hAPP(X54,bool,X55,esk150_3(X54,X55,X56)))
| hBOOL(hAPP(fun(X54,bool),bool,hAPP(fun(X54,bool),fun(fun(X54,bool),bool),ord_less_eq(fun(X54,bool)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X56)),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X55))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1737])])])]) ).
fof(c_0_2905,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),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45))),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_2906,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),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46))),
inference(variable_rename,[status(thm)],[c_0_1739]) ).
fof(c_0_2907,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X44,bool,X46,X47))
| ~ hBOOL(hAPP(X44,bool,X45,X47))
| hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X45),X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1740])]) ).
fof(c_0_2908,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(X41,X40,X42,hAPP(X40,X41,X43,esk110_4(X40,X41,X42,X43))) != ti(X40,esk110_4(X40,X41,X42,X43))
| 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) = ti(fun(X41,X40),X42) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1741])])]) ).
fof(c_0_2909,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_1742])])])])]) ).
fof(c_0_2910,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_1743])]) ).
fof(c_0_2911,plain,
! [X37,X38,X39,X40] :
( ~ order(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(X37),X38),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_1744])])]) ).
fof(c_0_2912,plain,
! [X37,X38,X39,X40] :
( ~ preorder(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(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_1745])])]) ).
fof(c_0_2913,plain,
! [X37,X38,X39,X40] :
( ~ order(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_eq(X37),X38),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_1746])])]) ).
fof(c_0_2914,plain,
! [X37,X38,X39,X40] :
( ~ preorder(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_eq(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_1747])])]) ).
fof(c_0_2915,plain,
! [X37,X38,X39,X40] :
( ~ preorder(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),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_1748])])]) ).
fof(c_0_2916,plain,
! [X37,X38,X39,X40] :
( ~ order(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),X38),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_1749])])]) ).
fof(c_0_2917,plain,
! [X37,X38,X39,X40] :
( ~ preorder(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),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_1750])])]) ).
fof(c_0_2918,plain,
! [X37,X38,X39,X40] :
( ~ order(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),X38),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_1751])])]) ).
fof(c_0_2919,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(X40,X39,hAPP(fun(X39,X40),fun(X40,X39),hAPP(fun(X39,bool),fun(fun(X39,X40),fun(X40,X39)),the_inv_into(X39,X40),top_top(fun(X39,bool))),X42),hAPP(X39,X40,X42,X41)) = ti(X39,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1752])]) ).
fof(c_0_2920,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(X40,X39,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),hAPP(X39,X40,X42,X41)) = ti(X39,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1753])]) ).
fof(c_0_2921,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
c_0_1754 ).
fof(c_0_2922,plain,
! [X39,X40,X41,X42,X43] :
( ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X40),fun(fun(X39,bool),bool),inj_on(X39,X40),X43),top_top(fun(X39,bool))))
| hAPP(X39,X40,X43,X41) != ti(X40,X42)
| hAPP(X40,X39,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))),X43),X42) = ti(X39,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1755])]) ).
fof(c_0_2923,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_1756])]) ).
fof(c_0_2924,axiom,
arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
c_0_1757 ).
fof(c_0_2925,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_1758])]) ).
fof(c_0_2926,plain,
! [X50,X51,X52] :
( ~ comm_semiring_1(X50)
| hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),X51),hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),X52),X51)) = hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),X52),one_one(X50))),X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1759])])]) ).
fof(c_0_2927,plain,
! [X38,X39,X40,X41] :
( ~ semilattice_inf(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1760])])]) ).
fof(c_0_2928,plain,
! [X37,X38,X39,X40] :
( ~ lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1761])])]) ).
fof(c_0_2929,plain,
! [X37,X38,X39,X40] :
( ~ semilattice_inf(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1762])])]) ).
fof(c_0_2930,plain,
! [X37,X38,X39,X40] :
( ~ semilattice_sup(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1763])])]) ).
fof(c_0_2931,plain,
! [X37,X38,X39,X40] :
( ~ lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1764])])]) ).
fof(c_0_2932,plain,
! [X38,X39,X40,X41] :
( ~ semilattice_sup(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1765])])]) ).
fof(c_0_2933,plain,
! [X38,X39,X40,X41] :
( ~ ab_semigroup_mult(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),times_times(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1766])])]) ).
fof(c_0_2934,plain,
! [X96,X97,X98,X99] :
( ~ comm_semiring_1(X96)
| hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),X98)),X99) = hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X97),hAPP(X96,X96,hAPP(X96,fun(X96,X96),times_times(X96),X98),X99)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1767])])]) ).
fof(c_0_2935,plain,
! [X95,X96,X97,X98] :
( ~ comm_semiring_1(X95)
| hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X96),hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X97),X98)) = hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X96),X97)),X98) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1768])])]) ).
fof(c_0_2936,plain,
! [X38,X39,X40,X41] :
( ~ comm_semiring_1(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1769])])]) ).
fof(c_0_2937,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_1770])])]) ).
fof(c_0_2938,plain,
! [X38,X39,X40,X41] :
( ~ ab_semigroup_add(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40)),X41) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X40),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1771])])]) ).
fof(c_0_2939,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_1772])])]) ).
fof(c_0_2940,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_1773])])])]) ).
fof(c_0_2941,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_1774])])])]) ).
fof(c_0_2942,plain,
! [X52,X53,X54] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53)),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X53),X54)),
inference(variable_rename,[status(thm)],[c_0_1775]) ).
fof(c_0_2943,plain,
! [X52,X53,X54] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X54)),
inference(variable_rename,[status(thm)],[c_0_1776]) ).
fof(c_0_2944,plain,
! [X58,X59,X60,X61,X62] :
( ( ~ hBOOL(hAPP(fun(X58,bool),bool,hAPP(X58,fun(fun(X58,bool),bool),member(X58),X59),hAPP(X58,fun(X58,bool),ord_atLeast(X58),X60)))
| hBOOL(hAPP(X58,bool,hAPP(X58,fun(X58,bool),ord_less_eq(X58),X60),X59))
| ~ ord(X58) )
& ( ~ hBOOL(hAPP(X58,bool,hAPP(X58,fun(X58,bool),ord_less_eq(X58),X62),X61))
| hBOOL(hAPP(fun(X58,bool),bool,hAPP(X58,fun(fun(X58,bool),bool),member(X58),X61),hAPP(X58,fun(X58,bool),ord_atLeast(X58),X62)))
| ~ ord(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_1777])])])])]) ).
fof(c_0_2945,plain,
! [X58,X59,X60,X61,X62] :
( ( ~ hBOOL(hAPP(fun(X58,bool),bool,hAPP(X58,fun(fun(X58,bool),bool),member(X58),X59),hAPP(X58,fun(X58,bool),ord_greaterThan(X58),X60)))
| hBOOL(hAPP(X58,bool,hAPP(X58,fun(X58,bool),ord_less(X58),X60),X59))
| ~ ord(X58) )
& ( ~ hBOOL(hAPP(X58,bool,hAPP(X58,fun(X58,bool),ord_less(X58),X62),X61))
| hBOOL(hAPP(fun(X58,bool),bool,hAPP(X58,fun(fun(X58,bool),bool),member(X58),X61),hAPP(X58,fun(X58,bool),ord_greaterThan(X58),X62)))
| ~ ord(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_1778])])])])]) ).
fof(c_0_2946,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| hAPP(nat,nat,suc,X52) = X53
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X52)),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1779])]) ).
fof(c_0_2947,plain,
! [X113,X114,X115] :
( ( ~ hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),X115))
| hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),hAPP(fun(X113,bool),fun(X113,bool),hAPP(fun(X113,bool),fun(fun(X113,bool),fun(X113,bool)),semilattice_inf_inf(fun(X113,bool)),X115),X114))) )
& ( ~ hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),X114))
| hBOOL(hAPP(fun(X113,bool),bool,finite_finite_1(X113),hAPP(fun(X113,bool),fun(X113,bool),hAPP(fun(X113,bool),fun(fun(X113,bool),fun(X113,bool)),semilattice_inf_inf(fun(X113,bool)),X115),X114))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1780])])]) ).
fof(c_0_2948,plain,
! [X41,X42,X43,X44] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X42),fun(fun(X41,bool),bool),inj_on(X41,X42),X43),X44))
| hAPP(fun(X42,bool),nat,finite_card(X42),hAPP(fun(X41,bool),fun(X42,bool),hAPP(fun(X41,X42),fun(fun(X41,bool),fun(X42,bool)),image(X41,X42),X43),X44)) = hAPP(fun(X41,bool),nat,finite_card(X41),X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1781])]) ).
fof(c_0_2949,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X52)),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1782])]) ).
fof(c_0_2950,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X44,bool,X46,X47))
| hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46),X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1783])]) ).
fof(c_0_2951,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X44,bool,X46,X47))
| hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45),X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1784])]) ).
fof(c_0_2952,plain,
! [X44,X45,X46,X47] :
( ( ~ hBOOL(hAPP(X44,bool,X46,X47))
| hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46),X47)) )
& ( ~ hBOOL(hAPP(X44,bool,X45,X47))
| hBOOL(hAPP(X44,bool,hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46),X47)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1785])])]) ).
fof(c_0_2953,plain,
! [X31] : 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)),X31))) = hAPP(nat,nat,suc,X31),
inference(variable_rename,[status(thm)],[c_0_1786]) ).
fof(c_0_2954,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_1787])]) ).
fof(c_0_2955,plain,
! [X47,X48,X49,X50] :
( ( hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),esk77_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),esk78_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,esk77_4(X47,X48,X49,X50)) = hAPP(X48,X47,X49,esk78_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,esk77_4(X47,X48,X49,X50)) != ti(X48,esk78_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_1788])])])])]) ).
fof(c_0_2956,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_1789])])])])]) ).
fof(c_0_2957,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),hAPP(nat,nat,suc,X53)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53))
| X52 = hAPP(nat,nat,suc,X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1790])]) ).
fof(c_0_2958,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,esk93_2(X74,X75)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1791])])]) ).
fof(c_0_2959,plain,
! [X64,X65,X66] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk87_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,esk87_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,esk87_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_1792])])])]) ).
fof(c_0_2960,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_1793])])])])]) ).
fof(c_0_2961,plain,
! [X31] : 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)),X31))) = X31,
inference(variable_rename,[status(thm)],[c_0_1794]) ).
fof(c_0_2962,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_1795])])])])])]) ).
fof(c_0_2963,plain,
! [X44,X45,X46] :
( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk60_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),esk60_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_1796])])])]) ).
fof(c_0_2964,plain,
! [X109,X110,X111,X112,X113,X114,X115,X116,X117] :
( hAPP(fun(X109,X110),fun(X109,X111),hAPP(fun(X110,X111),fun(fun(X109,X110),fun(X109,X111)),comp(X110,X111,X109),X113),X114) != hAPP(fun(X109,X112),fun(X109,X111),hAPP(fun(X112,X111),fun(fun(X109,X112),fun(X109,X111)),comp(X112,X111,X109),X115),X116)
| hAPP(X110,X111,X113,hAPP(X109,X110,X114,X117)) = hAPP(X112,X111,X115,hAPP(X109,X112,X116,X117)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1797])])]) ).
fof(c_0_2965,plain,
! [X108,X109,X110,X111,X112,X113,X114,X115,X116] :
( hAPP(fun(X108,X109),fun(X108,X110),hAPP(fun(X109,X110),fun(fun(X108,X109),fun(X108,X110)),comp(X109,X110,X108),X113),X114) != hAPP(fun(X108,X111),fun(X108,X110),hAPP(fun(X111,X110),fun(fun(X108,X111),fun(X108,X110)),comp(X111,X110,X108),X115),X116)
| hAPP(X109,X110,X113,hAPP(X108,X109,X114,X112)) = hAPP(X111,X110,X115,hAPP(X108,X111,X116,X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1798])]) ).
fof(c_0_2966,plain,
! [X39,X40] :
( ~ hBOOL(hAPP(fun(X39,bool),bool,finite_finite_1(X39),top_top(fun(X39,bool))))
| ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X39),fun(fun(X39,bool),bool),inj_on(X39,X39),X40),top_top(fun(X39,bool))))
| hAPP(fun(X39,bool),fun(X39,bool),hAPP(fun(X39,X39),fun(fun(X39,bool),fun(X39,bool)),image(X39,X39),X40),top_top(fun(X39,bool))) = 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_1799])])])]) ).
fof(c_0_2967,plain,
! [X39,X40,X41,X42] :
( ( hAPP(fun(X39,bool),nat,hAPP(fun(X39,nat),fun(fun(X39,bool),nat),big_co1399186613setsum(X39,nat),X40),X41) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),X42),X41))
| hAPP(X39,nat,X40,X42) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X39,bool),bool,finite_finite_1(X39),X41)) )
& ( hBOOL(hAPP(fun(X39,bool),bool,hAPP(X39,fun(fun(X39,bool),bool),member(X39),esk174_3(X39,X40,X41)),X41))
| hAPP(fun(X39,bool),nat,hAPP(fun(X39,nat),fun(fun(X39,bool),nat),big_co1399186613setsum(X39,nat),X40),X41) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X39,bool),bool,finite_finite_1(X39),X41)) )
& ( hAPP(X39,nat,X40,esk174_3(X39,X40,X41)) != zero_zero(nat)
| hAPP(fun(X39,bool),nat,hAPP(fun(X39,nat),fun(fun(X39,bool),nat),big_co1399186613setsum(X39,nat),X40),X41) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X39,bool),bool,finite_finite_1(X39),X41)) ) ),
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_1800])])])])]) ).
fof(c_0_2968,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_1801])])])])]) ).
fof(c_0_2969,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_1802])])]) ).
fof(c_0_2970,plain,
! [X52,X53] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),hAPP(nat,nat,suc,X53)))
| X53 = X52 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1803])]) ).
fof(c_0_2971,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),hAPP(nat,nat,suc,X53)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| X52 = X53 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1804])]) ).
fof(c_0_2972,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_1805])])])]) ).
fof(c_0_2973,plain,
! [X52] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X52)),X52)),
inference(variable_rename,[status(thm)],[c_0_1806]) ).
fof(c_0_2974,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X58)),X59) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X58)),X60)
| X59 = X60 )
& ( X62 != X63
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X61)),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X61)),X63) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1807])])])]) ).
fof(c_0_2975,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_1808])])])])]) ).
fof(c_0_2976,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_1809])])])])]) ).
fof(c_0_2977,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_1810])]) ).
fof(c_0_2978,plain,
! [X39,X40,X41,X42,X43,X44] : hAPP(X39,X40,hAPP(fun(X39,X41),fun(X39,X40),hAPP(fun(X41,X40),fun(fun(X39,X41),fun(X39,X40)),comp(X41,X40,X39),hAPP(X40,fun(X41,X40),combk(X40,X41),X42)),X43),X44) = ti(X40,X42),
inference(variable_rename,[status(thm)],[c_0_1811]) ).
fof(c_0_2979,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),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(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_1812])])])])])]) ).
fof(c_0_2980,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),esk71_1(X61))) )
& ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk72_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),esk72_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_1813])])])])])]) ).
fof(c_0_2981,plain,
! [X64,X65] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X64),X65)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X64)),hAPP(nat,nat,suc,X65)),
inference(variable_rename,[status(thm)],[c_0_1814]) ).
fof(c_0_2982,plain,
! [X64,X65] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X64),X65)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X64)),hAPP(nat,nat,suc,X65)),
inference(variable_rename,[status(thm)],[c_0_1815]) ).
fof(c_0_2983,plain,
! [X63,X64,X66] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk80_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),esk80_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),esk80_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_1816])])])])]) ).
fof(c_0_2984,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_1817])])])]) ).
fof(c_0_2985,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_1818])])])])]) ).
fof(c_0_2986,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_1819])])])]) ).
fof(c_0_2987,plain,
! [X36,X37,X38] :
( ~ order(X36)
| ~ 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),X38),X37))
| ti(X36,X37) = ti(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1820])])]) ).
fof(c_0_2988,plain,
! [X36,X37,X38] :
( ~ order(X36)
| ~ 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),X38),X37))
| ti(X36,X38) = ti(X36,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1821])])]) ).
fof(c_0_2989,plain,
! [X39,X40] :
( ~ hBOOL(hAPP(fun(X39,bool),bool,finite_finite_1(X39),top_top(fun(X39,bool))))
| hAPP(fun(X39,bool),fun(X39,bool),hAPP(fun(X39,X39),fun(fun(X39,bool),fun(X39,bool)),image(X39,X39),X40),top_top(fun(X39,bool))) != top_top(fun(X39,bool))
| hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X39),fun(fun(X39,bool),bool),inj_on(X39,X39),X40),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_1822])])])]) ).
fof(c_0_2990,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_1823])])]) ).
fof(c_0_2991,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| ~ 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1824])])]) ).
fof(c_0_2992,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_1825])])])])]) ).
fof(c_0_2993,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_1826])])])])]) ).
fof(c_0_2994,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_1827])])])])]) ).
fof(c_0_2995,plain,
! [X36,X37,X38] :
( ~ preorder(X36)
| ~ 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1828])])]) ).
fof(c_0_2996,plain,
! [X36,X37,X38] :
( ~ preorder(X36)
| ~ 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1829])])]) ).
fof(c_0_2997,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_1830])])]) ).
fof(c_0_2998,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_1831])])]) ).
fof(c_0_2999,plain,
! [X36,X37,X38] :
( ~ preorder(X36)
| ~ 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1832])])]) ).
fof(c_0_3000,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),hAPP(nat,nat,suc,X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1833])]) ).
fof(c_0_3001,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),hAPP(nat,nat,suc,X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1834])]) ).
fof(c_0_3002,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),hAPP(nat,nat,suc,X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1835])]) ).
fof(c_0_3003,plain,
! [X40,X41,X42,X43,X44] :
( ~ lattice(X41)
| hAPP(X40,X41,hAPP(fun(X40,X41),fun(X40,X41),hAPP(fun(X40,X41),fun(fun(X40,X41),fun(X40,X41)),semilattice_inf_inf(fun(X40,X41)),X42),X43),X44) = hAPP(X41,X41,hAPP(X41,fun(X41,X41),semilattice_inf_inf(X41),hAPP(X40,X41,X42,X44)),hAPP(X40,X41,X43,X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1836])])]) ).
fof(c_0_3004,plain,
! [X40,X41,X42,X43,X44] :
( ~ lattice(X41)
| hAPP(X40,X41,hAPP(fun(X40,X41),fun(X40,X41),hAPP(fun(X40,X41),fun(fun(X40,X41),fun(X40,X41)),semilattice_inf_inf(fun(X40,X41)),X42),X43),X44) = hAPP(X41,X41,hAPP(X41,fun(X41,X41),semilattice_inf_inf(X41),hAPP(X40,X41,X42,X44)),hAPP(X40,X41,X43,X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1837])])]) ).
fof(c_0_3005,plain,
! [X40,X41,X42,X43,X44] :
( ~ lattice(X41)
| hAPP(X40,X41,hAPP(fun(X40,X41),fun(X40,X41),hAPP(fun(X40,X41),fun(fun(X40,X41),fun(X40,X41)),semilattice_sup_sup(fun(X40,X41)),X42),X43),X44) = hAPP(X41,X41,hAPP(X41,fun(X41,X41),semilattice_sup_sup(X41),hAPP(X40,X41,X42,X44)),hAPP(X40,X41,X43,X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1838])])]) ).
fof(c_0_3006,plain,
! [X40,X41,X42,X43,X44] :
( ~ lattice(X41)
| hAPP(X40,X41,hAPP(fun(X40,X41),fun(X40,X41),hAPP(fun(X40,X41),fun(fun(X40,X41),fun(X40,X41)),semilattice_sup_sup(fun(X40,X41)),X42),X43),X44) = hAPP(X41,X41,hAPP(X41,fun(X41,X41),semilattice_sup_sup(X41),hAPP(X40,X41,X42,X44)),hAPP(X40,X41,X43,X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1839])])]) ).
fof(c_0_3007,plain,
! [X58,X59,X60] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X58) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59)
| X58 = X59
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X60)) )
& ( X58 != X59
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X58) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X60)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1840])])]) ).
fof(c_0_3008,plain,
! [X2] :
( ~ linordered_semidom(X2)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),one_one(X2)),one_one(X2)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1841])]) ).
fof(c_0_3009,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X52))
| X52 = X53 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1842])]) ).
fof(c_0_3010,plain,
! [X50,X51] :
( ~ comm_semiring_1(X50)
| hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),X51),X51) = hAPP(X50,X50,hAPP(X50,fun(X50,X50),times_times(X50),hAPP(X50,X50,hAPP(X50,fun(X50,X50),plus_plus(X50),one_one(X50)),one_one(X50))),X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1843])])]) ).
fof(c_0_3011,plain,
! [X22,X23] :
( ~ linordered_ring(X22)
| hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less_eq(X22),zero_zero(X22)),hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1844])])]) ).
fof(c_0_3012,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_1845])])]) ).
fof(c_0_3013,plain,
! [X38,X39,X40,X41] :
( ~ semilattice_inf(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X40),X41)) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X40),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_inf_inf(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1846])])]) ).
fof(c_0_3014,plain,
! [X37,X38,X39,X40] :
( ~ lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1847])])]) ).
fof(c_0_3015,plain,
! [X37,X38,X39,X40] :
( ~ semilattice_inf(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X39),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_inf_inf(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1848])])]) ).
fof(c_0_3016,plain,
! [X37,X38,X39,X40] :
( ~ semilattice_sup(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1849])])]) ).
fof(c_0_3017,plain,
! [X37,X38,X39,X40] :
( ~ lattice(X37)
| hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),X40)) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X39),hAPP(X37,X37,hAPP(X37,fun(X37,X37),semilattice_sup_sup(X37),X38),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1850])])]) ).
fof(c_0_3018,plain,
! [X38,X39,X40,X41] :
( ~ semilattice_sup(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X39),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X40),X41)) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X40),hAPP(X38,X38,hAPP(X38,fun(X38,X38),semilattice_sup_sup(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1851])])]) ).
fof(c_0_3019,plain,
! [X95,X96,X97,X98] :
( ~ comm_semiring_1(X95)
| hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X96),hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X97),X98)) = hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X97),hAPP(X95,X95,hAPP(X95,fun(X95,X95),times_times(X95),X96),X98)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1852])])]) ).
fof(c_0_3020,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_1853])])]) ).
fof(c_0_3021,plain,
! [X36,X37,X38] :
( ~ semilattice_sup(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X38),X37))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1854])])]) ).
fof(c_0_3022,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X38),X37))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1855])])]) ).
fof(c_0_3023,plain,
! [X36,X37,X38] :
( ~ semilattice_sup(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1856])])]) ).
fof(c_0_3024,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1857])])]) ).
fof(c_0_3025,plain,
! [X37,X38,X39] :
( ( hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),esk37_3(X37,X38,X39)),X39))
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X38))
| ~ dense_linorder(X37) )
& ( ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),esk37_3(X37,X38,X39)),X38))
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X38))
| ~ dense_linorder(X37) ) ),
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_1858])])])])]) ).
fof(c_0_3026,plain,
! [X85,X86] :
( ( hAPP(fun(X85,bool),fun(nat,bool),hAPP(fun(X85,nat),fun(fun(X85,bool),fun(nat,bool)),image(X85,nat),esk122_2(X85,X86)),X86) = 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)),esk123_2(X85,X86)))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X86)) )
& ( hBOOL(hAPP(fun(X85,bool),bool,hAPP(fun(X85,nat),fun(fun(X85,bool),bool),inj_on(X85,nat),esk122_2(X85,X86)),X86))
| ~ hBOOL(hAPP(fun(X85,bool),bool,finite_finite_1(X85),X86)) ) ),
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_1859])])])])]) ).
fof(c_0_3027,plain,
! [X41,X42] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X41,bool),nat,finite_card(X41),X42)))
| hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1860])]) ).
fof(c_0_3028,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_1861])]) ).
fof(c_0_3029,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_1862])]) ).
fof(c_0_3030,plain,
! [X40,X41,X42,X43] :
( hAPP(X40,X41,X42,hAPP(X41,X40,X43,esk128_4(X40,X41,X42,X43))) != ti(X41,esk128_4(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),X42),top_top(fun(X40,bool))) = top_top(fun(X41,bool)) ),
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_1863])])])])]) ).
fof(c_0_3031,plain,
! [X44,X45,X46] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46)) = hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46),
inference(variable_rename,[status(thm)],[c_0_1864]) ).
fof(c_0_3032,plain,
! [X44,X45,X46] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46)) = hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46),
inference(variable_rename,[status(thm)],[c_0_1865]) ).
fof(c_0_3033,plain,
! [X50] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X50))),
inference(variable_rename,[status(thm)],[c_0_1866]) ).
fof(c_0_3034,plain,
! [X52,X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53))),
inference(variable_rename,[status(thm)],[c_0_1867]) ).
fof(c_0_3035,plain,
! [X52,X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X52))),
inference(variable_rename,[status(thm)],[c_0_1868]) ).
fof(c_0_3036,plain,
! [X37,X38,X39] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X37),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X38),X39)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X38),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X37),X39)),
inference(variable_rename,[status(thm)],[c_0_1869]) ).
fof(c_0_3037,plain,
! [X63,X64,X66] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk82_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),esk82_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,esk82_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_1870])])])])]) ).
fof(c_0_3038,plain,
! [X54,X55,X56,X57] :
( ~ hBOOL(hAPP(X54,bool,X56,X57))
| ~ hBOOL(hAPP(fun(X54,bool),bool,hAPP(fun(X54,bool),fun(fun(X54,bool),bool),ord_less_eq(fun(X54,bool)),X56),X55))
| hBOOL(hAPP(X54,bool,X55,X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1871])]) ).
fof(c_0_3039,plain,
! [X54,X55,X56,X57] :
( ~ hBOOL(hAPP(fun(X54,bool),bool,hAPP(fun(X54,bool),fun(fun(X54,bool),bool),ord_less_eq(fun(X54,bool)),X56),X57))
| ~ hBOOL(hAPP(X54,bool,X56,X55))
| hBOOL(hAPP(X54,bool,X57,X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1872])]) ).
fof(c_0_3040,plain,
! [X41,X42] :
( hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),top_top(fun(X41,bool))))
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42))
| ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk70_2(X41,X42)),X42)) ),
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_1873])])])])]) ).
fof(c_0_3041,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))
| hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46) = ti(fun(X44,bool),X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1874])]) ).
fof(c_0_3042,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))
| hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X45) = ti(fun(X44,bool),X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1875])]) ).
fof(c_0_3043,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))
| hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45) = ti(fun(X44,bool),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1876])]) ).
fof(c_0_3044,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))
| hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46) = ti(fun(X44,bool),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1877])]) ).
fof(c_0_3045,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))
| hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46) = ti(fun(X44,bool),X46) )
& ( hAPP(fun(X47,bool),fun(X47,bool),hAPP(fun(X47,bool),fun(fun(X47,bool),fun(X47,bool)),semilattice_sup_sup(fun(X47,bool)),X48),X49) != 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(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1878])])])]) ).
fof(c_0_3046,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),esk86_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_1879])])])])]) ).
fof(c_0_3047,plain,
! [X121,X122,X123,X124,X125,X126] : hAPP(X121,X122,hAPP(fun(X121,X123),fun(X121,X122),hAPP(fun(X121,fun(X123,X122)),fun(fun(X121,X123),fun(X121,X122)),combs(X121,X123,X122),X124),X125),X126) = hAPP(X123,X122,hAPP(X121,fun(X123,X122),X124,X126),hAPP(X121,X123,X125,X126)),
inference(variable_rename,[status(thm)],[c_0_1880]) ).
fof(c_0_3048,plain,
! [X65,X66] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),esk94_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,esk94_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_1881])])])]) ).
fof(c_0_3049,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),esk88_2(X63,X64))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1882])])]) ).
fof(c_0_3050,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_1883])])])]) ).
fof(c_0_3051,plain,
! [X38,X39,X40,X41] :
( ~ order(X38)
| ti(X38,X40) != ti(X38,X41)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X41))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1884])])]) ).
fof(c_0_3052,plain,
! [X38,X39,X40,X41] :
( ~ order(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| ti(X38,X40) != ti(X38,X39)
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1885])])]) ).
fof(c_0_3053,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_1886])])])]) ).
fof(c_0_3054,plain,
! [X38,X39,X40,X41] :
( ~ order(X38)
| ti(X38,X40) != ti(X38,X41)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X41))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1887])])]) ).
fof(c_0_3055,plain,
! [X38,X39,X40,X41] :
( ~ order(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| ti(X38,X40) != ti(X38,X39)
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X39),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1888])])]) ).
fof(c_0_3056,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_1889])])]) ).
fof(c_0_3057,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_1890])])]) ).
fof(c_0_3058,plain,
! [X36,X37,X38] :
( ~ order(X36)
| ~ 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),X38))
| ti(X36,X37) = ti(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1891])])]) ).
fof(c_0_3059,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_1892])])]) ).
fof(c_0_3060,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_1893])])]) ).
fof(c_0_3061,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_1894])])])]) ).
fof(c_0_3062,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_1895])])])])]) ).
fof(c_0_3063,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_1896])])])])]) ).
fof(c_0_3064,plain,
! [X39,X40,X41,X42,X43] :
( ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X40),fun(fun(X39,bool),bool),inj_on(X39,X40),X43),top_top(fun(X39,bool))))
| hAPP(X39,X40,X43,X41) != hAPP(X39,X40,X43,X42)
| ti(X39,X41) = ti(X39,X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1897])]) ).
fof(c_0_3065,plain,
! [X39,X40,X41,X42,X43] :
( ( hAPP(X39,X40,X43,X41) != hAPP(X39,X40,X43,X42)
| ti(X39,X41) = ti(X39,X42)
| ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X40),fun(fun(X39,bool),bool),inj_on(X39,X40),X43),top_top(fun(X39,bool)))) )
& ( ti(X39,X41) != ti(X39,X42)
| hAPP(X39,X40,X43,X41) = hAPP(X39,X40,X43,X42)
| ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X40),fun(fun(X39,bool),bool),inj_on(X39,X40),X43),top_top(fun(X39,bool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1898])])]) ).
fof(c_0_3066,plain,
! [X38,X39,X40,X41] :
( ~ ord(X38)
| X40 != X41
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X41),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1899])])]) ).
fof(c_0_3067,plain,
! [X38,X39,X40,X41] :
( ~ ord(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X41))
| X41 != X39
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less_eq(X38),X40),X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1900])])]) ).
fof(c_0_3068,plain,
! [X38,X39,X40,X41] :
( ~ ord(X38)
| X40 != X41
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X41),X39))
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1901])])]) ).
fof(c_0_3069,plain,
! [X38,X39,X40,X41] :
( ~ ord(X38)
| ~ hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X41))
| X41 != X39
| hBOOL(hAPP(X38,bool,hAPP(X38,fun(X38,bool),ord_less(X38),X40),X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1902])])]) ).
fof(c_0_3070,plain,
! [X36,X37,X38] :
( ~ preorder(X36)
| ~ 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_eq(X36),X37),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1903])])]) ).
fof(c_0_3071,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X52)),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53)),
inference(variable_rename,[status(thm)],[c_0_1904]) ).
fof(c_0_3072,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_atLeastAtMost(nat),X78),X79))),
inference(variable_rename,[status(thm)],[c_0_1905]) ).
fof(c_0_3073,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_gr676655987ssThan(nat),X78),X79))),
inference(variable_rename,[status(thm)],[c_0_1906]) ).
fof(c_0_3074,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_gr1471790799AtMost(nat),X78),X79))),
inference(variable_rename,[status(thm)],[c_0_1907]) ).
fof(c_0_3075,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_1908]) ).
fof(c_0_3076,plain,
! [X63,X64] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk83_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),esk83_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_1909])])])]) ).
fof(c_0_3077,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_1910]) ).
fof(c_0_3078,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53))
| X52 = X53
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1911])]) ).
fof(c_0_3079,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_1912])])])])]) ).
fof(c_0_3080,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_1913])])])])]) ).
fof(c_0_3081,plain,
! [X36,X37] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X37))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X36),X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1914])]) ).
fof(c_0_3082,plain,
! [X52,X53] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) )
& ( X52 != X53
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1915])])]) ).
fof(c_0_3083,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1916])]) ).
fof(c_0_3084,plain,
! [X31,X32] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),hAPP(nat,nat,suc,zero_zero(nat))))
| X31 = zero_zero(nat) )
& ( X32 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),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_1917])])])]) ).
fof(c_0_3085,plain,
! [X2] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1918])]) ).
fof(c_0_3086,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk66_0),arrow_1568854078le_Lin)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1919])]) ).
fof(c_0_3087,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
c_0_1920 ).
fof(c_0_3088,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
c_0_1921 ).
fof(c_0_3089,plain,
! [X45,X46] :
( ( hBOOL(hAPP(nat,bool,X46,esk99_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,esk99_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_1922])])])]) ).
fof(c_0_3090,plain,
! [X121,X122,X123,X124,X125,X126] : hAPP(X121,X122,hAPP(X123,fun(X121,X122),hAPP(fun(X121,fun(X123,X122)),fun(X123,fun(X121,X122)),combc(X121,X123,X122),X124),X125),X126) = hAPP(X123,X122,hAPP(X121,fun(X123,X122),X124,X126),X125),
inference(variable_rename,[status(thm)],[c_0_1923]) ).
fof(c_0_3091,plain,
! [X121,X122,X123,X124,X125,X126] : hAPP(X121,X122,hAPP(fun(X121,X123),fun(X121,X122),hAPP(fun(X123,X122),fun(fun(X121,X123),fun(X121,X122)),combb(X123,X122,X121),X124),X125),X126) = hAPP(X123,X122,X124,hAPP(X121,X123,X125,X126)),
inference(variable_rename,[status(thm)],[c_0_1924]) ).
fof(c_0_3092,plain,
! [X40,X41,X42,X43,X44,X45] : hAPP(X40,X41,hAPP(fun(X40,X42),fun(X40,X41),hAPP(fun(X42,X41),fun(fun(X40,X42),fun(X40,X41)),comp(X42,X41,X40),X43),X44),X45) = hAPP(X42,X41,X43,hAPP(X40,X42,X44,X45)),
inference(variable_rename,[status(thm)],[c_0_1925]) ).
fof(c_0_3093,plain,
! [X40,X41,X42,X43,X44,X45] : hAPP(X40,X41,hAPP(fun(X40,X42),fun(X40,X41),hAPP(fun(X42,X41),fun(fun(X40,X42),fun(X40,X41)),comp(X42,X41,X40),X43),X44),X45) = hAPP(X42,X41,X43,hAPP(X40,X42,X44,X45)),
inference(variable_rename,[status(thm)],[c_0_1926]) ).
fof(c_0_3094,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),hAPP(nat,nat,suc,X53)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53)),
inference(variable_rename,[status(thm)],[c_0_1927]) ).
fof(c_0_3095,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X52)),X53) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),
inference(variable_rename,[status(thm)],[c_0_1928]) ).
fof(c_0_3096,plain,
! [X41,X42,X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X42),X43))
| hBOOL(hAPP(X41,bool,X43,X42)) )
& ( ~ hBOOL(hAPP(X44,bool,X46,X45))
| hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X46)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1929])])])]) ).
fof(c_0_3097,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_inf_inf(X8),X9),X10) = ti(X8,X9)
| ~ semilattice_inf(X8) )
& ( hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_inf_inf(X8),X11),X12) != ti(X8,X11)
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
| ~ semilattice_inf(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_1930])])])])]) ).
fof(c_0_3098,plain,
! [X36,X37,X38] :
( ~ semilattice_inf(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38))
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38) = ti(X36,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1931])])]) ).
fof(c_0_3099,plain,
! [X36,X37,X38] :
( ~ semilattice_inf(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38))
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X38),X37) = ti(X36,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1932])])]) ).
fof(c_0_3100,plain,
! [X36,X37,X38] :
( ~ semilattice_sup(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38))
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X38),X37) = ti(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1933])])]) ).
fof(c_0_3101,plain,
! [X36,X37,X38] :
( ~ semilattice_sup(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38))
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38) = ti(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1934])])]) ).
fof(c_0_3102,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_sup_sup(X8),X9),X10) = ti(X8,X10)
| ~ semilattice_sup(X8) )
& ( hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_sup_sup(X8),X11),X12) != ti(X8,X12)
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
| ~ semilattice_sup(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_1935])])])])]) ).
fof(c_0_3103,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),esk56_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_1936])])])])]) ).
fof(c_0_3104,plain,
! [X36,X37,X38] :
( ~ linordered_idom(X36)
| ti(X36,X37) = ti(X36,X38)
| 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1937])])]) ).
fof(c_0_3105,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_1938])])])])]) ).
fof(c_0_3106,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
| ti(X36,X37) = ti(X36,X38)
| 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_1939])])]) ).
fof(c_0_3107,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| ti(X36,X37) = ti(X36,X38)
| 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1940])])]) ).
fof(c_0_3108,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
| ti(X36,X37) = ti(X36,X38)
| 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_1941])])]) ).
fof(c_0_3109,plain,
! [X23,X24,X25] :
( ~ semilattice_inf(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_inf_inf(X23),X24),hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_inf_inf(X23),X24),X25)) = hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_inf_inf(X23),X24),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1942])])]) ).
fof(c_0_3110,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1943])])]) ).
fof(c_0_3111,plain,
! [X36,X37,X38] :
( ~ semilattice_inf(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1944])])]) ).
fof(c_0_3112,plain,
! [X36,X37,X38] :
( ~ semilattice_sup(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38)) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1945])])]) ).
fof(c_0_3113,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38)) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1946])])]) ).
fof(c_0_3114,plain,
! [X23,X24,X25] :
( ~ semilattice_sup(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_sup_sup(X23),X24),hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_sup_sup(X23),X24),X25)) = hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_sup_sup(X23),X24),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1947])])]) ).
fof(c_0_3115,plain,
! [X23,X24,X25] :
( ~ ab_sem1668676832m_mult(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),X25)) = hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1948])])]) ).
fof(c_0_3116,plain,
! [X54,X55,X56] :
( ( hBOOL(hAPP(X54,bool,X56,esk151_3(X54,X55,X56)))
| hBOOL(hAPP(fun(X54,bool),bool,hAPP(fun(X54,bool),fun(fun(X54,bool),bool),ord_less_eq(fun(X54,bool)),X56),X55)) )
& ( ~ hBOOL(hAPP(X54,bool,X55,esk151_3(X54,X55,X56)))
| hBOOL(hAPP(fun(X54,bool),bool,hAPP(fun(X54,bool),fun(fun(X54,bool),bool),ord_less_eq(fun(X54,bool)),X56),X55)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1949])])])]) ).
fof(c_0_3117,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1950])])]) ).
fof(c_0_3118,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| 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_eq(X36),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1951])])]) ).
fof(c_0_3119,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1952])])]) ).
fof(c_0_3120,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1953])])]) ).
fof(c_0_3121,plain,
! [X36,X37,X38] :
( ~ linorder(X36)
| 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),X38),X37)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1954])])]) ).
fof(c_0_3122,plain,
! [X61,X62] :
( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_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),esk76_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_1955])])])]) ).
fof(c_0_3123,plain,
! [X3,X4] :
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
| hBOOL(hAPP(fun(product_prod(X4,X3),bool),bool,finite_finite_1(product_prod(X4,X3)),top_top(fun(product_prod(X4,X3),bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1956])]) ).
fof(c_0_3124,plain,
! [X3,X4,X5,X6] :
( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
| ~ hBOOL(hAPP(fun(sum_sum(X3,X4),bool),bool,finite_finite_1(sum_sum(X3,X4)),top_top(fun(sum_sum(X3,X4),bool)))) )
& ( hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool))))
| ~ hBOOL(hAPP(fun(sum_sum(X3,X4),bool),bool,finite_finite_1(sum_sum(X3,X4)),top_top(fun(sum_sum(X3,X4),bool)))) )
& ( ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),top_top(fun(X5,bool))))
| ~ hBOOL(hAPP(fun(X6,bool),bool,finite_finite_1(X6),top_top(fun(X6,bool))))
| hBOOL(hAPP(fun(sum_sum(X5,X6),bool),bool,finite_finite_1(sum_sum(X5,X6)),top_top(fun(sum_sum(X5,X6),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_1957])])])])]) ).
fof(c_0_3125,plain,
! [X36,X37] :
( X36 = X37
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X37))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X37),X36)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1958])]) ).
fof(c_0_3126,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_1959])])])])]) ).
fof(c_0_3127,plain,
! [X52,X53] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X52)) ),
inference(variable_rename,[status(thm)],[c_0_1960]) ).
fof(c_0_3128,plain,
! [X108,X109,X110,X111,X112,X113,X114] :
( hAPP(fun(X108,X109),fun(X108,X110),hAPP(fun(X109,X110),fun(fun(X108,X109),fun(X108,X110)),comp(X109,X110,X108),X112),X113) != ti(fun(X108,X110),X114)
| hAPP(X109,X110,X112,hAPP(X108,X109,X113,X111)) = hAPP(X108,X110,X114,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1961])]) ).
fof(c_0_3129,plain,
! [X41,X42] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk149_2(X41,X42)),X42))
| top_top(fun(X41,bool)) = ti(fun(X41,bool),X42) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1962])])]) ).
fof(c_0_3130,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_1963])])])])]) ).
fof(c_0_3131,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_1964])])]) ).
fof(c_0_3132,plain,
! [X41,X42] :
( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk81_2(X41,X42)),X42))
| hAPP(fun(X41,bool),nat,finite_card(X41),X42) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42)) )
& ( one_one(nat) != zero_zero(nat)
| hAPP(fun(X41,bool),nat,finite_card(X41),X42) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1965])])])]) ).
fof(c_0_3133,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),hAPP(nat,nat,suc,X53)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)),
inference(variable_rename,[status(thm)],[c_0_1966]) ).
fof(c_0_3134,plain,
! [X87,X88,X89,X90] : hAPP(nat,X87,hAPP(fun(nat,X87),fun(nat,X87),hAPP(X87,fun(fun(nat,X87),fun(nat,X87)),nat_case(X87),X88),X89),hAPP(nat,nat,suc,X90)) = hAPP(nat,X87,X89,X90),
inference(variable_rename,[status(thm)],[c_0_1967]) ).
fof(c_0_3135,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X52)),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),hAPP(nat,nat,suc,X53)),
inference(variable_rename,[status(thm)],[c_0_1968]) ).
fof(c_0_3136,plain,
! [X105] : hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X105)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X105)),hAPP(nat,nat,suc,zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_1969]) ).
fof(c_0_3137,plain,
! [X105] : hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X105)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X105)),hAPP(nat,nat,suc,zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_1970]) ).
fof(c_0_3138,plain,
! [X3,X4] :
( ~ hBOOL(hAPP(fun(fun(X3,X4),bool),bool,finite_finite_1(fun(X3,X4)),top_top(fun(fun(X3,X4),bool))))
| hAPP(fun(X4,bool),nat,finite_card(X4),top_top(fun(X4,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
| hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1971])]) ).
fof(c_0_3139,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_1972])])])]) ).
fof(c_0_3140,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
c_0_1973 ).
fof(c_0_3141,plain,
! [X58,X59] :
( ( hBOOL(hAPP(nat,bool,X58,hAPP(nat,nat,suc,esk98_1(X58))))
| hBOOL(hAPP(nat,bool,X58,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X58,X59)) )
& ( ~ hBOOL(hAPP(nat,bool,X58,esk98_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_1974])])])])])]) ).
fof(c_0_3142,plain,
! [X78,X79] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X78)),X79) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X78),X79),
inference(variable_rename,[status(thm)],[c_0_1975]) ).
fof(c_0_3143,plain,
! [X78,X79] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X78)),X79) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X78),X79),
inference(variable_rename,[status(thm)],[c_0_1976]) ).
fof(c_0_3144,plain,
! [X52] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X52))
| X52 = hAPP(nat,nat,suc,esk89_1(X52)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1977])])]) ).
fof(c_0_3145,plain,
! [X34,X36,X37] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X34))
| X34 = hAPP(nat,nat,suc,esk84_1(X34)) )
& ( X36 != hAPP(nat,nat,suc,X37)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X36)) ) ),
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_1978])])])])]) ).
fof(c_0_3146,plain,
! [X47,X48,X49,X50,X52,X53,X54,X56] :
( ( hAPP(fun(X47,bool),fun(X48,bool),hAPP(fun(X47,X48),fun(fun(X47,bool),fun(X48,bool)),image(X47,X48),X49),top_top(fun(X47,bool))) != top_top(fun(X48,bool))
| ti(X48,X50) = hAPP(X47,X48,X49,esk129_4(X47,X48,X49,X50)) )
& ( ti(X53,esk130_3(X52,X53,X54)) != hAPP(X52,X53,X54,X56)
| hAPP(fun(X52,bool),fun(X53,bool),hAPP(fun(X52,X53),fun(fun(X52,bool),fun(X53,bool)),image(X52,X53),X54),top_top(fun(X52,bool))) = top_top(fun(X53,bool)) ) ),
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_1979])])])])]) ).
fof(c_0_3147,plain,
! [X39,X40,X41,X42] :
( hAPP(fun(X39,bool),fun(X40,bool),hAPP(fun(X39,X40),fun(fun(X39,bool),fun(X40,bool)),image(X39,X40),X42),top_top(fun(X39,bool))) != top_top(fun(X40,bool))
| ti(X40,X41) = hAPP(X39,X40,X42,esk127_4(X39,X40,X41,X42)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1980])])]) ).
fof(c_0_3148,plain,
! [X39,X40,X41,X42] :
( hAPP(fun(X39,bool),fun(X40,bool),hAPP(fun(X39,X40),fun(fun(X39,bool),fun(X40,bool)),image(X39,X40),X42),top_top(fun(X39,bool))) != top_top(fun(X40,bool))
| ti(X40,X41) = hAPP(X39,X40,X42,esk126_4(X39,X40,X41,X42)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1981])])]) ).
fof(c_0_3149,plain,
( hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))))
& hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1982])])]) ).
fof(c_0_3150,axiom,
hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_1983 ).
fof(c_0_3151,plain,
! [X41,X42,X43] : hAPP(fun(X41,fun(X42,bool)),fun(fun(X41,X42),bool),hAPP(fun(X41,bool),fun(fun(X41,fun(X42,bool)),fun(fun(X41,X42),bool)),pi(X41,X42),X43),hAPP(fun(X42,bool),fun(X41,fun(X42,bool)),combk(fun(X42,bool),X41),top_top(fun(X42,bool)))) = top_top(fun(fun(X41,X42),bool)),
inference(variable_rename,[status(thm)],[c_0_1984]) ).
fof(c_0_3152,plain,
! [X2] :
( ~ linordered_semidom(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),one_one(X2)),zero_zero(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1985])]) ).
fof(c_0_3153,plain,
! [X2] :
( ~ linordered_semidom(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),one_one(X2)),zero_zero(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1986])]) ).
fof(c_0_3154,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_1987])])]) ).
fof(c_0_3155,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_1988])])])])]) ).
fof(c_0_3156,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_1989])])])])]) ).
fof(c_0_3157,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_1990])])])])]) ).
fof(c_0_3158,plain,
! [X38,X39,X40,X41] :
( ~ cancel_semigroup_add(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40) != hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41)
| ti(X38,X40) = ti(X38,X41) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1991])])]) ).
fof(c_0_3159,plain,
! [X38,X39,X40,X41] :
( ~ cancel146912293up_add(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40) != hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X41)
| ti(X38,X40) = ti(X38,X41) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1992])])]) ).
fof(c_0_3160,plain,
! [X38,X39,X40,X41] :
( ~ cancel_semigroup_add(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40) != hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X41),X40)
| ti(X38,X39) = ti(X38,X41) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1993])])]) ).
fof(c_0_3161,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_1994])])])])]) ).
fof(c_0_3162,plain,
! [X36,X37,X38] :
( ~ order(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
| ti(X36,X37) != ti(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1995])])]) ).
fof(c_0_3163,plain,
! [X36,X37,X38] :
( ~ order(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
| ti(X36,X37) != ti(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1996])])]) ).
fof(c_0_3164,plain,
! [X36,X37,X38] :
( ~ order(X36)
| ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
| ti(X36,X38) != ti(X36,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1997])])]) ).
fof(c_0_3165,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_1998])])]) ).
fof(c_0_3166,plain,
! [X52] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X52))),
inference(variable_rename,[status(thm)],[c_0_1999]) ).
fof(c_0_3167,plain,
! [X36,X37,X38] :
( ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),fequal(X36),X37),X38))
| ti(X36,X37) = ti(X36,X38) ),
inference(variable_rename,[status(thm)],[c_0_2000]) ).
fof(c_0_3168,plain,
! [X52] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),hAPP(nat,nat,suc,X52))),
inference(variable_rename,[status(thm)],[c_0_2001]) ).
fof(c_0_3169,plain,
! [X35,X36] :
( ~ preorder(X35)
| ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X36)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2002])])]) ).
fof(c_0_3170,plain,
! [X31,X32] :
( ( X31 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X31)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X32))
| X32 != 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_2003])])])]) ).
fof(c_0_3171,plain,
! [X31,X32] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),zero_zero(nat)))
| X31 = zero_zero(nat) )
& ( X32 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),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_2004])])])]) ).
fof(c_0_3172,plain,
! [X52] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_2005]) ).
fof(c_0_3173,plain,
! [X52] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_2006]) ).
fof(c_0_3174,plain,
! [X52] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_2007]) ).
fof(c_0_3175,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| X53 != zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2008])]) ).
fof(c_0_3176,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_2009])]) ).
fof(c_0_3177,plain,
! [X52,X53] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X53))
| X53 != X52 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2010])]) ).
fof(c_0_3178,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X60)
| X58 = zero_zero(nat)
| X59 = X60 )
& ( X61 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63) )
& ( X62 != X63
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63) ) ),
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_2011])])])])]) ).
fof(c_0_3179,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X60)
| X59 = X60
| X58 = zero_zero(nat) )
& ( X62 != X63
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63) )
& ( X61 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X63) ) ),
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_2012])])])])]) ).
fof(c_0_3180,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X59) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X60),X59)
| X58 = X60
| X59 = zero_zero(nat) )
& ( X61 != X63
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X63),X62) )
& ( X62 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X63),X62) ) ),
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_2013])])])])]) ).
fof(c_0_3181,plain,
! [X52] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X52)),
inference(variable_rename,[status(thm)],[c_0_2014]) ).
fof(c_0_3182,plain,
! [X52] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X52)),
inference(variable_rename,[status(thm)],[c_0_2015]) ).
fof(c_0_3183,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_2016])])])]) ).
fof(c_0_3184,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_2017])])])]) ).
fof(c_0_3185,plain,
! [X41,X42] : hAPP(fun(X41,bool),nat,finite_card(X41),X42) = hAPP(fun(X41,bool),nat,hAPP(fun(X41,nat),fun(fun(X41,bool),nat),big_co1399186613setsum(X41,nat),hAPP(nat,fun(X41,nat),combk(nat,X41),one_one(nat))),X42),
inference(variable_rename,[status(thm)],[c_0_2018]) ).
fof(c_0_3186,plain,
! [X120,X121] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X120),X121))
| hBOOL(X120)
| hBOOL(X121) ),
inference(variable_rename,[status(thm)],[c_0_2019]) ).
fof(c_0_3187,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38)) = ti(X36,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2020])])]) ).
fof(c_0_3188,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38)) = ti(X36,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2021])])]) ).
fof(c_0_3189,plain,
! [X120,X121] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X120),X121))
| hBOOL(X121) ),
inference(variable_rename,[status(thm)],[c_0_2022]) ).
fof(c_0_3190,plain,
! [X120,X121] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X120),X121))
| hBOOL(X120) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2023])])]) ).
fof(c_0_3191,plain,
! [X40,X41,X42,X43] :
( hAPP(X40,X41,X42,esk21_4(X40,X41,X42,X43)) != hAPP(X40,X41,X43,esk21_4(X40,X41,X42,X43))
| ti(fun(X40,X41),X42) = ti(fun(X40,X41),X43) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2024])])]) ).
fof(c_0_3192,plain,
! [X44,X45,X46] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X45),X46) = hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),X46),X45),
inference(variable_rename,[status(thm)],[c_0_2025]) ).
fof(c_0_3193,plain,
! [X44,X45,X46] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X45),X46) = hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),X46),X45),
inference(variable_rename,[status(thm)],[c_0_2026]) ).
fof(c_0_3194,plain,
! [X3,X4] :
( ~ hBOOL(hAPP(fun(fun(X3,X4),bool),bool,finite_finite_1(fun(X3,X4)),top_top(fun(fun(X3,X4),bool))))
| 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_2027])]) ).
fof(c_0_3195,plain,
! [X87,X88,X89] : hAPP(nat,X87,hAPP(fun(nat,X87),fun(nat,X87),hAPP(X87,fun(fun(nat,X87),fun(nat,X87)),nat_case(X87),X88),X89),zero_zero(nat)) = ti(X87,X88),
inference(variable_rename,[status(thm)],[c_0_2028]) ).
fof(c_0_3196,plain,
! [X78,X79] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X78),hAPP(nat,nat,suc,X79)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X78),X79),
inference(variable_rename,[status(thm)],[c_0_2029]) ).
fof(c_0_3197,plain,
! [X41,X42,X43] :
( ~ comm_monoid_add(X42)
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),hAPP(X42,fun(X41,X42),combk(X42,X41),zero_zero(X42))),X43) = zero_zero(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2030])])]) ).
fof(c_0_3198,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_2031])]) ).
fof(c_0_3199,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_2032])]) ).
fof(c_0_3200,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_2033])])]) ).
fof(c_0_3201,plain,
! [X41,X42] : hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,bool),fun(fun(X41,bool),bool),ord_less_eq(fun(X41,bool)),X42),top_top(fun(X41,bool)))),
inference(variable_rename,[status(thm)],[c_0_2034]) ).
fof(c_0_3202,plain,
! [X3,X4] : ti(fun(fun(X3,fun(X3,X3)),fun(X3,fun(fun(fun(X4,X3),fun(fun(X4,bool),X3)),bool))),finite_folding_image(X3,X4)) = finite_folding_image(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2035]) ).
fof(c_0_3203,plain,
! [X36,X37,X38] : hAPP(X36,X36,hAPP(X36,fun(X36,X36),hAPP(bool,fun(X36,fun(X36,X36)),if(X36),fFalse),X37),X38) = ti(X36,X38),
inference(variable_rename,[status(thm)],[c_0_2036]) ).
fof(c_0_3204,plain,
! [X36,X37,X38] : hAPP(X36,X36,hAPP(X36,fun(X36,X36),hAPP(bool,fun(X36,fun(X36,X36)),if(X36),fTrue),X37),X38) = ti(X36,X37),
inference(variable_rename,[status(thm)],[c_0_2037]) ).
fof(c_0_3205,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_2038])])])])]) ).
fof(c_0_3206,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_2039])])])])]) ).
fof(c_0_3207,plain,
! [X41,X42] : hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,bool),fun(fun(X41,bool),bool),ord_less_eq(fun(X41,bool)),X42),X42)),
inference(variable_rename,[status(thm)],[c_0_2040]) ).
fof(c_0_3208,plain,
! [X41,X42] :
( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),top_top(fun(X41,bool))))
| hAPP(fun(X41,bool),nat,finite_card(X41),X42) != hAPP(fun(X41,bool),nat,finite_card(X41),top_top(fun(X41,bool)))
| ti(fun(X41,bool),X42) = top_top(fun(X41,bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2041])])])]) ).
fof(c_0_3209,plain,
! [X41,X42] : hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X41),fun(fun(X41,bool),bool),inj_on(X41,X41),combi(X41)),X42)),
inference(variable_rename,[status(thm)],[c_0_2042]) ).
fof(c_0_3210,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_2043 ).
fof(c_0_3211,plain,
! [X27] : hBOOL(hAPP(fun(X27,bool),bool,hAPP(X27,fun(fun(X27,bool),bool),member(X27),esk148_1(X27)),top_top(fun(X27,bool)))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_2044])]) ).
fof(c_0_3212,plain,
! [X3,X4] : ti(fun(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X4,X3),fun(fun(fun(X4,bool),X3),bool)))),finite908156982e_idem(X3,X4)) = finite908156982e_idem(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2045]) ).
fof(c_0_3213,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_2046]) ).
fof(c_0_3214,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_2047]) ).
fof(c_0_3215,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_2048]) ).
fof(c_0_3216,plain,
! [X2] :
( ~ ring_1(X2)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),one_one(X2)),ring_1_Ints(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2049])]) ).
fof(c_0_3217,plain,
! [X2] :
( ~ ring_1(X2)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),zero_zero(X2)),ring_1_Ints(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2050])]) ).
fof(c_0_3218,plain,
! [X55,X56,X57,X58] :
( ( X55 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X56 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) != hAPP(nat,nat,suc,zero_zero(nat)) )
& ( X57 != hAPP(nat,nat,suc,zero_zero(nat))
| X58 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2051])])])])]) ).
fof(c_0_3219,plain,
! [X2,X3] :
( ( ~ hBOOL(hAPP(fun(option(X2),bool),bool,finite_finite_1(option(X2)),top_top(fun(option(X2),bool))))
| hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) )
& ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
| hBOOL(hAPP(fun(option(X3),bool),bool,finite_finite_1(option(X3)),top_top(fun(option(X3),bool)))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2052])])])]) ).
fof(c_0_3220,plain,
! [X36,X37,X38] :
( ti(X36,X37) != ti(X36,X38)
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),fequal(X36),X37),X38)) ),
inference(variable_rename,[status(thm)],[c_0_2053]) ).
fof(c_0_3221,plain,
! [X2] :
( ~ linordered_semidom(X2)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),one_one(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2054])]) ).
fof(c_0_3222,plain,
! [X2] :
( ~ linordered_semidom(X2)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),zero_zero(X2)),one_one(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2055])]) ).
fof(c_0_3223,plain,
! [X23,X24,X25] :
( ~ semilattice_inf(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_inf_inf(X23),X24),X25) = hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_inf_inf(X23),X25),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2056])])]) ).
fof(c_0_3224,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X38),X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2057])])]) ).
fof(c_0_3225,plain,
! [X36,X37,X38] :
( ~ semilattice_inf(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X37),X38) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_inf_inf(X36),X38),X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2058])])]) ).
fof(c_0_3226,plain,
! [X36,X37,X38] :
( ~ semilattice_sup(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X38),X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2059])])]) ).
fof(c_0_3227,plain,
! [X36,X37,X38] :
( ~ lattice(X36)
| hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X37),X38) = hAPP(X36,X36,hAPP(X36,fun(X36,X36),semilattice_sup_sup(X36),X38),X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2060])])]) ).
fof(c_0_3228,plain,
! [X23,X24,X25] :
( ~ semilattice_sup(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_sup_sup(X23),X24),X25) = hAPP(X23,X23,hAPP(X23,fun(X23,X23),semilattice_sup_sup(X23),X25),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2061])])]) ).
fof(c_0_3229,plain,
! [X23,X24,X25] :
( ~ comm_semiring_1(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),X25) = hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2062])])]) ).
fof(c_0_3230,plain,
! [X38,X39,X40] :
( ~ comm_semiring_1(X38)
| hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X39),X40) = hAPP(X38,X38,hAPP(X38,fun(X38,X38),plus_plus(X38),X40),X39) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2063])])]) ).
fof(c_0_3231,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_2064])])]) ).
fof(c_0_3232,plain,
! [X3,X4] : hAPP(fun(X3,bool),fun(sum_sum(X4,X3),bool),hAPP(fun(X4,bool),fun(fun(X3,bool),fun(sum_sum(X4,X3),bool)),sum_Plus(X4,X3),top_top(fun(X4,bool))),top_top(fun(X3,bool))) = top_top(fun(sum_sum(X4,X3),bool)),
inference(variable_rename,[status(thm)],[c_0_2065]) ).
fof(c_0_3233,plain,
! [X36,X37,X38] :
( ~ preorder(X36)
| X37 != X38
| hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2066])])]) ).
fof(c_0_3234,plain,
! [X35,X36] :
( ~ preorder(X35)
| hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X36)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2067])])]) ).
fof(c_0_3235,plain,
! [X52] :
( X52 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2068])]) ).
fof(c_0_3236,plain,
! [X52] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X52)),
inference(variable_rename,[status(thm)],[c_0_2069]) ).
fof(c_0_3237,plain,
! [X52] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X52)),
inference(variable_rename,[status(thm)],[c_0_2070]) ).
fof(c_0_3238,plain,
! [X41,X42,X43,X44] :
( ~ comm_monoid_add(X42)
| hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X43),X44) = zero_zero(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2071])])]) ).
fof(c_0_3239,plain,
! [X41,X42,X43,X44] :
( ~ comm_monoid_add(X42)
| hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X44))
| hAPP(fun(X41,bool),X42,hAPP(fun(X41,X42),fun(fun(X41,bool),X42),big_co1399186613setsum(X41,X42),X43),X44) = zero_zero(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2072])])]) ).
fof(c_0_3240,plain,
! [X52,X53] :
( X52 != X53
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2073])]) ).
fof(c_0_3241,plain,
! [X52] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X52)),
inference(variable_rename,[status(thm)],[c_0_2074]) ).
fof(c_0_3242,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X53),X52),
inference(variable_rename,[status(thm)],[c_0_2075]) ).
fof(c_0_3243,plain,
! [X52,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X52),
inference(variable_rename,[status(thm)],[c_0_2076]) ).
fof(c_0_3244,plain,
! [X120,X121] :
( ~ hBOOL(X121)
| ~ hBOOL(X120)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X121),X120)) ),
inference(variable_rename,[status(thm)],[c_0_2077]) ).
fof(c_0_3245,plain,
! [X120,X121] :
( ~ hBOOL(X121)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X120),X121)) ),
inference(variable_rename,[status(thm)],[c_0_2078]) ).
fof(c_0_3246,plain,
! [X120,X121] :
( ~ hBOOL(X121)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X121),X120)) ),
inference(variable_rename,[status(thm)],[c_0_2079]) ).
fof(c_0_3247,axiom,
hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
c_0_2080 ).
fof(c_0_3248,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
c_0_2081 ).
fof(c_0_3249,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
c_0_2082 ).
fof(c_0_3250,plain,
! [X16,X17,X18,X19,X20] :
( ( hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X17),X18) != zero_zero(X16)
| ti(X16,X17) = zero_zero(X16)
| ti(X16,X18) = zero_zero(X16)
| ~ ring_n68954251visors(X16) )
& ( ti(X16,X19) != zero_zero(X16)
| hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X19),X20) = zero_zero(X16)
| ~ ring_n68954251visors(X16) )
& ( ti(X16,X20) != zero_zero(X16)
| hAPP(X16,X16,hAPP(X16,fun(X16,X16),times_times(X16),X19),X20) = zero_zero(X16)
| ~ ring_n68954251visors(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_2083])])])])]) ).
fof(c_0_3251,plain,
! [X23,X24,X25] :
( ~ no_zero_divisors(X23)
| ti(X23,X25) = zero_zero(X23)
| ti(X23,X24) = zero_zero(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X25),X24) != zero_zero(X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2084])])]) ).
fof(c_0_3252,plain,
! [X23,X24,X25] :
( ~ no_zero_divisors(X23)
| hAPP(X23,X23,hAPP(X23,fun(X23,X23),times_times(X23),X24),X25) != zero_zero(X23)
| ti(X23,X24) = zero_zero(X23)
| ti(X23,X25) = zero_zero(X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2085])])]) ).
fof(c_0_3253,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_2086])])])])]) ).
fof(c_0_3254,plain,
! [X44,X45] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_inf_inf(fun(X44,bool)),top_top(fun(X44,bool))),X45) = ti(fun(X44,bool),X45),
inference(variable_rename,[status(thm)],[c_0_2087]) ).
fof(c_0_3255,plain,
! [X44,X45] : hAPP(fun(X44,bool),fun(X44,bool),hAPP(fun(X44,bool),fun(fun(X44,bool),fun(X44,bool)),semilattice_sup_sup(fun(X44,bool)),top_top(fun(X44,bool))),X45) = top_top(fun(X44,bool)),
inference(variable_rename,[status(thm)],[c_0_2088]) ).
fof(c_0_3256,plain,
! [X8,X9,X10,X11,X12] :
( ( ti(X8,X9) = top_top(X8)
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_inf_inf(X8),X9),X10) != top_top(X8)
| ~ bounded_lattice_top(X8) )
& ( ti(X8,X10) = top_top(X8)
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_inf_inf(X8),X9),X10) != top_top(X8)
| ~ bounded_lattice_top(X8) )
& ( ti(X8,X11) != top_top(X8)
| ti(X8,X12) != top_top(X8)
| hAPP(X8,X8,hAPP(X8,fun(X8,X8),semilattice_inf_inf(X8),X11),X12) = top_top(X8)
| ~ bounded_lattice_top(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_2089])])])])]) ).
fof(c_0_3257,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_2090])])])])]) ).
fof(c_0_3258,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_2091])])])])]) ).
fof(c_0_3259,plain,
! [X41,X42] : hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,bool),fun(fun(X41,bool),fun(X41,bool)),semilattice_inf_inf(fun(X41,bool)),X42),top_top(fun(X41,bool))) = ti(fun(X41,bool),X42),
inference(variable_rename,[status(thm)],[c_0_2092]) ).
fof(c_0_3260,plain,
! [X41,X42] : hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,bool),fun(fun(X41,bool),fun(X41,bool)),semilattice_sup_sup(fun(X41,bool)),X42),top_top(fun(X41,bool))) = top_top(fun(X41,bool)),
inference(variable_rename,[status(thm)],[c_0_2093]) ).
fof(c_0_3261,plain,
! [X55,X56,X57,X58] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) != zero_zero(nat)
| X55 = zero_zero(nat)
| X56 = zero_zero(nat) )
& ( X57 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X58) = zero_zero(nat) )
& ( X58 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2094])])])])]) ).
fof(c_0_3262,plain,
! [X52,X53] :
( X52 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),X53)
| X53 = one_one(nat)
| X52 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2095])]) ).
fof(c_0_3263,plain,
! [X55,X56,X57,X58] :
( ( X55 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) )
& ( X56 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) )
& ( X57 != one_one(nat)
| X58 != one_one(nat)
| one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2096])])])])]) ).
fof(c_0_3264,plain,
! [X55,X56,X57,X58] :
( ( X55 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) != one_one(nat) )
& ( X56 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X55),X56) != one_one(nat) )
& ( X57 != one_one(nat)
| X58 != one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X58) = one_one(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_2097])])])])]) ).
fof(c_0_3265,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_2098])])])])]) ).
fof(c_0_3266,plain,
! [X52,X53] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53) != X52
| X53 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2099])]) ).
fof(c_0_3267,plain,
! [X41,X42] : hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,bool),fun(fun(X41,bool),fun(X41,bool)),semilattice_inf_inf(fun(X41,bool)),X42),X42) = ti(fun(X41,bool),X42),
inference(variable_rename,[status(thm)],[c_0_2100]) ).
fof(c_0_3268,plain,
! [X41,X42] : hAPP(fun(X41,bool),fun(X41,bool),hAPP(fun(X41,bool),fun(fun(X41,bool),fun(X41,bool)),semilattice_sup_sup(fun(X41,bool)),X42),X42) = ti(fun(X41,bool),X42),
inference(variable_rename,[status(thm)],[c_0_2101]) ).
fof(c_0_3269,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_2102]) ).
fof(c_0_3270,plain,
! [X3,X4] : ti(fun(fun(X3,fun(X3,X3)),fun(fun(X4,X3),fun(X3,fun(fun(X4,bool),X3)))),finite_fold_image(X3,X4)) = finite_fold_image(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2103]) ).
fof(c_0_3271,plain,
! [X52] : hAPP(nat,nat,suc,X52) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X52),
inference(variable_rename,[status(thm)],[c_0_2104]) ).
fof(c_0_3272,plain,
! [X52] : hAPP(nat,nat,suc,X52) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),one_one(nat)),
inference(variable_rename,[status(thm)],[c_0_2105]) ).
fof(c_0_3273,plain,
! [X58] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X58)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X58),
inference(variable_rename,[status(thm)],[c_0_2106]) ).
fof(c_0_3274,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_2107]) ).
fof(c_0_3275,plain,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
c_0_2108 ).
fof(c_0_3276,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
c_0_2109 ).
fof(c_0_3277,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
c_0_2110 ).
fof(c_0_3278,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
c_0_2111 ).
fof(c_0_3279,plain,
! [X4,X5,X6] : ti(fun(fun(X4,bool),fun(fun(X5,X6),fun(fun(X4,X5),fun(X4,X6)))),compose(X4,X5,X6)) = compose(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_2112]) ).
fof(c_0_3280,plain,
! [X2] : top_top(fun(X2,bool)) = hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(bool,fun(X2,bool),combk(bool,X2),fTrue)),
inference(variable_rename,[status(thm)],[c_0_2113]) ).
fof(c_0_3281,plain,
! [X8,X9,X10,X11,X12] :
( ( hAPP(X8,fun(X8,bool),ord_atLeast(X8),X9) != hAPP(X8,fun(X8,bool),ord_atLeast(X8),X10)
| ti(X8,X9) = ti(X8,X10)
| ~ linorder(X8) )
& ( ti(X8,X11) != ti(X8,X12)
| hAPP(X8,fun(X8,bool),ord_atLeast(X8),X11) = hAPP(X8,fun(X8,bool),ord_atLeast(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_2114])])])])]) ).
fof(c_0_3282,plain,
! [X8,X9,X10,X11,X12] :
( ( hAPP(X8,fun(X8,bool),ord_greaterThan(X8),X9) != hAPP(X8,fun(X8,bool),ord_greaterThan(X8),X10)
| ti(X8,X9) = ti(X8,X10)
| ~ linorder(X8) )
& ( ti(X8,X11) != ti(X8,X12)
| hAPP(X8,fun(X8,bool),ord_greaterThan(X8),X11) = hAPP(X8,fun(X8,bool),ord_greaterThan(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_2115])])])])]) ).
fof(c_0_3283,plain,
! [X120,X121,X122,X123] : hAPP(X120,X121,hAPP(X121,fun(X120,X121),combk(X121,X120),X122),X123) = ti(X121,X122),
inference(variable_rename,[status(thm)],[c_0_2116]) ).
fof(c_0_3284,plain,
! [X35,X36] :
( ~ bounded_lattice_top(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),top_top(X35)),X36) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2117])])]) ).
fof(c_0_3285,plain,
! [X22,X23] :
( ~ comm_monoid_mult(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),one_one(X22)),X23) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2118])])]) ).
fof(c_0_3286,plain,
! [X22,X23] :
( ~ monoid_mult(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),one_one(X22)),X23) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2119])])]) ).
fof(c_0_3287,plain,
! [X22,X23] :
( ~ comm_semiring_1(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),one_one(X22)),X23) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2120])])]) ).
fof(c_0_3288,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_2121])])]) ).
fof(c_0_3289,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_2122])])]) ).
fof(c_0_3290,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_2123])])]) ).
fof(c_0_3291,plain,
! [X35,X36] :
( ~ bounded_lattice_top(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X36),top_top(X35)) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2124])])]) ).
fof(c_0_3292,plain,
! [X22,X23] :
( ~ comm_monoid_mult(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),one_one(X22)) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2125])])]) ).
fof(c_0_3293,plain,
! [X22,X23] :
( ~ monoid_mult(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),one_one(X22)) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2126])])]) ).
fof(c_0_3294,plain,
! [X22,X23] :
( ~ comm_semiring_1(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),one_one(X22)) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2127])])]) ).
fof(c_0_3295,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_2128])])]) ).
fof(c_0_3296,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_2129])])]) ).
fof(c_0_3297,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_2130])])]) ).
fof(c_0_3298,plain,
! [X41,X42] :
( hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42))
| hAPP(fun(X41,bool),nat,finite_card(X41),X42) = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2131])]) ).
fof(c_0_3299,plain,
! [X35,X36] :
( ~ bounded_lattice_top(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),top_top(X35)),X36) = top_top(X35) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2132])])]) ).
fof(c_0_3300,plain,
! [X22,X23] :
( ~ mult_zero(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),zero_zero(X22)),X23) = zero_zero(X22) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2133])])]) ).
fof(c_0_3301,plain,
! [X22,X23] :
( ~ comm_semiring_1(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),zero_zero(X22)),X23) = zero_zero(X22) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2134])])]) ).
fof(c_0_3302,plain,
! [X35,X36] :
( ~ lattice(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X36),X36) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2135])])]) ).
fof(c_0_3303,plain,
! [X35,X36] :
( ~ lattice(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),X36) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2136])])]) ).
fof(c_0_3304,plain,
! [X22,X23] :
( ~ semilattice_inf(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),semilattice_inf_inf(X22),X23),X23) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2137])])]) ).
fof(c_0_3305,plain,
! [X35,X36] :
( ~ semilattice_inf(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_inf_inf(X35),X36),X36) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2138])])]) ).
fof(c_0_3306,plain,
! [X35,X36] :
( ~ semilattice_sup(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),X36) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2139])])]) ).
fof(c_0_3307,plain,
! [X22,X23] :
( ~ semilattice_sup(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),semilattice_sup_sup(X22),X23),X23) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2140])])]) ).
fof(c_0_3308,plain,
! [X35,X36] :
( ~ ab_sem1668676832m_mult(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),times_times(X35),X36),X36) = ti(X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2141])])]) ).
fof(c_0_3309,plain,
! [X22,X23] :
( ~ ab_sem1668676832m_mult(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),X23) = ti(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2142])])]) ).
fof(c_0_3310,plain,
! [X35,X36] :
( ~ bounded_lattice_top(X35)
| hAPP(X35,X35,hAPP(X35,fun(X35,X35),semilattice_sup_sup(X35),X36),top_top(X35)) = top_top(X35) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2143])])]) ).
fof(c_0_3311,plain,
! [X22,X23] :
( ~ mult_zero(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),zero_zero(X22)) = zero_zero(X22) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2144])])]) ).
fof(c_0_3312,plain,
! [X22,X23] :
( ~ comm_semiring_1(X22)
| hAPP(X22,X22,hAPP(X22,fun(X22,X22),times_times(X22),X23),zero_zero(X22)) = zero_zero(X22) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2145])])]) ).
fof(c_0_3313,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
c_0_2146 ).
fof(c_0_3314,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
c_0_2147 ).
fof(c_0_3315,plain,
! [X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X52) = zero_zero(nat),
inference(variable_rename,[status(thm)],[c_0_2148]) ).
fof(c_0_3316,plain,
! [X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X52) = X52,
inference(variable_rename,[status(thm)],[c_0_2149]) ).
fof(c_0_3317,plain,
! [X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X52) = X52,
inference(variable_rename,[status(thm)],[c_0_2150]) ).
fof(c_0_3318,plain,
! [X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),zero_zero(nat)) = zero_zero(nat),
inference(variable_rename,[status(thm)],[c_0_2151]) ).
fof(c_0_3319,plain,
! [X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X52),one_one(nat)) = X52,
inference(variable_rename,[status(thm)],[c_0_2152]) ).
fof(c_0_3320,plain,
! [X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X50),zero_zero(nat)) = X50,
inference(variable_rename,[status(thm)],[c_0_2153]) ).
fof(c_0_3321,plain,
! [X3,X4] : ti(fun(fun(X3,fun(X4,X4)),fun(fun(fun(X3,bool),fun(X4,X4)),bool)),finite_folding_idem(X3,X4)) = finite_folding_idem(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2154]) ).
fof(c_0_3322,plain,
! [X119] :
( ~ hBOOL(hAPP(bool,bool,fNot,X119))
| ~ hBOOL(X119) ),
inference(variable_rename,[status(thm)],[c_0_2155]) ).
fof(c_0_3323,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_2156])])])]) ).
fof(c_0_3324,plain,
! [X36,X37] :
( hAPP(nat,nat,suc,X36) != hAPP(nat,nat,suc,X37)
| X36 = X37 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2157])]) ).
fof(c_0_3325,plain,
! [X3,X4] : ti(fun(fun(X3,bool),fun(fun(X3,fun(X4,bool)),fun(fun(X3,X4),bool))),pi(X3,X4)) = pi(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2158]) ).
fof(c_0_3326,plain,
! [X6,X7,X8,X9] : ti(X6,hAPP(X7,X6,X8,X9)) = hAPP(X7,X6,X8,X9),
inference(variable_rename,[status(thm)],[c_0_2159]) ).
fof(c_0_3327,plain,
! [X2] : ti(fun(fun(X2,nat),fun(fun(product_prod(X2,X2),bool),fun(product_prod(X2,X2),bool))),mlex_prod(X2)) = mlex_prod(X2),
inference(variable_rename,[status(thm)],[c_0_2160]) ).
fof(c_0_3328,plain,
! [X2] :
( ~ finite_finite(X2)
| hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2161])]) ).
fof(c_0_3329,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_2162 ).
fof(c_0_3330,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_2163]) ).
fof(c_0_3331,plain,
! [X7,X8] : hBOOL(hAPP(X7,bool,top_top(fun(X7,bool)),X8)),
inference(variable_rename,[status(thm)],[c_0_2164]) ).
fof(c_0_3332,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_2165]) ).
fof(c_0_3333,plain,
! [X3,X4] : ti(fun(fun(X3,bool),fun(fun(X4,bool),fun(sum_sum(X3,X4),bool))),sum_Plus(X3,X4)) = sum_Plus(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2166]) ).
fof(c_0_3334,plain,
! [X41,X42] :
( ~ finite_finite(X41)
| hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2167])])]) ).
fof(c_0_3335,plain,
! [X41,X42] :
( ~ finite_finite(X41)
| hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2168])])]) ).
fof(c_0_3336,plain,
! [X6,X7,X8,X9] : hAPP(X6,X7,X8,ti(X6,X9)) = hAPP(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_2169]) ).
fof(c_0_3337,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_2170]) ).
fof(c_0_3338,plain,
! [X4,X5,X6] : ti(fun(fun(X4,X5),fun(fun(X6,X4),fun(X6,X5))),comp(X4,X5,X6)) = comp(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_2171]) ).
fof(c_0_3339,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_2172]) ).
fof(c_0_3340,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_2173]) ).
fof(c_0_3341,plain,
! [X119] :
( hBOOL(X119)
| hBOOL(hAPP(bool,bool,fNot,X119)) ),
inference(variable_rename,[status(thm)],[c_0_2174]) ).
fof(c_0_3342,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
c_0_2175 ).
fof(c_0_3343,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
c_0_2176 ).
fof(c_0_3344,plain,
! [X50] : zero_zero(nat) != hAPP(nat,nat,suc,X50),
inference(variable_rename,[status(thm)],[c_0_2177]) ).
fof(c_0_3345,plain,
! [X71] : zero_zero(nat) != hAPP(nat,nat,suc,X71),
inference(variable_rename,[status(thm)],[c_0_2178]) ).
fof(c_0_3346,plain,
! [X50] : hAPP(nat,nat,suc,X50) != zero_zero(nat),
inference(variable_rename,[status(thm)],[c_0_2179]) ).
fof(c_0_3347,plain,
! [X70] : hAPP(nat,nat,suc,X70) != zero_zero(nat),
inference(variable_rename,[status(thm)],[c_0_2180]) ).
fof(c_0_3348,plain,
! [X50] : zero_zero(nat) != hAPP(nat,nat,suc,X50),
inference(variable_rename,[status(thm)],[c_0_2181]) ).
fof(c_0_3349,plain,
! [X50] : hAPP(nat,nat,suc,X50) != zero_zero(nat),
inference(variable_rename,[status(thm)],[c_0_2182]) ).
fof(c_0_3350,plain,
! [X3,X4] : ti(fun(fun(X3,bool),fun(fun(X3,X4),fun(X4,X3))),hilbert_inv_into(X3,X4)) = hilbert_inv_into(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2183]) ).
fof(c_0_3351,plain,
! [X3,X4] : ti(fun(fun(X3,bool),fun(fun(X3,X4),fun(X4,X3))),the_inv_into(X3,X4)) = the_inv_into(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2184]) ).
fof(c_0_3352,plain,
! [X52] : X52 != hAPP(nat,nat,suc,X52),
inference(variable_rename,[status(thm)],[c_0_2185]) ).
fof(c_0_3353,plain,
! [X52] : hAPP(nat,nat,suc,X52) != X52,
inference(variable_rename,[status(thm)],[c_0_2186]) ).
fof(c_0_3354,plain,
! [X3,X4] : ti(fun(fun(X3,X4),fun(fun(X3,bool),fun(X3,X4))),restrict(X3,X4)) = restrict(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2187]) ).
fof(c_0_3355,plain,
! [X3,X4] : ti(fun(fun(product_prod(X3,X4),bool),fun(X3,fun(X4,bool))),in_rel(X3,X4)) = in_rel(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2188]) ).
fof(c_0_3356,plain,
! [X3,X4] : ti(fun(fun(X3,X4),fun(fun(X3,bool),fun(X4,bool))),image(X3,X4)) = image(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2189]) ).
fof(c_0_3357,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_2190]) ).
fof(c_0_3358,axiom,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
c_0_2191 ).
fof(c_0_3359,axiom,
hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
c_0_2192 ).
fof(c_0_3360,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_2193])])]) ).
fof(c_0_3361,axiom,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
c_0_2194 ).
fof(c_0_3362,plain,
! [X2] : ti(fun(X2,fun(fun(nat,X2),fun(nat,X2))),nat_case(X2)) = nat_case(X2),
inference(variable_rename,[status(thm)],[c_0_2195]) ).
fof(c_0_3363,plain,
! [X3,X4] :
( ~ comm_monoid_add(X4)
| ti(fun(fun(X3,X4),fun(fun(X3,bool),X4)),big_co1399186613setsum(X3,X4)) = big_co1399186613setsum(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2196])]) ).
fof(c_0_3364,plain,
! [X2] : ti(fun(product_prod(fun(X2,bool),fun(X2,bool)),bool),finite_psubset(X2)) = finite_psubset(X2),
inference(variable_rename,[status(thm)],[c_0_2197]) ).
fof(c_0_3365,plain,
! [X3,X4] : ti(fun(fun(X3,bool),fun(fun(X3,X4),bool)),extensional(X3,X4)) = extensional(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2198]) ).
fof(c_0_3366,plain,
! [X3,X4] : ti(fun(fun(X3,X4),fun(fun(X3,bool),bool)),inj_on(X3,X4)) = inj_on(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2199]) ).
fof(c_0_3367,plain,
! [X119,X120] : hAPP(X119,X119,combi(X119),X120) = ti(X119,X120),
inference(variable_rename,[status(thm)],[c_0_2200]) ).
fof(c_0_3368,plain,
! [X75] :
( X75 = zero_zero(nat)
| X75 = hAPP(nat,nat,suc,esk97_1(X75)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2201])])]) ).
fof(c_0_3369,plain,
! [X52] :
( X52 = zero_zero(nat)
| X52 = hAPP(nat,nat,suc,esk96_1(X52)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2202])])]) ).
fof(c_0_3370,axiom,
hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
c_0_2203 ).
fof(c_0_3371,plain,
! [X52] : hAPP(nat,nat,size_size(nat),X52) = X52,
inference(variable_rename,[status(thm)],[c_0_2204]) ).
fof(c_0_3372,axiom,
hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
c_0_2205 ).
fof(c_0_3373,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
c_0_2206 ).
fof(c_0_3374,plain,
! [X2] : ti(fun(fun(X2,nat),fun(product_prod(X2,X2),bool)),measure(X2)) = measure(X2),
inference(variable_rename,[status(thm)],[c_0_2207]) ).
fof(c_0_3375,axiom,
hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
c_0_2208 ).
fof(c_0_3376,axiom,
hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
c_0_2209 ).
fof(c_0_3377,plain,
! [X3,X4] : ti(fun(X3,fun(X4,product_prod(X3,X4))),product_Pair(X3,X4)) = product_Pair(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2210]) ).
fof(c_0_3378,plain,
! [X2] : ti(fun(bool,fun(X2,fun(X2,X2))),if(X2)) = if(X2),
inference(variable_rename,[status(thm)],[c_0_2211]) ).
fof(c_0_3379,plain,
! [X2] :
( ~ linorder(X2)
| ti(fun(X2,fun(X2,fun(X2,bool))),ord_gr676655987ssThan(X2)) = ord_gr676655987ssThan(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2212])]) ).
fof(c_0_3380,plain,
! [X2] :
( ~ linorder(X2)
| ti(fun(X2,fun(X2,fun(X2,bool))),ord_gr1471790799AtMost(X2)) = ord_gr1471790799AtMost(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2213])]) ).
fof(c_0_3381,plain,
! [X2] :
( ~ linorder(X2)
| ti(fun(X2,fun(X2,fun(X2,bool))),ord_atLeastLessThan(X2)) = ord_atLeastLessThan(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2214])]) ).
fof(c_0_3382,plain,
! [X2] :
( ~ order(X2)
| ti(fun(X2,fun(X2,fun(X2,bool))),ord_atLeastAtMost(X2)) = ord_atLeastAtMost(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2215])]) ).
fof(c_0_3383,plain,
! [X2] : ti(fun(X2,fun(fun(X2,bool),bool)),member(X2)) = member(X2),
inference(variable_rename,[status(thm)],[c_0_2216]) ).
fof(c_0_3384,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
c_0_2217 ).
fof(c_0_3385,plain,
! [X2] : ti(fun(fun(X2,bool),fun(X2,bool)),collect(X2)) = collect(X2),
inference(variable_rename,[status(thm)],[c_0_2218]) ).
fof(c_0_3386,plain,
! [X3,X4] : ti(fun(X3,fun(X4,X3)),combk(X3,X4)) = combk(X3,X4),
inference(variable_rename,[status(thm)],[c_0_2219]) ).
fof(c_0_3387,plain,
! [X2] :
( ~ semilattice_sup(X2)
| ti(fun(X2,fun(X2,X2)),semilattice_sup_sup(X2)) = semilattice_sup_sup(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2220])]) ).
fof(c_0_3388,plain,
! [X2] :
( ~ semilattice_inf(X2)
| ti(fun(X2,fun(X2,X2)),semilattice_inf_inf(X2)) = semilattice_inf_inf(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2221])]) ).
fof(c_0_3389,plain,
! [X2] :
( ~ no_zero_divisors(X2)
| ti(fun(X2,fun(X2,X2)),times_times(X2)) = times_times(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2222])]) ).
fof(c_0_3390,plain,
! [X2] :
( ~ mult_zero(X2)
| ti(fun(X2,fun(X2,X2)),times_times(X2)) = times_times(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2223])]) ).
fof(c_0_3391,plain,
! [X2] :
( ~ ab_semigroup_mult(X2)
| ti(fun(X2,fun(X2,X2)),times_times(X2)) = times_times(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2224])]) ).
fof(c_0_3392,plain,
! [X2] :
( ~ monoid_mult(X2)
| ti(fun(X2,fun(X2,X2)),times_times(X2)) = times_times(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2225])]) ).
fof(c_0_3393,plain,
! [X2] :
( ~ semiring(X2)
| ti(fun(X2,fun(X2,X2)),times_times(X2)) = times_times(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2226])]) ).
fof(c_0_3394,plain,
! [X2] :
( ~ cancel_semigroup_add(X2)
| ti(fun(X2,fun(X2,X2)),plus_plus(X2)) = plus_plus(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2227])]) ).
fof(c_0_3395,plain,
! [X2] :
( ~ ab_semigroup_add(X2)
| ti(fun(X2,fun(X2,X2)),plus_plus(X2)) = plus_plus(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2228])]) ).
fof(c_0_3396,plain,
! [X2] :
( ~ monoid_add(X2)
| ti(fun(X2,fun(X2,X2)),plus_plus(X2)) = plus_plus(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2229])]) ).
fof(c_0_3397,plain,
! [X2] :
( ~ ord(X2)
| ti(fun(X2,fun(X2,bool)),ord_greaterThan(X2)) = ord_greaterThan(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2230])]) ).
fof(c_0_3398,plain,
! [X2] :
( ~ ord(X2)
| ti(fun(X2,fun(X2,bool)),ord_atLeast(X2)) = ord_atLeast(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2231])]) ).
fof(c_0_3399,plain,
! [X3] :
( ~ ord(X3)
| ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2232])]) ).
fof(c_0_3400,plain,
! [X2] :
( ~ ord(X2)
| ti(fun(X2,fun(X2,bool)),ord_less(X2)) = ord_less(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2233])]) ).
fof(c_0_3401,plain,
! [X2] : ti(fun(X2,fun(X2,bool)),fequal(X2)) = fequal(X2),
inference(variable_rename,[status(thm)],[c_0_2234]) ).
fof(c_0_3402,plain,
! [X3] : ti(fun(fun(X3,bool),bool),finite_finite_1(X3)) = finite_finite_1(X3),
inference(variable_rename,[status(thm)],[c_0_2235]) ).
fof(c_0_3403,plain,
! [X2] : ti(fun(fun(X2,bool),nat),finite_card(X2)) = finite_card(X2),
inference(variable_rename,[status(thm)],[c_0_2236]) ).
fof(c_0_3404,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
c_0_2237 ).
fof(c_0_3405,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
c_0_2238 ).
fof(c_0_3406,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
c_0_2239 ).
fof(c_0_3407,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
c_0_2240 ).
fof(c_0_3408,plain,
! [X2] :
( ~ ring_1(X2)
| ti(fun(X2,bool),ring_1_Ints(X2)) = ring_1_Ints(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2241])]) ).
fof(c_0_3409,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_2242])])])])]) ).
fof(c_0_3410,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_2243])])])])]) ).
fof(c_0_3411,plain,
! [X118,X119] : ti(X118,ti(X118,X119)) = ti(X118,X119),
inference(variable_rename,[status(thm)],[c_0_2244]) ).
fof(c_0_3412,plain,
! [X2] : ti(fun(X2,X2),combi(X2)) = combi(X2),
inference(variable_rename,[status(thm)],[c_0_2245]) ).
fof(c_0_3413,plain,
! [X116,X117] :
( ~ finite_finite(X117)
| ~ finite_finite(X116)
| finite_finite(product_prod(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2246])]) ).
fof(c_0_3414,plain,
! [X116,X117] :
( ~ finite_finite(X117)
| ~ finite_finite(X116)
| finite_finite(sum_sum(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2247])]) ).
fof(c_0_3415,plain,
! [X116,X117] :
( ~ finite_finite(X117)
| ~ finite_finite(X116)
| finite_finite(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2248])]) ).
fof(c_0_3416,axiom,
ti(fun(nat,nat),size_size(nat)) = size_size(nat),
c_0_2249 ).
fof(c_0_3417,plain,
! [X116,X117] :
( ~ ord(X117)
| ord(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2250])]) ).
fof(c_0_3418,plain,
! [X116,X117] :
( ~ top(X117)
| top(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2251])]) ).
fof(c_0_3419,plain,
! [X116,X117] :
( ~ order(X117)
| order(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2252])]) ).
fof(c_0_3420,plain,
! [X116,X117] :
( ~ lattice(X117)
| lattice(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2253])]) ).
fof(c_0_3421,plain,
! [X116,X117] :
( ~ preorder(X117)
| preorder(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2254])]) ).
fof(c_0_3422,plain,
! [X116,X117] :
( ~ distrib_lattice(X117)
| distrib_lattice(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2255])]) ).
fof(c_0_3423,plain,
! [X116,X117] :
( ~ lattice(X117)
| semilattice_inf(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2256])]) ).
fof(c_0_3424,plain,
! [X116,X117] :
( ~ lattice(X117)
| semilattice_sup(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2257])]) ).
fof(c_0_3425,plain,
! [X116,X117] :
( ~ bounded_lattice(X117)
| bounded_lattice_top(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2258])]) ).
fof(c_0_3426,plain,
! [X116,X117] :
( ~ bounded_lattice(X117)
| bounded_lattice(fun(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2259])]) ).
fof(c_0_3427,axiom,
ti(fun(arrow_1998540521e_indi,nat),h) = h,
c_0_2260 ).
fof(c_0_3428,axiom,
ti(fun(bool,bool),fNot) = fNot,
c_0_2261 ).
fof(c_0_3429,axiom,
ti(fun(nat,nat),nat_size) = nat_size,
c_0_2262 ).
fof(c_0_3430,axiom,
ti(fun(nat,nat),suc) = suc,
c_0_2263 ).
fof(c_0_3431,axiom,
ti(fun(bool,nat),bool_size) = bool_size,
c_0_2264 ).
fof(c_0_3432,plain,
! [X2] :
( ~ top(X2)
| ti(X2,top_top(X2)) = top_top(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2265])]) ).
fof(c_0_3433,plain,
! [X2] :
( ~ zero(X2)
| ti(X2,zero_zero(X2)) = zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2266])]) ).
fof(c_0_3434,plain,
! [X2] :
( ~ one(X2)
| ti(X2,one_one(X2)) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2267])]) ).
fof(c_0_3435,plain,
! [X119] :
( ti(bool,X119) = fTrue
| ti(bool,X119) = fFalse ),
inference(variable_rename,[status(thm)],[c_0_2268]) ).
fof(c_0_3436,plain,
! [X119] :
( ti(bool,X119) = fTrue
| ti(bool,X119) = fFalse ),
inference(variable_rename,[status(thm)],[c_0_2269]) ).
fof(c_0_3437,plain,
! [X119] :
( ti(bool,X119) = fTrue
| ti(bool,X119) = fFalse ),
inference(variable_rename,[status(thm)],[c_0_2270]) ).
fof(c_0_3438,plain,
! [X2] : ti(X2,undefined(X2)) = undefined(X2),
inference(variable_rename,[status(thm)],[c_0_2271]) ).
fof(c_0_3439,plain,
! [X2] :
( ~ zero_neq_one(X2)
| one_one(X2) != zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2272])]) ).
fof(c_0_3440,plain,
! [X2] :
( ~ zero_neq_one(X2)
| zero_zero(X2) != one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2273])]) ).
fof(c_0_3441,plain,
! [X116] :
( ~ finite_finite(X116)
| finite_finite(option(X116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2274])]) ).
fof(c_0_3442,axiom,
ti(nat,n) = n,
c_0_2275 ).
fof(c_0_3443,axiom,
ti(arrow_2142409994le_alt,e) = e,
c_0_2276 ).
fof(c_0_3444,axiom,
ti(arrow_2142409994le_alt,b) = b,
c_0_2277 ).
fof(c_0_3445,axiom,
ti(arrow_2142409994le_alt,a) = a,
c_0_2278 ).
fof(c_0_3446,axiom,
ti(bool,fTrue) = fTrue,
c_0_2279 ).
fof(c_0_3447,axiom,
ti(bool,fFalse) = fFalse,
c_0_2280 ).
fof(c_0_3448,plain,
~ hBOOL(fFalse),
c_0_2281 ).
fof(c_0_3449,axiom,
hBOOL(fTrue),
c_0_2282 ).
fof(c_0_3450,axiom,
finite_finite(product_unit),
c_0_2283 ).
fof(c_0_3451,axiom,
ord(bool),
c_0_2284 ).
fof(c_0_3452,axiom,
top(bool),
c_0_2285 ).
fof(c_0_3453,axiom,
order(bool),
c_0_2286 ).
fof(c_0_3454,axiom,
lattice(bool),
c_0_2287 ).
fof(c_0_3455,axiom,
finite_finite(bool),
c_0_2288 ).
fof(c_0_3456,axiom,
preorder(bool),
c_0_2289 ).
fof(c_0_3457,axiom,
distrib_lattice(bool),
c_0_2290 ).
fof(c_0_3458,axiom,
semilattice_inf(bool),
c_0_2291 ).
fof(c_0_3459,axiom,
semilattice_sup(bool),
c_0_2292 ).
fof(c_0_3460,axiom,
bounded_lattice_top(bool),
c_0_2293 ).
fof(c_0_3461,axiom,
one(nat),
c_0_2294 ).
fof(c_0_3462,axiom,
zero(nat),
c_0_2295 ).
fof(c_0_3463,axiom,
ord(nat),
c_0_2296 ).
fof(c_0_3464,axiom,
semiring(nat),
c_0_2297 ).
fof(c_0_3465,axiom,
order(nat),
c_0_2298 ).
fof(c_0_3466,axiom,
mult_zero(nat),
c_0_2299 ).
fof(c_0_3467,axiom,
lattice(nat),
c_0_2300 ).
fof(c_0_3468,axiom,
semiring_0(nat),
c_0_2301 ).
fof(c_0_3469,axiom,
monoid_add(nat),
c_0_2302 ).
fof(c_0_3470,axiom,
monoid_mult(nat),
c_0_2303 ).
fof(c_0_3471,axiom,
linorder(nat),
c_0_2304 ).
fof(c_0_3472,axiom,
preorder(nat),
c_0_2305 ).
fof(c_0_3473,axiom,
zero_neq_one(nat),
c_0_2306 ).
fof(c_0_3474,axiom,
comm_semiring(nat),
c_0_2307 ).
fof(c_0_3475,axiom,
comm_semiring_1(nat),
c_0_2308 ).
fof(c_0_3476,axiom,
comm_monoid_add(nat),
c_0_2309 ).
fof(c_0_3477,axiom,
no_zero_divisors(nat),
c_0_2310 ).
fof(c_0_3478,axiom,
ordered_semiring(nat),
c_0_2311 ).
fof(c_0_3479,axiom,
ab_semigroup_add(nat),
c_0_2312 ).
fof(c_0_3480,axiom,
comm_monoid_mult(nat),
c_0_2313 ).
fof(c_0_3481,axiom,
ab_semigroup_mult(nat),
c_0_2314 ).
fof(c_0_3482,axiom,
distrib_lattice(nat),
c_0_2315 ).
fof(c_0_3483,axiom,
semilattice_inf(nat),
c_0_2316 ).
fof(c_0_3484,axiom,
semilattice_sup(nat),
c_0_2317 ).
fof(c_0_3485,axiom,
linordered_semidom(nat),
c_0_2318 ).
fof(c_0_3486,axiom,
linordered_semiring(nat),
c_0_2319 ).
fof(c_0_3487,axiom,
cancel_semigroup_add(nat),
c_0_2320 ).
fof(c_0_3488,axiom,
ordere1490568538miring(nat),
c_0_2321 ).
fof(c_0_3489,axiom,
ordere453448008miring(nat),
c_0_2322 ).
fof(c_0_3490,axiom,
cancel146912293up_add(nat),
c_0_2323 ).
fof(c_0_3491,axiom,
ordere216010020id_add(nat),
c_0_2324 ).
fof(c_0_3492,axiom,
ordere779506340up_add(nat),
c_0_2325 ).
fof(c_0_3493,axiom,
linord20386208strict(nat),
c_0_2326 ).
fof(c_0_3494,axiom,
linord893533164strict(nat),
c_0_2327 ).
fof(c_0_3495,axiom,
ordere236663937imp_le(nat),
c_0_2328 ).
fof(c_0_3496,axiom,
ordere223160158up_add(nat),
c_0_2329 ).
fof(c_0_3497,axiom,
semiri456707255roduct(nat),
c_0_2330 ).
fof(c_0_3498,axiom,
bounded_lattice(bool),
c_0_2331 ).
fof(c_0_3499,axiom,
a != b,
c_0_2332 ).
fof(c_0_3500,axiom,
c != d,
c_0_2333 ).
cnf(c_0_3501,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3502,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3503,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3504,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3505,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(split_conjunct,[status(thm)],[c_0_2335]) ).
cnf(c_0_3506,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(split_conjunct,[status(thm)],[c_0_2335]) ).
cnf(c_0_3507,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2335]) ).
cnf(c_0_3508,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3509,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3510,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2335]) ).
cnf(c_0_3511,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(split_conjunct,[status(thm)],[c_0_2337]) ).
cnf(c_0_3512,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(split_conjunct,[status(thm)],[c_0_2338]) ).
cnf(c_0_3513,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(split_conjunct,[status(thm)],[c_0_2339]) ).
cnf(c_0_3514,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2337]) ).
cnf(c_0_3515,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
inference(split_conjunct,[status(thm)],[c_0_2338]) ).
cnf(c_0_3516,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3517,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3518,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
inference(split_conjunct,[status(thm)],[c_0_2339]) ).
cnf(c_0_3519,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(split_conjunct,[status(thm)],[c_0_2340]) ).
cnf(c_0_3520,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(split_conjunct,[status(thm)],[c_0_2341]) ).
cnf(c_0_3521,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(split_conjunct,[status(thm)],[c_0_2342]) ).
cnf(c_0_3522,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
inference(split_conjunct,[status(thm)],[c_0_2343]) ).
cnf(c_0_3523,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3524,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3525,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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X5),X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X5)),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)))),X6)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2344]) ).
cnf(c_0_3526,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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X5),X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X5)),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)))),X6)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2345]) ).
cnf(c_0_3527,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6))
| ~ 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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_inf_inf(fun(product_prod(X2,X1),bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2344]) ).
cnf(c_0_3528,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6))
| ~ 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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_sup_sup(fun(product_prod(X2,X1),bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2345]) ).
cnf(c_0_3529,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk140_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3530,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk29_0),one_one(nat))))),lab)),lba)))),
inference(split_conjunct,[status(thm)],[c_0_2347]) ).
cnf(c_0_3531,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2348]) ).
cnf(c_0_3532,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2349]) ).
cnf(c_0_3533,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk29_0)) ),
inference(split_conjunct,[status(thm)],[c_0_2347]) ).
cnf(c_0_3534,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2348]) ).
cnf(c_0_3535,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2350]) ).
cnf(c_0_3536,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_301600364e_Prof)),
inference(split_conjunct,[status(thm)],[c_0_2351]) ).
cnf(c_0_3537,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk140_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3538,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_2352]) ).
cnf(c_0_3539,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_2352]) ).
cnf(c_0_3540,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3541,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk139_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3542,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,fun(X3,bool)),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,bool)),fun(X1,X2)),combs(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),collect(X3)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),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),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)),X5)))),X6)))),X7) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combs(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X7)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),X6))))),X5)
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2353]) ).
cnf(c_0_3543,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2354]) ).
cnf(c_0_3544,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X5,bool),X1,hAPP(fun(X5,X1),fun(fun(X5,bool),X1),big_co1399186613setsum(X5,X1),X6),X7)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X5,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X5,bool),X1)),fun(fun(X5,bool),fun(X2,X1)),combc(X2,fun(X5,bool),X1),hAPP(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1)),hAPP(fun(fun(X5,X1),fun(fun(X5,bool),X1)),fun(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1))),combb(fun(X5,X1),fun(fun(X5,bool),X1),X2),big_co1399186613setsum(X5,X1)),hAPP(fun(X5,X1),fun(X2,fun(X5,X1)),hAPP(fun(X2,fun(fun(X5,X1),fun(X5,X1))),fun(fun(X5,X1),fun(X2,fun(X5,X1))),combc(X2,fun(X5,X1),fun(X5,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1))),hAPP(fun(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1)))),combb(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1)),X2),combb(X1,X1,X5)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3))),X6))),X7)),X4)
| ~ semiring_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2355]) ).
cnf(c_0_3545,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) != hAPP(X1,X2,X8,esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2354]) ).
cnf(c_0_3546,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_2356]) ).
cnf(c_0_3547,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = hAPP(fun(X5,bool),X2,hAPP(fun(X5,X2),fun(fun(X5,bool),X2),big_co1399186613setsum(X5,X2),hAPP(fun(X5,fun(X1,bool)),fun(X5,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X5,fun(X1,bool)),fun(X5,X2)),combb(fun(X1,bool),X2,X5),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),collect(X1)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),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),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)),X4)))),hAPP(fun(X1,fun(X5,bool)),fun(X5,fun(X1,bool)),combc(X1,X5,bool),hAPP(fun(X1,X5),fun(X1,fun(X5,bool)),hAPP(fun(X5,fun(X5,bool)),fun(fun(X1,X5),fun(X1,fun(X5,bool))),combb(X5,fun(X5,bool),X1),fequal(X5)),X6)))))),hAPP(fun(X1,bool),fun(X5,bool),hAPP(fun(X1,X5),fun(fun(X1,bool),fun(X5,bool)),image(X1,X5),X6),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2357]) ).
cnf(c_0_3548,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3549,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk139_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3550,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),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)),X5)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2358]) ).
cnf(c_0_3551,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ 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),X4),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),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(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,esk117_4(X3,X1,X4,X2))))))) ),
inference(split_conjunct,[status(thm)],[c_0_2359]) ).
cnf(c_0_3552,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_2360]) ).
cnf(c_0_3553,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2361]) ).
cnf(c_0_3554,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2362]) ).
cnf(c_0_3555,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2362]) ).
cnf(c_0_3556,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),X5))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X5)),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2363]) ).
cnf(c_0_3557,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,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X3)),X4)),X5)),X6) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),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),X3))))),
inference(split_conjunct,[status(thm)],[c_0_2364]) ).
cnf(c_0_3558,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2365]) ).
cnf(c_0_3559,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2365]) ).
cnf(c_0_3560,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,esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk55_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2366]) ).
cnf(c_0_3561,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,esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk53_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2367]) ).
cnf(c_0_3562,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,esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2368]) ).
cnf(c_0_3563,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,esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk44_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2369]) ).
cnf(c_0_3564,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,esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk51_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2370]) ).
cnf(c_0_3565,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,esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk49_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2371]) ).
cnf(c_0_3566,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,esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk41_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2372]) ).
cnf(c_0_3567,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,esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk39_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2373]) ).
cnf(c_0_3568,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2374]) ).
cnf(c_0_3569,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2375]) ).
cnf(c_0_3570,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2375]) ).
cnf(c_0_3571,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2376]) ).
cnf(c_0_3572,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2376]) ).
cnf(c_0_3573,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2374]) ).
cnf(c_0_3574,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2375]) ).
cnf(c_0_3575,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2375]) ).
cnf(c_0_3576,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2376]) ).
cnf(c_0_3577,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(split_conjunct,[status(thm)],[c_0_2376]) ).
cnf(c_0_3578,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_2377]) ).
cnf(c_0_3579,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3580,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X3)),X4)),one_one(X2)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),one_one(X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2379]) ).
cnf(c_0_3581,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X3,bool),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X3,bool),fun(X1,X2)),combc(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),X5)),X6) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X1,bool),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X1,bool),fun(X3,X2)),combc(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),X6)),X5)
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2380]) ).
cnf(c_0_3582,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X2,X1)),esk26_2(X2,X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk24_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2381]) ).
cnf(c_0_3583,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3584,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3585,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3586,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3587,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2384]) ).
cnf(c_0_3588,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X2,X1)),esk26_2(X2,X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk24_2(X2,X1),X2)))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
inference(split_conjunct,[status(thm)],[c_0_2381]) ).
cnf(c_0_3589,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk24_2(X2,X1)),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
inference(split_conjunct,[status(thm)],[c_0_2381]) ).
cnf(c_0_3590,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3591,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3592,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2386]) ).
cnf(c_0_3593,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2386]) ).
cnf(c_0_3594,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| ti(arrow_2142409994le_alt,esk25_2(X2,X1)) != ti(arrow_2142409994le_alt,esk26_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2381]) ).
cnf(c_0_3595,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3596,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3597,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_2387]) ).
cnf(c_0_3598,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_2387]) ).
cnf(c_0_3599,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3600,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3601,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3602,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3603,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3604,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3605,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3606,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3607,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3608,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3609,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2386]) ).
cnf(c_0_3610,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2386]) ).
cnf(c_0_3611,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2388]) ).
cnf(c_0_3612,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2388]) ).
cnf(c_0_3613,plain,
( hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),hAPP(fun(X1,X6),fun(X1,X2),hAPP(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2))),compose(X1,X6,X2),X4),X7),X8)) = hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3))),compose(X1,X6,X3),X4),hAPP(fun(X6,X2),fun(X6,X3),hAPP(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3)),hAPP(fun(X6,bool),fun(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3))),compose(X6,X2,X3),X9),X5),X7)),X8)
| ~ hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X5),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X10),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X11))))
| ~ hBOOL(hAPP(fun(fun(X6,X2),bool),bool,hAPP(fun(X6,X2),fun(fun(fun(X6,X2),bool),bool),member(fun(X6,X2)),X7),hAPP(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool)),pi(X6,X2),X9),hAPP(fun(X2,bool),fun(X6,fun(X2,bool)),combk(fun(X2,bool),X6),X10))))
| ~ hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),X8),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X9)))) ),
inference(split_conjunct,[status(thm)],[c_0_2389]) ).
cnf(c_0_3614,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),esk54_6(X1,X2,X5,X6,X3,X4)),esk55_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_2366]) ).
cnf(c_0_3615,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),esk52_6(X1,X2,X5,X6,X3,X4)),esk53_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_2367]) ).
cnf(c_0_3616,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),esk47_6(X1,X2,X6,X3,X4,X5)),esk46_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_2368]) ).
cnf(c_0_3617,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),esk45_6(X1,X2,X6,X3,X4,X5)),esk44_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_2369]) ).
cnf(c_0_3618,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),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),X7))))
| ~ hBOOL(hAPP(fun(fun(X3,X2),bool),bool,hAPP(fun(X3,X2),fun(fun(fun(X3,X2),bool),bool),member(fun(X3,X2)),X5),hAPP(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool)),pi(X3,X2),X8),hAPP(fun(X2,bool),fun(X3,fun(X2,bool)),combk(fun(X2,bool),X3),X7))))
| ~ 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),X4),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X8)))) ),
inference(split_conjunct,[status(thm)],[c_0_2390]) ).
cnf(c_0_3619,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2391]) ).
cnf(c_0_3620,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_2392]) ).
cnf(c_0_3621,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),esk50_6(X1,X2,X6,X3,X4,X5)),esk51_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_2370]) ).
cnf(c_0_3622,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),esk48_6(X1,X2,X6,X3,X4,X5)),esk49_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_2371]) ).
cnf(c_0_3623,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),esk42_6(X1,X2,X5,X6,X3,X4)),esk41_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_2372]) ).
cnf(c_0_3624,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),esk40_6(X1,X2,X5,X6,X3,X4)),esk39_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_2373]) ).
cnf(c_0_3625,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3626,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7) = hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),the_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2393]) ).
cnf(c_0_3627,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),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7) = hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),hilbert_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2394]) ).
cnf(c_0_3628,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3629,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3630,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X3)),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)),X4)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2395]) ).
cnf(c_0_3631,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X3)),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)),X4)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2396]) ).
cnf(c_0_3632,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3633,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2388]) ).
cnf(c_0_3634,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2388]) ).
cnf(c_0_3635,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3636,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3637,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,esk59_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,esk59_5(X2,X1,X4,X5,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2399]) ).
cnf(c_0_3638,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3639,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3640,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2400]) ).
cnf(c_0_3641,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2400]) ).
cnf(c_0_3642,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),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2401]) ).
cnf(c_0_3643,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_2402]) ).
cnf(c_0_3644,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_2402]) ).
cnf(c_0_3645,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3646,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)),
inference(split_conjunct,[status(thm)],[c_0_2403]) ).
cnf(c_0_3647,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3648,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk132_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,esk132_5(X2,X1,X3,X5,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2404]) ).
cnf(c_0_3649,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(X2,X1,X5,esk173_5(X2,X1,X5,X4,X3)) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2391]) ).
cnf(c_0_3650,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_2387]) ).
cnf(c_0_3651,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3652,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),esk22_4(X1,X2,X4,X3)),esk23_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),esk22_4(X1,X2,X4,X3)),esk23_4(X1,X2,X4,X3))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2405]) ).
cnf(c_0_3653,plain,
hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
inference(split_conjunct,[status(thm)],[c_0_2406]) ).
cnf(c_0_3654,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3655,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3656,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3657,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk137_6(X2,X1,X5,X4,X6,X3)),X3))
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2407]) ).
cnf(c_0_3658,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_2408]) ).
cnf(c_0_3659,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_2408]) ).
cnf(c_0_3660,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),esk75_2(X2,X1)),hAPP(nat,nat,X1,esk75_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2409]) ).
cnf(c_0_3661,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),X4),X5)),X6)),X7) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X4,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X5),X7)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X6),X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X4),X8),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2410]) ).
cnf(c_0_3662,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3663,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_2411]) ).
cnf(c_0_3664,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_2412]) ).
cnf(c_0_3665,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_2402]) ).
cnf(c_0_3666,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_2402]) ).
cnf(c_0_3667,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),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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(split_conjunct,[status(thm)],[c_0_2413]) ).
cnf(c_0_3668,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3669,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3670,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3671,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3672,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3673,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3674,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3675,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3676,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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)),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),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X3))))
| hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3) != ti(fun(X1,bool),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2414]) ).
cnf(c_0_3677,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3678,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3679,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_2415]) ).
cnf(c_0_3680,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2416]) ).
cnf(c_0_3681,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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2417]) ).
cnf(c_0_3682,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),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,esk133_5(X2,X1,X3,X5,X4))),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2418]) ).
cnf(c_0_3683,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,esk137_6(X2,X1,X5,X4,X6,X3)) != hAPP(X2,X1,X6,esk137_6(X2,X1,X5,X4,X6,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2407]) ).
cnf(c_0_3684,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3685,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3686,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2419]) ).
cnf(c_0_3687,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3688,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3689,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2395]) ).
cnf(c_0_3690,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2396]) ).
cnf(c_0_3691,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3692,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3693,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3694,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3695,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3696,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3697,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3698,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3699,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3700,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3701,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3702,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3703,plain,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk147_6(X4,X1,X5,X6,X2,X3)),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2420]) ).
cnf(c_0_3704,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3705,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3706,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3707,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3708,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = 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),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_2421]) ).
cnf(c_0_3709,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = 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),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_2422]) ).
cnf(c_0_3710,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3711,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3712,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2423]) ).
cnf(c_0_3713,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3714,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_2424]) ).
cnf(c_0_3715,plain,
( hAPP(fun(X1,bool),X2,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X6,hAPP(fun(X1,bool),X2,X3,X4)),hAPP(fun(X1,bool),X2,X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X6),X7),X8),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2425]) ).
cnf(c_0_3716,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_2426]) ).
cnf(c_0_3717,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_2427]) ).
cnf(c_0_3718,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3719,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3720,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_2428]) ).
cnf(c_0_3721,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(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk131_5(X1,X2,X3,X5,X4))),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2429]) ).
cnf(c_0_3722,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3723,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3724,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3725,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2400]) ).
cnf(c_0_3726,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3727,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3728,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3729,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3730,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3731,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3732,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3733,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3734,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3735,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3736,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3737,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3738,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3739,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3740,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3741,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3742,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),esk22_4(X1,X2,X4,X3)),esk23_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),esk22_4(X1,X2,X4,X3)),esk23_4(X1,X2,X4,X3))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2405]) ).
cnf(c_0_3743,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3744,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk14_4(X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2430]) ).
cnf(c_0_3745,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3746,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3747,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3748,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3749,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(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),X5),X4)),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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2431]) ).
cnf(c_0_3750,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2432]) ).
cnf(c_0_3751,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2433]) ).
cnf(c_0_3752,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_2434]) ).
cnf(c_0_3753,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3754,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3755,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2435]) ).
cnf(c_0_3756,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3757,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3758,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,esk124_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2436]) ).
cnf(c_0_3759,plain,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hAPP(X1,X4,X5,esk147_6(X4,X1,X5,X6,X2,X3)) != hAPP(X1,X4,X6,esk147_6(X4,X1,X5,X6,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2420]) ).
cnf(c_0_3760,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3761,plain,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2437]) ).
cnf(c_0_3762,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3763,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),X5) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3)),X5)),X4)
| ~ semiring_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2438]) ).
cnf(c_0_3764,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_2415]) ).
cnf(c_0_3765,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_2439]) ).
cnf(c_0_3766,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X1),X2),X3)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2440]) ).
cnf(c_0_3767,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X1),X2),X3)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2441]) ).
cnf(c_0_3768,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_2436]) ).
cnf(c_0_3769,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)),the_inv_into(X1,X2),X3),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X6))
| ~ 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(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2442]) ).
cnf(c_0_3770,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk11_1(X1))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk10_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3771,plain,
( ~ linord581940658strict(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2443]) ).
cnf(c_0_3772,plain,
( hBOOL(hAPP(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(X1,bool,X4,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),top_top(fun(X1,bool))),X3),esk108_5(X1,X2,X5,X4,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2444]) ).
cnf(c_0_3773,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),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2445]) ).
cnf(c_0_3774,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),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2446]) ).
cnf(c_0_3775,plain,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2447]) ).
cnf(c_0_3776,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2448]) ).
cnf(c_0_3777,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_2449]) ).
cnf(c_0_3778,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X6)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X4),X5)),X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2450]) ).
cnf(c_0_3779,plain,
hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
inference(split_conjunct,[status(thm)],[c_0_2451]) ).
cnf(c_0_3780,plain,
( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X3),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X4)),X5) = ti(fun(X1,X2),X5)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2452]) ).
cnf(c_0_3781,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_2453]) ).
cnf(c_0_3782,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),hAPP(fun(X5,bool),fun(X1,bool),hAPP(fun(X5,X1),fun(fun(X5,bool),fun(X1,bool)),image(X5,X1),X6),X7)) = hAPP(fun(X5,bool),X2,hAPP(X2,fun(fun(X5,bool),X2),hAPP(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2))),finite_fold_image(X2,X5),times_times(X2)),hAPP(fun(X5,X1),fun(X5,X2),hAPP(fun(X1,X2),fun(fun(X5,X1),fun(X5,X2)),comp(X1,X2,X5),X3),X6)),X4),X7)
| ~ hBOOL(hAPP(fun(X5,bool),bool,hAPP(fun(X5,X1),fun(fun(X5,bool),bool),inj_on(X5,X1),X6),X7))
| ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),X7))
| ~ ab_semigroup_mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2454]) ).
cnf(c_0_3783,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),esk59_5(X2,X1,X4,X5,X3)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2399]) ).
cnf(c_0_3784,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3785,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(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2455]) ).
cnf(c_0_3786,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X6),X4),X7),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2456]) ).
cnf(c_0_3787,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),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),esk133_5(X2,X1,X3,X5,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2418]) ).
cnf(c_0_3788,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_3789,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_3790,plain,
( hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X3),X4),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)) = ti(fun(X1,X2),X4)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_2459]) ).
cnf(c_0_3791,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3792,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_2460]) ).
cnf(c_0_3793,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_2461]) ).
cnf(c_0_3794,plain,
( hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2436]) ).
cnf(c_0_3795,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2455]) ).
cnf(c_0_3796,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
inference(split_conjunct,[status(thm)],[c_0_2462]) ).
cnf(c_0_3797,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_2463]) ).
cnf(c_0_3798,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_2464]) ).
cnf(c_0_3799,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3800,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3801,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3802,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3803,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3804,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3805,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X1),X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3806,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X1),X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3807,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_3808,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_3809,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_3810,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_3811,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(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2465]) ).
cnf(c_0_3812,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_2466]) ).
cnf(c_0_3813,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk132_5(X2,X1,X3,X5,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2404]) ).
cnf(c_0_3814,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,esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk92_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2467]) ).
cnf(c_0_3815,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_2463]) ).
cnf(c_0_3816,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,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_2468]) ).
cnf(c_0_3817,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2469]) ).
cnf(c_0_3818,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2470]) ).
cnf(c_0_3819,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2471]) ).
cnf(c_0_3820,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2472]) ).
cnf(c_0_3821,plain,
( hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_2436]) ).
cnf(c_0_3822,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3823,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)),X5)
| ~ semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2473]) ).
cnf(c_0_3824,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_2474]) ).
cnf(c_0_3825,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X6),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2475]) ).
cnf(c_0_3826,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2476]) ).
cnf(c_0_3827,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2477]) ).
cnf(c_0_3828,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2477]) ).
cnf(c_0_3829,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_2478]) ).
cnf(c_0_3830,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),esk107_4(X3,X1,X4,X2)),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),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(split_conjunct,[status(thm)],[c_0_2479]) ).
cnf(c_0_3831,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[c_0_2480]) ).
cnf(c_0_3832,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_2481]) ).
cnf(c_0_3833,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(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2479]) ).
cnf(c_0_3834,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_2405]) ).
cnf(c_0_3835,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_2405]) ).
cnf(c_0_3836,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2436]) ).
cnf(c_0_3837,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk125_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2436]) ).
cnf(c_0_3838,plain,
( 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),X4),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3839,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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2483]) ).
cnf(c_0_3840,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_2484]) ).
cnf(c_0_3841,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X2),fun(fun(X4,bool),bool),inj_on(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2485]) ).
cnf(c_0_3842,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_2486]) ).
cnf(c_0_3843,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),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(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),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_2472]) ).
cnf(c_0_3844,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2487]) ).
cnf(c_0_3845,plain,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2447]) ).
cnf(c_0_3846,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3847,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_2449]) ).
cnf(c_0_3848,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk11_1(X1))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk10_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3849,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X4),X5))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2488]) ).
cnf(c_0_3850,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_2461]) ).
cnf(c_0_3851,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2445]) ).
cnf(c_0_3852,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2446]) ).
cnf(c_0_3853,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2489]) ).
cnf(c_0_3854,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2489]) ).
cnf(c_0_3855,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_atLeastAtMost(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_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2490]) ).
cnf(c_0_3856,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_atLeastAtMost(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_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2490]) ).
cnf(c_0_3857,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3858,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3859,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2491]) ).
cnf(c_0_3860,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2491]) ).
cnf(c_0_3861,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2492]) ).
cnf(c_0_3862,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2492]) ).
cnf(c_0_3863,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_3864,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_3865,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr676655987ssThan(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_3866,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_3867,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr1471790799AtMost(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_3868,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_3869,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk145_5(X1,X2,X5,X3,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2496]) ).
cnf(c_0_3870,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2378]) ).
cnf(c_0_3871,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_2436]) ).
cnf(c_0_3872,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk125_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_2436]) ).
cnf(c_0_3873,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3874,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2443]) ).
cnf(c_0_3875,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2443]) ).
cnf(c_0_3876,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2497]) ).
cnf(c_0_3877,plain,
( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_2455]) ).
cnf(c_0_3878,plain,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2498]) ).
cnf(c_0_3879,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_2426]) ).
cnf(c_0_3880,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_2499]) ).
cnf(c_0_3881,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_2499]) ).
cnf(c_0_3882,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_2500]) ).
cnf(c_0_3883,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_3884,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_3885,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3886,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3887,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_3888,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_3889,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2501]) ).
cnf(c_0_3890,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk111_5(X3,X1,X4,X5,X2)),X5))
| ~ 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),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_2502]) ).
cnf(c_0_3891,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| ~ 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_2503]) ).
cnf(c_0_3892,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| ~ 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_2504]) ).
cnf(c_0_3893,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_2505]) ).
cnf(c_0_3894,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(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk131_5(X1,X2,X3,X5,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2429]) ).
cnf(c_0_3895,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3896,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3897,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_2466]) ).
cnf(c_0_3898,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2506]) ).
cnf(c_0_3899,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_2507]) ).
cnf(c_0_3900,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_2508]) ).
cnf(c_0_3901,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_2509]) ).
cnf(c_0_3902,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_2510]) ).
cnf(c_0_3903,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_2511]) ).
cnf(c_0_3904,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)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2512]) ).
cnf(c_0_3905,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)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2513]) ).
cnf(c_0_3906,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_3907,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2515]) ).
cnf(c_0_3908,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2516]) ).
cnf(c_0_3909,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2517]) ).
cnf(c_0_3910,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2518]) ).
cnf(c_0_3911,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2519]) ).
cnf(c_0_3912,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2520]) ).
cnf(c_0_3913,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2521]) ).
cnf(c_0_3914,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,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2522]) ).
cnf(c_0_3915,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2523]) ).
cnf(c_0_3916,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hAPP(X1,X2,X3,esk145_5(X1,X2,X5,X3,X4)) != hAPP(X1,X2,X5,esk145_5(X1,X2,X5,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2496]) ).
cnf(c_0_3917,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk109_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_2524]) ).
cnf(c_0_3918,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk103_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_2525]) ).
cnf(c_0_3919,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2526]) ).
cnf(c_0_3920,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2527]) ).
cnf(c_0_3921,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2528]) ).
cnf(c_0_3922,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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)),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),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2529]) ).
cnf(c_0_3923,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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)),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),X2),X4))
| ~ ordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2530]) ).
cnf(c_0_3924,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ ordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2531]) ).
cnf(c_0_3925,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_2532]) ).
cnf(c_0_3926,plain,
( 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),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2533]) ).
cnf(c_0_3927,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(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2534]) ).
cnf(c_0_3928,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),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2535]) ).
cnf(c_0_3929,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),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2536]) ).
cnf(c_0_3930,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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_2537]) ).
cnf(c_0_3931,plain,
( 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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3932,plain,
( 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),X3),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3933,plain,
( 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),X4),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3934,plain,
( 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),X4),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3935,plain,
( 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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3936,plain,
( 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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3937,plain,
( 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),X4),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3938,plain,
( 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),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3939,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_2540]) ).
cnf(c_0_3940,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)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),X4) = ti(fun(X2,bool),X7)
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X5),X8) != ti(fun(X2,bool),X7)
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X4) != ti(fun(X3,bool),X8) ),
inference(split_conjunct,[status(thm)],[c_0_2541]) ).
cnf(c_0_3941,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2542]) ).
cnf(c_0_3942,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_3943,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_2411]) ).
cnf(c_0_3944,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_2412]) ).
cnf(c_0_3945,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_2544]) ).
cnf(c_0_3946,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3947,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,X4)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2545]) ).
cnf(c_0_3948,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3949,plain,
( hBOOL(hAPP(X1,bool,X4,X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk108_5(X1,X2,X5,X4,X3)),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)))))
| ~ 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_2444]) ).
cnf(c_0_3950,plain,
( hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X4),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))),X5))),X5) = ti(fun(X1,X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),top_top(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2546]) ).
cnf(c_0_3951,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk15_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2430]) ).
cnf(c_0_3952,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2547]) ).
cnf(c_0_3953,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3954,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_3955,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_3956,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X1),X2)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2550]) ).
cnf(c_0_3957,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X1),X2)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2551]) ).
cnf(c_0_3958,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,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2552]) ).
cnf(c_0_3959,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3960,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X4),top_top(fun(X3,bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2553]) ).
cnf(c_0_3961,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_2554]) ).
cnf(c_0_3962,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_2555]) ).
cnf(c_0_3963,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_2556]) ).
cnf(c_0_3964,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_2557]) ).
cnf(c_0_3965,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_2558]) ).
cnf(c_0_3966,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_2559]) ).
cnf(c_0_3967,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_2560]) ).
cnf(c_0_3968,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_2561]) ).
cnf(c_0_3969,plain,
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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_2562]) ).
cnf(c_0_3970,plain,
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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_2563]) ).
cnf(c_0_3971,plain,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2501]) ).
cnf(c_0_3972,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_2564]) ).
cnf(c_0_3973,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),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_2565]) ).
cnf(c_0_3974,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_3975,plain,
( 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_3976,plain,
( 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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_3977,plain,
( 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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_3978,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_2568]) ).
cnf(c_0_3979,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_2569]) ).
cnf(c_0_3980,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,esk43_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,esk43_4(X1,X2,X3,X4))))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2570]) ).
cnf(c_0_3981,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,esk30_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk30_4(X2,X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2571]) ).
cnf(c_0_3982,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk166_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk167_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_3983,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)),the_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)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2573]) ).
cnf(c_0_3984,plain,
( hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X3),X4),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X5),X4)),X3)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)
| hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2574]) ).
cnf(c_0_3985,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3986,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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_2576]) ).
cnf(c_0_3987,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_2532]) ).
cnf(c_0_3988,plain,
( 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_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2489]) ).
cnf(c_0_3989,plain,
( 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| ~ 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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2490]) ).
cnf(c_0_3990,plain,
( 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2491]) ).
cnf(c_0_3991,plain,
( 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2492]) ).
cnf(c_0_3992,plain,
( 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_3993,plain,
( 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_3994,plain,
( 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| ~ 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),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_3995,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ 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_2577]) ).
cnf(c_0_3996,plain,
( ti(X1,X3) = ti(X1,X5)
| ti(X1,X2) = ti(X1,X4)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_3997,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X4) = ti(X1,X5)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3998,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),X4),X3)),X5)) = ti(fun(X2,bool),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3999,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_4000,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_4001,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(nat,X1,X2,X4))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2583]) ).
cnf(c_0_4002,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X1)),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2584]) ).
cnf(c_0_4003,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_4004,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| 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),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_4005,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk135_3(X1,X2,X3)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_4006,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk170_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk171_4(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4007,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk170_4(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4008,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2586]) ).
cnf(c_0_4009,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk79_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_2587]) ).
cnf(c_0_4010,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk79_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_2587]) ).
cnf(c_0_4011,plain,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),esk111_5(X3,X1,X4,X5,X2)))
| ~ 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),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_2502]) ).
cnf(c_0_4012,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2588]) ).
cnf(c_0_4013,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2589]) ).
cnf(c_0_4014,plain,
( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,X3)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_4015,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2518]) ).
cnf(c_0_4016,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ linord893533164strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2591]) ).
cnf(c_0_4017,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2592]) ).
cnf(c_0_4018,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2593]) ).
cnf(c_0_4019,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2519]) ).
cnf(c_0_4020,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_4021,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_4022,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ ordere1490568538miring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_4023,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ ordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_4024,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X2),X4))
| ~ ordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2596]) ).
cnf(c_0_4025,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2520]) ).
cnf(c_0_4026,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_4027,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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),X4),X2))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2598]) ).
cnf(c_0_4028,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2521]) ).
cnf(c_0_4029,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_4030,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_4031,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2599]) ).
cnf(c_0_4032,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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),X4),X2))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2600]) ).
cnf(c_0_4033,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk166_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,esk167_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4034,plain,
( hBOOL(hAPP(X1,bool,X2,esk166_4(X1,X2,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk167_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4035,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2601]) ).
cnf(c_0_4036,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(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))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2602]) ).
cnf(c_0_4037,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_2603]) ).
cnf(c_0_4038,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_2604]) ).
cnf(c_0_4039,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_2605]) ).
cnf(c_0_4040,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_2606]) ).
cnf(c_0_4041,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_2607]) ).
cnf(c_0_4042,plain,
( 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))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4043,plain,
( 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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4044,plain,
( 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),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4045,plain,
( 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)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4046,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2533]) ).
cnf(c_0_4047,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2534]) ).
cnf(c_0_4048,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_4049,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ 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),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_4050,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ 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),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2609]) ).
cnf(c_0_4051,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2610]) ).
cnf(c_0_4052,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2611]) ).
cnf(c_0_4053,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_2612]) ).
cnf(c_0_4054,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_2613]) ).
cnf(c_0_4055,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2614]) ).
cnf(c_0_4056,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2615]) ).
cnf(c_0_4057,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2616]) ).
cnf(c_0_4058,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(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))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2617]) ).
cnf(c_0_4059,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(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))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2618]) ).
cnf(c_0_4060,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_2511]) ).
cnf(c_0_4061,plain,
( hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk154_1(X1)),X2)) = hAPP(nat,nat,X1,esk154_1(X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,hAPP(nat,nat,suc,esk153_1(X1)))),hAPP(nat,nat,X1,esk153_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2619]) ).
cnf(c_0_4062,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk171_4(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4063,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_4064,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
inference(split_conjunct,[status(thm)],[c_0_2621]) ).
cnf(c_0_4065,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_2622]) ).
cnf(c_0_4066,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_2623]) ).
cnf(c_0_4067,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_4068,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),esk111_5(X3,X1,X4,X5,X2))
| ~ 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),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_2502]) ).
cnf(c_0_4069,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_4070,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_4071,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_4072,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_4073,plain,
( 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_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2489]) ).
cnf(c_0_4074,plain,
( 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_atLeastAtMost(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_eq(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2490]) ).
cnf(c_0_4075,plain,
( 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2491]) ).
cnf(c_0_4076,plain,
( 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2492]) ).
cnf(c_0_4077,plain,
( 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_4078,plain,
( 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_gr676655987ssThan(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))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_4079,plain,
( 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_gr1471790799AtMost(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))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_4080,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)))) ),
inference(split_conjunct,[status(thm)],[c_0_2624]) ).
cnf(c_0_4081,plain,
( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)) = hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)
| ~ hBOOL(hAPP(fun(fun(X3,bool),fun(X2,X2)),bool,hAPP(fun(X3,fun(X2,X2)),fun(fun(fun(X3,bool),fun(X2,X2)),bool),finite_folding_idem(X3,X2),X4),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2625]) ).
cnf(c_0_4082,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
| hAPP(X2,X1,X5,hAPP(X1,X2,X3,esk69_5(X2,X1,X5,X3,X4))) != ti(X1,esk69_5(X2,X1,X5,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2626]) ).
cnf(c_0_4083,plain,
( ti(X1,X5) = ti(X1,esk104_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))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_4084,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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(X1,fun(fun(X1,bool),bool),member(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2576]) ).
cnf(c_0_4085,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_4086,plain,
( hBOOL(hAPP(X1,bool,X4,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_2614]) ).
cnf(c_0_4087,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5)) = ti(fun(X2,bool),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),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_2629]) ).
cnf(c_0_4088,plain,
( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)),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),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2630]) ).
cnf(c_0_4089,plain,
( ti(X2,X4) = hAPP(X1,X2,X3,esk104_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))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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))))) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_4090,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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(split_conjunct,[status(thm)],[c_0_2552]) ).
cnf(c_0_4091,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_2631]) ).
cnf(c_0_4092,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_2632]) ).
cnf(c_0_4093,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_2633]) ).
cnf(c_0_4094,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2634]) ).
cnf(c_0_4095,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2634]) ).
cnf(c_0_4096,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_4097,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_4098,plain,
( ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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(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_2636]) ).
cnf(c_0_4099,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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(X2,X4) != hAPP(X1,X2,X3,X5)
| ti(X1,esk105_5(X1,X2,X4,X3,X5)) != ti(X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_4100,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_2637]) ).
cnf(c_0_4101,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_2638]) ).
cnf(c_0_4102,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_2639]) ).
cnf(c_0_4103,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_2640]) ).
cnf(c_0_4104,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)),top_top(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),top_top(fun(X2,bool))) != top_top(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2641]) ).
cnf(c_0_4105,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_4106,plain,
( hBOOL(hAPP(X1,bool,X2,esk166_4(X1,X2,X4,X5)))
| hBOOL(hAPP(X1,bool,X2,esk167_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4107,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_4108,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_4109,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
inference(split_conjunct,[status(thm)],[c_0_2643]) ).
cnf(c_0_4110,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_2509]) ).
cnf(c_0_4111,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_2644]) ).
cnf(c_0_4112,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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_4113,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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2646]) ).
cnf(c_0_4114,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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2647]) ).
cnf(c_0_4115,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_2648]) ).
cnf(c_0_4116,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_2649]) ).
cnf(c_0_4117,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_2650]) ).
cnf(c_0_4118,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_2651]) ).
cnf(c_0_4119,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_2651]) ).
cnf(c_0_4120,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_2554]) ).
cnf(c_0_4121,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_2555]) ).
cnf(c_0_4122,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_2652]) ).
cnf(c_0_4123,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_2653]) ).
cnf(c_0_4124,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_2558]) ).
cnf(c_0_4125,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_2559]) ).
cnf(c_0_4126,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_2654]) ).
cnf(c_0_4127,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_2655]) ).
cnf(c_0_4128,plain,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk134_5(X2,X1,X3,X5,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2656]) ).
cnf(c_0_4129,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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(X1,fun(fun(X1,bool),bool),member(X1),esk172_3(X1,X3,X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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(split_conjunct,[status(thm)],[c_0_2657]) ).
cnf(c_0_4130,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X3),X4)),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2658]) ).
cnf(c_0_4131,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X4),X5)) = hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X3,X1),fun(X3,X1),hAPP(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),combb(X1,X1,X3),hAPP(X1,fun(X1,X1),times_times(X1),X2)),X4)),X5)
| ~ semiring_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2659]) ).
cnf(c_0_4132,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk136_4(X2,X1,X4,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_4133,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,esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk79_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_2587]) ).
cnf(c_0_4134,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,esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk79_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_2587]) ).
cnf(c_0_4135,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_5(X2,X1,X5,X3,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2626]) ).
cnf(c_0_4136,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_4137,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2662]) ).
cnf(c_0_4138,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2663]) ).
cnf(c_0_4139,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2535]) ).
cnf(c_0_4140,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2536]) ).
cnf(c_0_4141,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2664]) ).
cnf(c_0_4142,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_2665]) ).
cnf(c_0_4143,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_2666]) ).
cnf(c_0_4144,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_2568]) ).
cnf(c_0_4145,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_2667]) ).
cnf(c_0_4146,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_2569]) ).
cnf(c_0_4147,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),esk107_4(X3,X1,X4,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),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(split_conjunct,[status(thm)],[c_0_2479]) ).
cnf(c_0_4148,plain,
hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
inference(split_conjunct,[status(thm)],[c_0_2668]) ).
cnf(c_0_4149,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_2669]) ).
cnf(c_0_4150,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
inference(split_conjunct,[status(thm)],[c_0_2670]) ).
cnf(c_0_4151,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_4152,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2672]) ).
cnf(c_0_4153,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2673]) ).
cnf(c_0_4154,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2674]) ).
cnf(c_0_4155,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(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),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_4156,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(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),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_4157,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),X2),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2676]) ).
cnf(c_0_4158,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2677]) ).
cnf(c_0_4159,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2))
| ~ ordere453448008miring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2678]) ).
cnf(c_0_4160,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4161,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_4162,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_2679]) ).
cnf(c_0_4163,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_2680]) ).
cnf(c_0_4164,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_2681]) ).
cnf(c_0_4165,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_2682]) ).
cnf(c_0_4166,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2683]) ).
cnf(c_0_4167,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2684]) ).
cnf(c_0_4168,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(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),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_4169,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2685]) ).
cnf(c_0_4170,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) = hAPP(X1,X2,X3,esk105_5(X1,X2,X4,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(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_4171,plain,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2636]) ).
cnf(c_0_4172,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(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),X2,hAPP(fun(X4,X2),fun(fun(X4,bool),X2),big_co1399186613setsum(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2686]) ).
cnf(c_0_4173,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))
| ~ 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_2586]) ).
cnf(c_0_4174,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),zero_zero(X1)))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2687]) ).
cnf(c_0_4175,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ 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_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2688]) ).
cnf(c_0_4176,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ 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))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2689]) ).
cnf(c_0_4177,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2690]) ).
cnf(c_0_4178,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2691]) ).
cnf(c_0_4179,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_4180,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2693]) ).
cnf(c_0_4181,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ 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_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_4182,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ 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))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_4183,plain,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(fun(X2,bool),fun(X1,X1),X3,X5)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X6),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2696]) ).
cnf(c_0_4184,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk15_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2430]) ).
cnf(c_0_4185,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk109_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_2524]) ).
cnf(c_0_4186,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk103_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_2525]) ).
cnf(c_0_4187,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4))))
| ~ hBOOL(hAPP(X1,bool,X4,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2614]) ).
cnf(c_0_4188,plain,
( hAPP(fun(X1,bool),fun(X2,X2),X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X3,X4)),hAPP(fun(X1,bool),fun(X2,X2),X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X6),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2697]) ).
cnf(c_0_4189,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X3),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2698]) ).
cnf(c_0_4190,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2535]) ).
cnf(c_0_4191,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2536]) ).
cnf(c_0_4192,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_2699]) ).
cnf(c_0_4193,plain,
( 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),esk117_4(X3,X1,X4,X2)),X2))
| ~ 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),X4),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2359]) ).
cnf(c_0_4194,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_2700]) ).
cnf(c_0_4195,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_2701]) ).
cnf(c_0_4196,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4197,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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(split_conjunct,[status(thm)],[c_0_2703]) ).
cnf(c_0_4198,plain,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X5,X6)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2704]) ).
cnf(c_0_4199,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk168_4(X1,X2,X4,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4200,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk168_4(X1,X2,X5,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4201,plain,
( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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_2647]) ).
cnf(c_0_4202,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4203,plain,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4204,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_4205,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2706]) ).
cnf(c_0_4206,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_4207,plain,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_4208,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_2708]) ).
cnf(c_0_4209,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_2709]) ).
cnf(c_0_4210,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_2710]) ).
cnf(c_0_4211,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4212,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4213,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),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,finite_finite_1(X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_4214,plain,
( 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),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2712]) ).
cnf(c_0_4215,plain,
( 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),times_times(X1),X3),X2)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2713]) ).
cnf(c_0_4216,plain,
( hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6),X7) = hAPP(X3,X2,X5,hAPP(X1,X3,X6,X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2714]) ).
cnf(c_0_4217,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),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_2715]) ).
cnf(c_0_4218,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),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_2716]) ).
cnf(c_0_4219,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_2509]) ).
cnf(c_0_4220,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_2717]) ).
cnf(c_0_4221,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_2718]) ).
cnf(c_0_4222,plain,
( 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))
| ~ 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),X4),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2719]) ).
cnf(c_0_4223,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_2720]) ).
cnf(c_0_4224,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X2)),
inference(split_conjunct,[status(thm)],[c_0_2721]) ).
cnf(c_0_4225,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X3)),
inference(split_conjunct,[status(thm)],[c_0_2722]) ).
cnf(c_0_4226,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(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_2723]) ).
cnf(c_0_4227,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_2724]) ).
cnf(c_0_4228,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_2725]) ).
cnf(c_0_4229,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_4230,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_4231,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_4232,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_4233,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_4234,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_4235,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_2728]) ).
cnf(c_0_4236,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_2729]) ).
cnf(c_0_4237,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),X3)) = ti(fun(X2,bool),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_2730]) ).
cnf(c_0_4238,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk116_4(X1,X3,X2,X4))
| ~ 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(split_conjunct,[status(thm)],[c_0_2731]) ).
cnf(c_0_4239,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,esk136_4(X2,X1,X4,X3)) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_4240,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
inference(split_conjunct,[status(thm)],[c_0_2732]) ).
cnf(c_0_4241,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2733]) ).
cnf(c_0_4242,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2734]) ).
cnf(c_0_4243,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk163_2(X1,X3)),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4244,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk115_2(X1,X3)),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4245,plain,
( 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),X2),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4246,plain,
( 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),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4247,plain,
( 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),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4248,plain,
( 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),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4249,plain,
( 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(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),top_top(fun(X1,bool))),X3),esk106_3(X1,X2,X3))) != ti(X2,esk106_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2738]) ).
cnf(c_0_4250,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X3),zero_zero(X2)),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2739]) ).
cnf(c_0_4251,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),plus_plus(X1)),X3),zero_zero(X1)),X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2740]) ).
cnf(c_0_4252,plain,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4)
| hAPP(X1,X2,X3,esk134_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X5,esk134_5(X2,X1,X3,X5,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2656]) ).
cnf(c_0_4253,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_2631]) ).
cnf(c_0_4254,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_2632]) ).
cnf(c_0_4255,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_2633]) ).
cnf(c_0_4256,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk164_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4257,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk112_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4258,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2743]) ).
cnf(c_0_4259,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4260,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2745]) ).
cnf(c_0_4261,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2746]) ).
cnf(c_0_4262,plain,
hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),hAPP(fun(X1,X5),fun(X1,X2),hAPP(fun(X5,X2),fun(fun(X1,X5),fun(X1,X2)),comp(X5,X2,X1),X6),X7)) = hAPP(fun(X1,X5),fun(X1,X3),hAPP(fun(X5,X3),fun(fun(X1,X5),fun(X1,X3)),comp(X5,X3,X1),hAPP(fun(X5,X2),fun(X5,X3),hAPP(fun(X2,X3),fun(fun(X5,X2),fun(X5,X3)),comp(X2,X3,X5),X4),X6)),X7),
inference(split_conjunct,[status(thm)],[c_0_2747]) ).
cnf(c_0_4263,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_2748]) ).
cnf(c_0_4264,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_2749]) ).
cnf(c_0_4265,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_2749]) ).
cnf(c_0_4266,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_2750]) ).
cnf(c_0_4267,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_2751]) ).
cnf(c_0_4268,plain,
hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),X6) = hAPP(fun(X1,bool),fun(X1,X3),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X1,X3)),restrict(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X5),X6)),X4),
inference(split_conjunct,[status(thm)],[c_0_2752]) ).
cnf(c_0_4269,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,esk57_4(X2,X1,X4,X3)),esk58_4(X2,X1,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_4270,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)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),top_top(fun(X3,bool))) != top_top(fun(X2,bool))
| 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))) != top_top(fun(X3,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2754]) ).
cnf(c_0_4271,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(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),ord_atLeast(X1),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4272,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ 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),ord_greaterThan(X1),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2756]) ).
cnf(c_0_4273,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk18_2(X1,X2)),arrow_301600364e_Prof)) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_4274,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2757]) ).
cnf(c_0_4275,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2758]) ).
cnf(c_0_4276,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),times_times(X1),X2),X3)))
| ~ ordered_ring(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2759]) ).
cnf(c_0_4277,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),times_times(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))
| ~ ordere453448008miring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2760]) ).
cnf(c_0_4278,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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)) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4279,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_2761]) ).
cnf(c_0_4280,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_2762]) ).
cnf(c_0_4281,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_2763]) ).
cnf(c_0_4282,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_2764]) ).
cnf(c_0_4283,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_2765]) ).
cnf(c_0_4284,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ 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)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2766]) ).
cnf(c_0_4285,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),times_times(X1),X2),X3)))
| ~ ordered_ring(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))) ),
inference(split_conjunct,[status(thm)],[c_0_2759]) ).
cnf(c_0_4286,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),times_times(X1),X2),X3)))
| ~ 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)))
| ~ ordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_4287,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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))) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4288,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),esk27_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_4289,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_2769]) ).
cnf(c_0_4290,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_2770]) ).
cnf(c_0_4291,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_2771]) ).
cnf(c_0_4292,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_2772]) ).
cnf(c_0_4293,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_2773]) ).
cnf(c_0_4294,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(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),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2774]) ).
cnf(c_0_4295,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2775]) ).
cnf(c_0_4296,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2776]) ).
cnf(c_0_4297,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),esk100_3(X1,X2,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_2777]) ).
cnf(c_0_4298,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_2778]) ).
cnf(c_0_4299,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_2779]) ).
cnf(c_0_4300,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
inference(split_conjunct,[status(thm)],[c_0_2780]) ).
cnf(c_0_4301,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
inference(split_conjunct,[status(thm)],[c_0_2781]) ).
cnf(c_0_4302,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)),comp(X3,X2,X1),X4),X5)),X6) = 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),X6)),
inference(split_conjunct,[status(thm)],[c_0_2782]) ).
cnf(c_0_4303,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_2783]) ).
cnf(c_0_4304,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk164_2(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4305,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk112_2(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4306,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_2784]) ).
cnf(c_0_4307,plain,
( hBOOL(hAPP(nat,bool,X1,esk163_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4308,plain,
( hBOOL(hAPP(nat,bool,X1,esk115_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4309,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_2785]) ).
cnf(c_0_4310,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_2786]) ).
cnf(c_0_4311,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_2787]) ).
cnf(c_0_4312,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_2788]) ).
cnf(c_0_4313,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ distrib_lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2789]) ).
cnf(c_0_4314,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ distrib_lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2790]) ).
cnf(c_0_4315,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2791]) ).
cnf(c_0_4316,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2792]) ).
cnf(c_0_4317,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_2793]) ).
cnf(c_0_4318,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ 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(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_4319,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_2795]) ).
cnf(c_0_4320,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_2525]) ).
cnf(c_0_4321,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_2796]) ).
cnf(c_0_4322,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk176_4(X1,X3,X2,X4)),X2))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4323,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_2798]) ).
cnf(c_0_4324,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| ~ 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_2799]) ).
cnf(c_0_4325,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_2786]) ).
cnf(c_0_4326,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2800]) ).
cnf(c_0_4327,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2801]) ).
cnf(c_0_4328,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_4329,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_4330,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2802]) ).
cnf(c_0_4331,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2802]) ).
cnf(c_0_4332,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_2803]) ).
cnf(c_0_4333,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_2804]) ).
cnf(c_0_4334,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_2805]) ).
cnf(c_0_4335,plain,
( 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)))
| ~ ring_char_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2806]) ).
cnf(c_0_4336,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2545]) ).
cnf(c_0_4337,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_2807]) ).
cnf(c_0_4338,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_2808]) ).
cnf(c_0_4339,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2774]) ).
cnf(c_0_4340,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2774]) ).
cnf(c_0_4341,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2809]) ).
cnf(c_0_4342,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2809]) ).
cnf(c_0_4343,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_2607]) ).
cnf(c_0_4344,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X4,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2810]) ).
cnf(c_0_4345,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_2811]) ).
cnf(c_0_4346,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_2812]) ).
cnf(c_0_4347,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_2813]) ).
cnf(c_0_4348,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_2814]) ).
cnf(c_0_4349,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_2815]) ).
cnf(c_0_4350,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_2816]) ).
cnf(c_0_4351,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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))
| hAPP(X2,X1,X4,X6) != ti(X1,X5)
| ~ 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_2817]) ).
cnf(c_0_4352,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_2818]) ).
cnf(c_0_4353,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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_4354,plain,
( 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),times_times(nat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_4355,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk178_4(X1,X3,X2,X4)),X2))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4356,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_4357,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_4358,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_2821]) ).
cnf(c_0_4359,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_4360,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_4361,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_2823]) ).
cnf(c_0_4362,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_2824]) ).
cnf(c_0_4363,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_2825]) ).
cnf(c_0_4364,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_2826]) ).
cnf(c_0_4365,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_2827]) ).
cnf(c_0_4366,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_2828]) ).
cnf(c_0_4367,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk162_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4368,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk114_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4369,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_4370,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2830]) ).
cnf(c_0_4371,plain,
( hBOOL(hAPP(X1,bool,X2,X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_4372,plain,
( hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_4373,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_2832]) ).
cnf(c_0_4374,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_2833]) ).
cnf(c_0_4375,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_2834]) ).
cnf(c_0_4376,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_2835]) ).
cnf(c_0_4377,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_2836]) ).
cnf(c_0_4378,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_2837]) ).
cnf(c_0_4379,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk165_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4380,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk113_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4381,plain,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(X2,fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X3,X4)) = hAPP(X2,fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2838]) ).
cnf(c_0_4382,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_4383,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2840]) ).
cnf(c_0_4384,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2841]) ).
cnf(c_0_4385,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2842]) ).
cnf(c_0_4386,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_2843]) ).
cnf(c_0_4387,plain,
( hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X7,X2,hAPP(fun(X7,X8),fun(X7,X2),hAPP(fun(X8,X2),fun(fun(X7,X8),fun(X7,X2)),comp(X8,X2,X7),X9),X10),X11)
| hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)) != hAPP(X8,X2,X9,hAPP(X7,X8,X10,X11)) ),
inference(split_conjunct,[status(thm)],[c_0_2844]) ).
cnf(c_0_4388,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2845]) ).
cnf(c_0_4389,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ distrib_lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2846]) ).
cnf(c_0_4390,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ distrib_lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2847]) ).
cnf(c_0_4391,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2848]) ).
cnf(c_0_4392,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2849]) ).
cnf(c_0_4393,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_2850]) ).
cnf(c_0_4394,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2851]) ).
cnf(c_0_4395,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2852]) ).
cnf(c_0_4396,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2853]) ).
cnf(c_0_4397,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2854]) ).
cnf(c_0_4398,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_2749]) ).
cnf(c_0_4399,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_2855]) ).
cnf(c_0_4400,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_2856]) ).
cnf(c_0_4401,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_2857]) ).
cnf(c_0_4402,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_2858]) ).
cnf(c_0_4403,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_2859]) ).
cnf(c_0_4404,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_2860]) ).
cnf(c_0_4405,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_2821]) ).
cnf(c_0_4406,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_2821]) ).
cnf(c_0_4407,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk15_1(X1)),arrow_301600364e_Prof)) ),
inference(split_conjunct,[status(thm)],[c_0_2430]) ).
cnf(c_0_4408,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk10_1(X1)),arrow_301600364e_Prof)) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_4409,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk11_1(X1)),arrow_301600364e_Prof)) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_4410,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_2571]) ).
cnf(c_0_4411,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_2861]) ).
cnf(c_0_4412,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_2862]) ).
cnf(c_0_4413,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_2863]) ).
cnf(c_0_4414,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_2864]) ).
cnf(c_0_4415,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_2864]) ).
cnf(c_0_4416,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_2865]) ).
cnf(c_0_4417,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_2866]) ).
cnf(c_0_4418,plain,
( 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),ord_atLeast(X1),X2)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2755]) ).
cnf(c_0_4419,plain,
( 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),ord_greaterThan(X1),X2)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2756]) ).
cnf(c_0_4420,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X3)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))
| hAPP(nat,X1,X2,zero_zero(nat)) != zero_zero(X1)
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2867]) ).
cnf(c_0_4421,plain,
( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2))
| hAPP(nat,nat,X1,zero_zero(nat)) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2868]) ).
cnf(c_0_4422,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_4423,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_2870]) ).
cnf(c_0_4424,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,esk57_4(X2,X1,X4,X3)),esk58_4(X2,X1,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2753]) ).
cnf(c_0_4425,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_2784]) ).
cnf(c_0_4426,plain,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = ti(fun(X1,X2),X3)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_4427,plain,
( ti(X1,X4) = ti(X1,X6)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X2) != ti(X1,X5)
| ~ semiri456707255roduct(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4428,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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,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_2738]) ).
cnf(c_0_4429,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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,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_2873]) ).
cnf(c_0_4430,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_4431,plain,
( ti(fun(X1,bool),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk119_2(X1,X2)),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)),esk118_2(X1,X2))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2733]) ).
cnf(c_0_4432,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_2807]) ).
cnf(c_0_4433,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_2808]) ).
cnf(c_0_4434,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2874]) ).
cnf(c_0_4435,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2875]) ).
cnf(c_0_4436,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2876]) ).
cnf(c_0_4437,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2877]) ).
cnf(c_0_4438,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_2878]) ).
cnf(c_0_4439,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_2879]) ).
cnf(c_0_4440,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_2880]) ).
cnf(c_0_4441,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_2881]) ).
cnf(c_0_4442,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_2748]) ).
cnf(c_0_4443,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_2748]) ).
cnf(c_0_4444,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_2882]) ).
cnf(c_0_4445,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_2883]) ).
cnf(c_0_4446,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_2884]) ).
cnf(c_0_4447,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_2885]) ).
cnf(c_0_4448,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_2886]) ).
cnf(c_0_4449,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_2887]) ).
cnf(c_0_4450,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_2888]) ).
cnf(c_0_4451,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_2889]) ).
cnf(c_0_4452,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_2821]) ).
cnf(c_0_4453,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk95_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_2890]) ).
cnf(c_0_4454,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_2891]) ).
cnf(c_0_4455,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_2892]) ).
cnf(c_0_4456,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_2893]) ).
cnf(c_0_4457,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_2894]) ).
cnf(c_0_4458,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_2895]) ).
cnf(c_0_4459,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_2896]) ).
cnf(c_0_4460,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_2897]) ).
cnf(c_0_4461,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_4462,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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(split_conjunct,[status(thm)],[c_0_2898]) ).
cnf(c_0_4463,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_2864]) ).
cnf(c_0_4464,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_2899]) ).
cnf(c_0_4465,plain,
( ti(fun(X1,bool),X4) = ti(fun(X1,bool),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(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_2900]) ).
cnf(c_0_4466,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_2832]) ).
cnf(c_0_4467,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_2833]) ).
cnf(c_0_4468,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_2901]) ).
cnf(c_0_4469,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,esk176_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4470,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,esk146_3(X1,X4,X2))),hAPP(X1,nat,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2902]) ).
cnf(c_0_4471,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_2880]) ).
cnf(c_0_4472,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_2870]) ).
cnf(c_0_4473,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,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4) = 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_2903]) ).
cnf(c_0_4474,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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,X3,esk150_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2904]) ).
cnf(c_0_4475,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| one_one(nat) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2657]) ).
cnf(c_0_4476,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2))),
inference(split_conjunct,[status(thm)],[c_0_2905]) ).
cnf(c_0_4477,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),
inference(split_conjunct,[status(thm)],[c_0_2906]) ).
cnf(c_0_4478,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2907]) ).
cnf(c_0_4479,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(X2,X1,X4,hAPP(X1,X2,X3,esk110_4(X1,X2,X4,X3))) != ti(X1,esk110_4(X1,X2,X4,X3))
| 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_2908]) ).
cnf(c_0_4480,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_2784]) ).
cnf(c_0_4481,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_2909]) ).
cnf(c_0_4482,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_2910]) ).
cnf(c_0_4483,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_2911]) ).
cnf(c_0_4484,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_2912]) ).
cnf(c_0_4485,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_2913]) ).
cnf(c_0_4486,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_2914]) ).
cnf(c_0_4487,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_2915]) ).
cnf(c_0_4488,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_2916]) ).
cnf(c_0_4489,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_2917]) ).
cnf(c_0_4490,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_2918]) ).
cnf(c_0_4491,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_2919]) ).
cnf(c_0_4492,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_2920]) ).
cnf(c_0_4493,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ti(X1,X4) != ti(X1,esk176_4(X1,X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4494,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
inference(split_conjunct,[status(thm)],[c_0_2921]) ).
cnf(c_0_4495,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_2922]) ).
cnf(c_0_4496,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_2923]) ).
cnf(c_0_4497,plain,
arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
inference(split_conjunct,[status(thm)],[c_0_2924]) ).
cnf(c_0_4498,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_2925]) ).
cnf(c_0_4499,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2926]) ).
cnf(c_0_4500,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2927]) ).
cnf(c_0_4501,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4502,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2929]) ).
cnf(c_0_4503,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2930]) ).
cnf(c_0_4504,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4505,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2932]) ).
cnf(c_0_4506,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ ab_semigroup_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2933]) ).
cnf(c_0_4507,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2934]) ).
cnf(c_0_4508,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4509,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_2936]) ).
cnf(c_0_4510,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_2937]) ).
cnf(c_0_4511,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_2938]) ).
cnf(c_0_4512,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_2939]) ).
cnf(c_0_4513,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_2940]) ).
cnf(c_0_4514,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_2821]) ).
cnf(c_0_4515,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_2941]) ).
cnf(c_0_4516,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_2941]) ).
cnf(c_0_4517,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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| hBOOL(hAPP(X1,bool,X2,esk150_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2904]) ).
cnf(c_0_4518,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| hAPP(X1,nat,X3,esk178_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4519,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4520,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_2943]) ).
cnf(c_0_4521,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4522,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2945]) ).
cnf(c_0_4523,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_2946]) ).
cnf(c_0_4524,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2583]) ).
cnf(c_0_4525,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4526,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4527,plain,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ti(X1,esk175_3(X1,X3,X2)) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4528,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_2941]) ).
cnf(c_0_4529,plain,
( 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,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2948]) ).
cnf(c_0_4530,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_2949]) ).
cnf(c_0_4531,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_2892]) ).
cnf(c_0_4532,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_2893]) ).
cnf(c_0_4533,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2950]) ).
cnf(c_0_4534,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4535,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2952]) ).
cnf(c_0_4536,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2952]) ).
cnf(c_0_4537,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ti(X1,X4) != ti(X1,esk178_4(X1,X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4538,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_2953]) ).
cnf(c_0_4539,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_2954]) ).
cnf(c_0_4540,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),esk77_4(X2,X1,X3,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4541,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),esk78_4(X2,X1,X3,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4542,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_2788]) ).
cnf(c_0_4543,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),esk32_4(X1,X2,X3,X4)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2788]) ).
cnf(c_0_4544,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_2956]) ).
cnf(c_0_4545,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_2957]) ).
cnf(c_0_4546,plain,
( X2 = hAPP(nat,nat,suc,esk95_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_2890]) ).
cnf(c_0_4547,plain,
( X1 = hAPP(nat,nat,suc,esk93_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_2958]) ).
cnf(c_0_4548,plain,
( hBOOL(hAPP(nat,bool,X3,X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk87_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_2959]) ).
cnf(c_0_4549,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_2960]) ).
cnf(c_0_4550,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_4551,plain,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,esk169_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4552,plain,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,esk169_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_4553,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_2961]) ).
cnf(c_0_4554,plain,
( 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))))
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2900]) ).
cnf(c_0_4555,plain,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ti(X1,esk177_3(X1,X3,X2)) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4556,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_2962]) ).
cnf(c_0_4557,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),esk60_3(X1,X3,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4558,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_2798]) ).
cnf(c_0_4559,plain,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6))
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9) ),
inference(split_conjunct,[status(thm)],[c_0_2964]) ).
cnf(c_0_4560,plain,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6))
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9) ),
inference(split_conjunct,[status(thm)],[c_0_2965]) ).
cnf(c_0_4561,plain,
( hBOOL(hAPP(nat,bool,X3,X1))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,esk87_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_2959]) ).
cnf(c_0_4562,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_2870]) ).
cnf(c_0_4563,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_2966]) ).
cnf(c_0_4564,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_2821]) ).
cnf(c_0_4565,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_2821]) ).
cnf(c_0_4566,plain,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ 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),X4),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4567,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_2968]) ).
cnf(c_0_4568,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_2969]) ).
cnf(c_0_4569,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_2970]) ).
cnf(c_0_4570,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_2971]) ).
cnf(c_0_4571,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_2972]) ).
cnf(c_0_4572,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_2973]) ).
cnf(c_0_4573,plain,
( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4574,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_2975]) ).
cnf(c_0_4575,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_2976]) ).
cnf(c_0_4576,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4577,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2945]) ).
cnf(c_0_4578,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_2977]) ).
cnf(c_0_4579,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_2975]) ).
cnf(c_0_4580,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_2976]) ).
cnf(c_0_4581,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_2962]) ).
cnf(c_0_4582,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X4)),X5),X6) = ti(X2,X4),
inference(split_conjunct,[status(thm)],[c_0_2978]) ).
cnf(c_0_4583,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2979]) ).
cnf(c_0_4584,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk71_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_2980]) ).
cnf(c_0_4585,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
inference(split_conjunct,[status(thm)],[c_0_2981]) ).
cnf(c_0_4586,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
inference(split_conjunct,[status(thm)],[c_0_2982]) ).
cnf(c_0_4587,plain,
( hBOOL(hAPP(X1,bool,X2,esk168_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4588,plain,
( hBOOL(hAPP(X1,bool,X2,esk168_4(X1,X2,X5,X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_4589,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),esk80_2(X2,X1)),one_one(nat))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2983]) ).
cnf(c_0_4590,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_2984]) ).
cnf(c_0_4591,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk175_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4592,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_2863]) ).
cnf(c_0_4593,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_2985]) ).
cnf(c_0_4594,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_2986]) ).
cnf(c_0_4595,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_2987]) ).
cnf(c_0_4596,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_2988]) ).
cnf(c_0_4597,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_2989]) ).
cnf(c_0_4598,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_2990]) ).
cnf(c_0_4599,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_2991]) ).
cnf(c_0_4600,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_2960]) ).
cnf(c_0_4601,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_2992]) ).
cnf(c_0_4602,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_2993]) ).
cnf(c_0_4603,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_2994]) ).
cnf(c_0_4604,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_2995]) ).
cnf(c_0_4605,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_2996]) ).
cnf(c_0_4606,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_2997]) ).
cnf(c_0_4607,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_2998]) ).
cnf(c_0_4608,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_2999]) ).
cnf(c_0_4609,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_2939]) ).
cnf(c_0_4610,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_3000]) ).
cnf(c_0_4611,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_2972]) ).
cnf(c_0_4612,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_2956]) ).
cnf(c_0_4613,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_3001]) ).
cnf(c_0_4614,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_2968]) ).
cnf(c_0_4615,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_3002]) ).
cnf(c_0_4616,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3003]) ).
cnf(c_0_4617,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3004]) ).
cnf(c_0_4618,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3005]) ).
cnf(c_0_4619,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3006]) ).
cnf(c_0_4620,plain,
( X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3007]) ).
cnf(c_0_4621,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_3008]) ).
cnf(c_0_4622,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_3009]) ).
cnf(c_0_4623,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3010]) ).
cnf(c_0_4624,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),times_times(X1),X2),X2)))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4625,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_3012]) ).
cnf(c_0_4626,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3013]) ).
cnf(c_0_4627,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3014]) ).
cnf(c_0_4628,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3015]) ).
cnf(c_0_4629,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3016]) ).
cnf(c_0_4630,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3017]) ).
cnf(c_0_4631,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3018]) ).
cnf(c_0_4632,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3019]) ).
cnf(c_0_4633,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_3020]) ).
cnf(c_0_4634,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,esk87_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2959]) ).
cnf(c_0_4635,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3021]) ).
cnf(c_0_4636,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3022]) ).
cnf(c_0_4637,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3023]) ).
cnf(c_0_4638,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3024]) ).
cnf(c_0_4639,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_3025]) ).
cnf(c_0_4640,plain,
( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),esk122_2(X1,X2)),X2) = 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)),esk123_2(X1,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3026]) ).
cnf(c_0_4641,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_3027]) ).
cnf(c_0_4642,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_3028]) ).
cnf(c_0_4643,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_3029]) ).
cnf(c_0_4644,plain,
( 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(X1,X2,X3,hAPP(X2,X1,X4,esk128_4(X1,X2,X3,X4))) != ti(X2,esk128_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_3030]) ).
cnf(c_0_4645,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk177_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4646,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_3031]) ).
cnf(c_0_4647,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_3032]) ).
cnf(c_0_4648,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1))),
inference(split_conjunct,[status(thm)],[c_0_3033]) ).
cnf(c_0_4649,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_3034]) ).
cnf(c_0_4650,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_3035]) ).
cnf(c_0_4651,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_2821]) ).
cnf(c_0_4652,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_3036]) ).
cnf(c_0_4653,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk18_2(X1,X2)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk18_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_4654,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),esk82_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3037]) ).
cnf(c_0_4655,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),esk80_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2983]) ).
cnf(c_0_4656,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_3038]) ).
cnf(c_0_4657,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_3039]) ).
cnf(c_0_4658,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),esk70_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3040]) ).
cnf(c_0_4659,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),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(split_conjunct,[status(thm)],[c_0_3041]) ).
cnf(c_0_4660,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),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)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3042]) ).
cnf(c_0_4661,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),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)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3043]) ).
cnf(c_0_4662,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3044]) ).
cnf(c_0_4663,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3045]) ).
cnf(c_0_4664,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_3046]) ).
cnf(c_0_4665,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_3047]) ).
cnf(c_0_4666,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),esk60_3(X1,X3,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4667,plain,
( X2 = hAPP(nat,nat,suc,X1)
| 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),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3048]) ).
cnf(c_0_4668,plain,
( X1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk88_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3049]) ).
cnf(c_0_4669,plain,
( X1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk86_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3046]) ).
cnf(c_0_4670,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_2962]) ).
cnf(c_0_4671,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_3050]) ).
cnf(c_0_4672,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_2986]) ).
cnf(c_0_4673,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_3051]) ).
cnf(c_0_4674,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_3052]) ).
cnf(c_0_4675,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_3053]) ).
cnf(c_0_4676,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_3054]) ).
cnf(c_0_4677,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_3055]) ).
cnf(c_0_4678,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_3056]) ).
cnf(c_0_4679,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_3057]) ).
cnf(c_0_4680,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_3058]) ).
cnf(c_0_4681,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_2984]) ).
cnf(c_0_4682,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_3059]) ).
cnf(c_0_4683,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_3060]) ).
cnf(c_0_4684,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_3061]) ).
cnf(c_0_4685,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_3062]) ).
cnf(c_0_4686,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_3063]) ).
cnf(c_0_4687,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_3064]) ).
cnf(c_0_4688,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_3065]) ).
cnf(c_0_4689,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_3066]) ).
cnf(c_0_4690,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_3067]) ).
cnf(c_0_4691,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_3068]) ).
cnf(c_0_4692,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_3069]) ).
cnf(c_0_4693,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk174_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4694,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_3070]) ).
cnf(c_0_4695,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_3062]) ).
cnf(c_0_4696,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_2960]) ).
cnf(c_0_4697,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_3063]) ).
cnf(c_0_4698,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_2969]) ).
cnf(c_0_4699,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_2940]) ).
cnf(c_0_4700,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3071]) ).
cnf(c_0_4701,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_3072]) ).
cnf(c_0_4702,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_3073]) ).
cnf(c_0_4703,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_3074]) ).
cnf(c_0_4704,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_3075]) ).
cnf(c_0_4705,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk83_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3076]) ).
cnf(c_0_4706,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3007]) ).
cnf(c_0_4707,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_3077]) ).
cnf(c_0_4708,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_3078]) ).
cnf(c_0_4709,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_3079]) ).
cnf(c_0_4710,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_3080]) ).
cnf(c_0_4711,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_3081]) ).
cnf(c_0_4712,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_3082]) ).
cnf(c_0_4713,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_3083]) ).
cnf(c_0_4714,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_3079]) ).
cnf(c_0_4715,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_3080]) ).
cnf(c_0_4716,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_3084]) ).
cnf(c_0_4717,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) != ti(fun(X1,bool),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3045]) ).
cnf(c_0_4718,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk27_2(X1,X2)),arrow_1568854078le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_4719,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_3085]) ).
cnf(c_0_4720,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_3065]) ).
cnf(c_0_4721,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk66_0),arrow_1568854078le_Lin)),
inference(split_conjunct,[status(thm)],[c_0_3086]) ).
cnf(c_0_4722,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk20_0),arrow_1568854078le_Lin)),
inference(split_conjunct,[status(thm)],[c_0_2778]) ).
cnf(c_0_4723,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk19_0),arrow_1568854078le_Lin)),
inference(split_conjunct,[status(thm)],[c_0_2779]) ).
cnf(c_0_4724,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
inference(split_conjunct,[status(thm)],[c_0_3087]) ).
cnf(c_0_4725,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
inference(split_conjunct,[status(thm)],[c_0_3088]) ).
cnf(c_0_4726,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,esk165_2(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4727,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,esk113_2(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4728,plain,
( hBOOL(hAPP(nat,bool,X1,esk162_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4729,plain,
( hBOOL(hAPP(nat,bool,X1,esk114_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4730,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_3050]) ).
cnf(c_0_4731,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk99_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3089]) ).
cnf(c_0_4732,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_2878]) ).
cnf(c_0_4733,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_2878]) ).
cnf(c_0_4734,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),esk135_3(X1,X2,X3)),one_one(X1)))
| ~ linord1117847801e_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_4735,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_3025]) ).
cnf(c_0_4736,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_3090]) ).
cnf(c_0_4737,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_3091]) ).
cnf(c_0_4738,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_4739,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_3093]) ).
cnf(c_0_4740,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_3094]) ).
cnf(c_0_4741,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
| ti(X1,esk77_4(X2,X1,X3,X4)) != ti(X1,esk78_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4742,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,esk32_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2788]) ).
cnf(c_0_4743,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_3095]) ).
cnf(c_0_4744,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4745,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,esk77_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,esk78_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4746,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,esk32_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2788]) ).
cnf(c_0_4747,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)),esk135_3(X1,X2,X3)))
| ~ linord1117847801e_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_4748,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)),esk100_3(X1,X2,X3)))
| ~ linordered_field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2777]) ).
cnf(c_0_4749,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_2976]) ).
cnf(c_0_4750,plain,
( hAPP(X1,nat,X3,esk175_3(X1,X3,X2)) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4751,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_3096]) ).
cnf(c_0_4752,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3097]) ).
cnf(c_0_4753,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3098]) ).
cnf(c_0_4754,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4755,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3100]) ).
cnf(c_0_4756,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3101]) ).
cnf(c_0_4757,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4758,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk83_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_3076]) ).
cnf(c_0_4759,plain,
( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk56_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_3103]) ).
cnf(c_0_4760,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_3061]) ).
cnf(c_0_4761,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_3104]) ).
cnf(c_0_4762,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_3105]) ).
cnf(c_0_4763,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_2994]) ).
cnf(c_0_4764,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_3106]) ).
cnf(c_0_4765,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_3053]) ).
cnf(c_0_4766,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_3107]) ).
cnf(c_0_4767,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_3108]) ).
cnf(c_0_4768,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3109]) ).
cnf(c_0_4769,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3110]) ).
cnf(c_0_4770,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4771,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3112]) ).
cnf(c_0_4772,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3113]) ).
cnf(c_0_4773,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3114]) ).
cnf(c_0_4774,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3115]) ).
cnf(c_0_4775,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(X1,bool,X3,esk151_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3116]) ).
cnf(c_0_4776,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_3117]) ).
cnf(c_0_4777,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_3118]) ).
cnf(c_0_4778,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_3119]) ).
cnf(c_0_4779,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_2992]) ).
cnf(c_0_4780,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_2993]) ).
cnf(c_0_4781,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_3120]) ).
cnf(c_0_4782,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_3121]) ).
cnf(c_0_4783,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(X2,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3122]) ).
cnf(c_0_4784,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk74_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2979]) ).
cnf(c_0_4785,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),esk72_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2980]) ).
cnf(c_0_4786,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_3123]) ).
cnf(c_0_4787,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_3124]) ).
cnf(c_0_4788,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_3125]) ).
cnf(c_0_4789,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_3126]) ).
cnf(c_0_4790,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_3127]) ).
cnf(c_0_4791,plain,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X4,X2,X7,X6)
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != ti(fun(X4,X2),X7) ),
inference(split_conjunct,[status(thm)],[c_0_3128]) ).
cnf(c_0_4792,plain,
( top_top(fun(X1,bool)) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk149_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3129]) ).
cnf(c_0_4793,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_3130]) ).
cnf(c_0_4794,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_3130]) ).
cnf(c_0_4795,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_3131]) ).
cnf(c_0_4796,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_3131]) ).
cnf(c_0_4797,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),esk81_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3132]) ).
cnf(c_0_4798,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_3133]) ).
cnf(c_0_4799,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),hAPP(nat,nat,suc,X4)) = hAPP(nat,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_3134]) ).
cnf(c_0_4800,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_3135]) ).
cnf(c_0_4801,plain,
hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X1)),hAPP(nat,nat,suc,zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_3136]) ).
cnf(c_0_4802,plain,
( X2 = hAPP(nat,nat,suc,X1)
| X2 = hAPP(nat,nat,suc,esk94_2(X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3048]) ).
cnf(c_0_4803,plain,
hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X1)),hAPP(nat,nat,suc,zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_3137]) ).
cnf(c_0_4804,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),esk122_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3026]) ).
cnf(c_0_4805,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk82_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3037]) ).
cnf(c_0_4806,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk80_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2983]) ).
cnf(c_0_4807,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_2956]) ).
cnf(c_0_4808,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_3138]) ).
cnf(c_0_4809,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3097]) ).
cnf(c_0_4810,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4811,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_3139]) ).
cnf(c_0_4812,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk29_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
inference(split_conjunct,[status(thm)],[c_0_2347]) ).
cnf(c_0_4813,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
inference(split_conjunct,[status(thm)],[c_0_2348]) ).
cnf(c_0_4814,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
inference(split_conjunct,[status(thm)],[c_0_3140]) ).
cnf(c_0_4815,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(X1,bool,X2,esk151_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_3116]) ).
cnf(c_0_4816,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_3103]) ).
cnf(c_0_4817,plain,
( hAPP(X1,nat,X3,esk177_3(X1,X3,X2)) = one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4818,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_1(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3141]) ).
cnf(c_0_4819,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2),
inference(split_conjunct,[status(thm)],[c_0_3142]) ).
cnf(c_0_4820,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4821,plain,
( X1 = hAPP(nat,nat,suc,esk89_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_3144]) ).
cnf(c_0_4822,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_3145]) ).
cnf(c_0_4823,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk129_4(X3,X1,X4,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))) != top_top(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_4824,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk127_4(X3,X1,X2,X4))
| 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))) != top_top(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_3147]) ).
cnf(c_0_4825,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk126_4(X3,X1,X2,X4))
| 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))) != top_top(fun(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_3148]) ).
cnf(c_0_4826,plain,
hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3149]) ).
cnf(c_0_4827,plain,
hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3150]) ).
cnf(c_0_4828,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_3151]) ).
cnf(c_0_4829,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_3096]) ).
cnf(c_0_4830,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_3152]) ).
cnf(c_0_4831,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_3153]) ).
cnf(c_0_4832,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_3154]) ).
cnf(c_0_4833,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_3155]) ).
cnf(c_0_4834,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_3156]) ).
cnf(c_0_4835,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_3157]) ).
cnf(c_0_4836,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_3158]) ).
cnf(c_0_4837,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_3159]) ).
cnf(c_0_4838,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_3160]) ).
cnf(c_0_4839,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_3161]) ).
cnf(c_0_4840,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_3063]) ).
cnf(c_0_4841,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_3105]) ).
cnf(c_0_4842,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_3105]) ).
cnf(c_0_4843,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_2994]) ).
cnf(c_0_4844,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_3162]) ).
cnf(c_0_4845,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_3163]) ).
cnf(c_0_4846,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_3164]) ).
cnf(c_0_4847,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_3165]) ).
cnf(c_0_4848,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_3084]) ).
cnf(c_0_4849,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_3166]) ).
cnf(c_0_4850,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_3167]) ).
cnf(c_0_4851,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_2962]) ).
cnf(c_0_4852,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_2968]) ).
cnf(c_0_4853,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_3168]) ).
cnf(c_0_4854,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3169]) ).
cnf(c_0_4855,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_3139]) ).
cnf(c_0_4856,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_3170]) ).
cnf(c_0_4857,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_3171]) ).
cnf(c_0_4858,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_3172]) ).
cnf(c_0_4859,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_3173]) ).
cnf(c_0_4860,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_3174]) ).
cnf(c_0_4861,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_3175]) ).
cnf(c_0_4862,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4863,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3176]) ).
cnf(c_0_4864,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3177]) ).
cnf(c_0_4865,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3126]) ).
cnf(c_0_4866,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3126]) ).
cnf(c_0_4867,plain,
( X1 = X2
| X3 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4868,plain,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4869,plain,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4870,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3181]) ).
cnf(c_0_4871,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3182]) ).
cnf(c_0_4872,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_3183]) ).
cnf(c_0_4873,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_3184]) ).
cnf(c_0_4874,plain,
hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X2),
inference(split_conjunct,[status(thm)],[c_0_3185]) ).
cnf(c_0_4875,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3186]) ).
cnf(c_0_4876,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = ti(X1,X2)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3187]) ).
cnf(c_0_4877,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = ti(X1,X2)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3188]) ).
cnf(c_0_4878,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3189]) ).
cnf(c_0_4879,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3190]) ).
cnf(c_0_4880,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,esk174_3(X1,X3,X2)) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4881,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(X2,X1)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3122]) ).
cnf(c_0_4882,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_2979]) ).
cnf(c_0_4883,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),esk72_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2980]) ).
cnf(c_0_4884,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,esk21_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk21_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_3191]) ).
cnf(c_0_4885,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4886,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2),
inference(split_conjunct,[status(thm)],[c_0_3193]) ).
cnf(c_0_4887,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_3194]) ).
cnf(c_0_4888,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_3124]) ).
cnf(c_0_4889,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_3124]) ).
cnf(c_0_4890,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3195]) ).
cnf(c_0_4891,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2),
inference(split_conjunct,[status(thm)],[c_0_3196]) ).
cnf(c_0_4892,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),zero_zero(X2))),X3) = zero_zero(X2)
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3197]) ).
cnf(c_0_4893,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_2909]) ).
cnf(c_0_4894,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_2909]) ).
cnf(c_0_4895,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_3198]) ).
cnf(c_0_4896,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_3199]) ).
cnf(c_0_4897,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_3200]) ).
cnf(c_0_4898,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_3200]) ).
cnf(c_0_4899,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_2975]) ).
cnf(c_0_4900,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_3201]) ).
cnf(c_0_4901,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3202]) ).
cnf(c_0_4902,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_3203]) ).
cnf(c_0_4903,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_3204]) ).
cnf(c_0_4904,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_3205]) ).
cnf(c_0_4905,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_3206]) ).
cnf(c_0_4906,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_3207]) ).
cnf(c_0_4907,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,esk98_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_3141]) ).
cnf(c_0_4908,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_3208]) ).
cnf(c_0_4909,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_3130]) ).
cnf(c_0_4910,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_3209]) ).
cnf(c_0_4911,plain,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3149]) ).
cnf(c_0_4912,plain,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3210]) ).
cnf(c_0_4913,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_3145]) ).
cnf(c_0_4914,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk148_1(X1)),top_top(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3211]) ).
cnf(c_0_4915,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_3212]) ).
cnf(c_0_4916,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_3213]) ).
cnf(c_0_4917,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_3214]) ).
cnf(c_0_4918,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_3215]) ).
cnf(c_0_4919,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_3216]) ).
cnf(c_0_4920,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_3217]) ).
cnf(c_0_4921,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_3205]) ).
cnf(c_0_4922,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_3205]) ).
cnf(c_0_4923,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_3206]) ).
cnf(c_0_4924,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_3206]) ).
cnf(c_0_4925,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3218]) ).
cnf(c_0_4926,plain,
( X2 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3218]) ).
cnf(c_0_4927,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_3219]) ).
cnf(c_0_4928,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,esk99_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[c_0_3089]) ).
cnf(c_0_4929,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,esk82_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3037]) ).
cnf(c_0_4930,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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(split_conjunct,[status(thm)],[c_0_3218]) ).
cnf(c_0_4931,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_3219]) ).
cnf(c_0_4932,plain,
( 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))
| ti(X2,esk130_3(X1,X2,X3)) != hAPP(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_4933,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_3156]) ).
cnf(c_0_4934,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_3157]) ).
cnf(c_0_4935,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_3155]) ).
cnf(c_0_4936,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_3062]) ).
cnf(c_0_4937,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_2985]) ).
cnf(c_0_4938,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_2985]) ).
cnf(c_0_4939,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_3220]) ).
cnf(c_0_4940,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_3221]) ).
cnf(c_0_4941,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_3222]) ).
cnf(c_0_4942,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_3161]) ).
cnf(c_0_4943,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_3205]) ).
cnf(c_0_4944,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_3206]) ).
cnf(c_0_4945,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3223]) ).
cnf(c_0_4946,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3224]) ).
cnf(c_0_4947,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_4948,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3226]) ).
cnf(c_0_4949,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3227]) ).
cnf(c_0_4950,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4951,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3229]) ).
cnf(c_0_4952,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_3230]) ).
cnf(c_0_4953,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_3231]) ).
cnf(c_0_4954,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_3232]) ).
cnf(c_0_4955,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_3233]) ).
cnf(c_0_4956,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_3234]) ).
cnf(c_0_4957,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_3235]) ).
cnf(c_0_4958,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_3170]) ).
cnf(c_0_4959,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_3236]) ).
cnf(c_0_4960,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_3237]) ).
cnf(c_0_4961,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_3171]) ).
cnf(c_0_4962,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3238]) ).
cnf(c_0_4963,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3239]) ).
cnf(c_0_4964,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2740]) ).
cnf(c_0_4965,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4966,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4967,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4968,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_3082]) ).
cnf(c_0_4969,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_3079]) ).
cnf(c_0_4970,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_3240]) ).
cnf(c_0_4971,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4972,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4973,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4974,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_3183]) ).
cnf(c_0_4975,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_3184]) ).
cnf(c_0_4976,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_3241]) ).
cnf(c_0_4977,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_3242]) ).
cnf(c_0_4978,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_3243]) ).
cnf(c_0_4979,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3244]) ).
cnf(c_0_4980,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3245]) ).
cnf(c_0_4981,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3246]) ).
cnf(c_0_4982,plain,
( hBOOL(hAPP(X1,bool,X2,esk146_3(X1,X4,X2)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2902]) ).
cnf(c_0_4983,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_3205]) ).
cnf(c_0_4984,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_3205]) ).
cnf(c_0_4985,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_3206]) ).
cnf(c_0_4986,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_3206]) ).
cnf(c_0_4987,plain,
hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
inference(split_conjunct,[status(thm)],[c_0_3247]) ).
cnf(c_0_4988,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
inference(split_conjunct,[status(thm)],[c_0_3248]) ).
cnf(c_0_4989,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
inference(split_conjunct,[status(thm)],[c_0_3249]) ).
cnf(c_0_4990,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3250]) ).
cnf(c_0_4991,plain,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3251]) ).
cnf(c_0_4992,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3252]) ).
cnf(c_0_4993,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_3253]) ).
cnf(c_0_4994,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_3254]) ).
cnf(c_0_4995,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X2) = top_top(fun(X1,bool)),
inference(split_conjunct,[status(thm)],[c_0_3255]) ).
cnf(c_0_4996,plain,
( ti(X1,X2) = top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4997,plain,
( ti(X1,X3) = top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_4998,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_3257]) ).
cnf(c_0_4999,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_3258]) ).
cnf(c_0_5000,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),top_top(fun(X1,bool))) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_5001,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
inference(split_conjunct,[status(thm)],[c_0_3260]) ).
cnf(c_0_5002,plain,
( X1 = zero_zero(nat)
| X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_5003,plain,
( X1 = zero_zero(nat)
| X2 = one_one(nat)
| X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_5004,plain,
( X1 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_5005,plain,
( X2 = one_one(nat)
| one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_5006,plain,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_5007,plain,
( X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_5008,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_3265]) ).
cnf(c_0_5009,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_3265]) ).
cnf(c_0_5010,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_3266]) ).
cnf(c_0_5011,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_3267]) ).
cnf(c_0_5012,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_3268]) ).
cnf(c_0_5013,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_3269]) ).
cnf(c_0_5014,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_3132]) ).
cnf(c_0_5015,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3270]) ).
cnf(c_0_5016,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_3271]) ).
cnf(c_0_5017,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_3272]) ).
cnf(c_0_5018,plain,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X1),
inference(split_conjunct,[status(thm)],[c_0_3273]) ).
cnf(c_0_5019,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_3274]) ).
cnf(c_0_5020,plain,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3275]) ).
cnf(c_0_5021,plain,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
inference(split_conjunct,[status(thm)],[c_0_3276]) ).
cnf(c_0_5022,plain,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
inference(split_conjunct,[status(thm)],[c_0_3277]) ).
cnf(c_0_5023,plain,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
inference(split_conjunct,[status(thm)],[c_0_3278]) ).
cnf(c_0_5024,plain,
ti(fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)))),compose(X1,X2,X3)) = compose(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_3279]) ).
cnf(c_0_5025,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_3280]) ).
cnf(c_0_5026,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3281]) ).
cnf(c_0_5027,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_3282]) ).
cnf(c_0_5028,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
| ~ bounded_lattice_top(X1)
| ti(X1,X3) != top_top(X1)
| ti(X1,X2) != top_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3256]) ).
cnf(c_0_5029,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_3283]) ).
cnf(c_0_5030,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_3253]) ).
cnf(c_0_5031,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3250]) ).
cnf(c_0_5032,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3250]) ).
cnf(c_0_5033,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_3257]) ).
cnf(c_0_5034,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_3258]) ).
cnf(c_0_5035,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X2) = ti(X1,X2)
| ~ bounded_lattice_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3284]) ).
cnf(c_0_5036,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3285]) ).
cnf(c_0_5037,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3286]) ).
cnf(c_0_5038,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3287]) ).
cnf(c_0_5039,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_3288]) ).
cnf(c_0_5040,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_3289]) ).
cnf(c_0_5041,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_3290]) ).
cnf(c_0_5042,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),top_top(X1)) = ti(X1,X2)
| ~ bounded_lattice_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_5043,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3292]) ).
cnf(c_0_5044,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3293]) ).
cnf(c_0_5045,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_5046,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_3295]) ).
cnf(c_0_5047,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_3296]) ).
cnf(c_0_5048,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_3297]) ).
cnf(c_0_5049,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_2709]) ).
cnf(c_0_5050,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_3298]) ).
cnf(c_0_5051,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X2) = top_top(X1)
| ~ bounded_lattice_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3299]) ).
cnf(c_0_5052,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ mult_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3300]) ).
cnf(c_0_5053,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3301]) ).
cnf(c_0_5054,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3302]) ).
cnf(c_0_5055,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3303]) ).
cnf(c_0_5056,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3304]) ).
cnf(c_0_5057,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3305]) ).
cnf(c_0_5058,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3306]) ).
cnf(c_0_5059,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3307]) ).
cnf(c_0_5060,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3308]) ).
cnf(c_0_5061,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3309]) ).
cnf(c_0_5062,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),top_top(X1)) = top_top(X1)
| ~ bounded_lattice_top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3310]) ).
cnf(c_0_5063,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ mult_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3311]) ).
cnf(c_0_5064,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3312]) ).
cnf(c_0_5065,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
inference(split_conjunct,[status(thm)],[c_0_3313]) ).
cnf(c_0_5066,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
inference(split_conjunct,[status(thm)],[c_0_3314]) ).
cnf(c_0_5067,plain,
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)
| X2 != one_one(nat)
| X1 != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_5068,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X2 != one_one(nat)
| X1 != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_5069,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_3265]) ).
cnf(c_0_5070,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3315]) ).
cnf(c_0_5071,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_5072,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_5073,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3316]) ).
cnf(c_0_5074,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3317]) ).
cnf(c_0_5075,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3318]) ).
cnf(c_0_5076,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),one_one(nat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3319]) ).
cnf(c_0_5077,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3320]) ).
cnf(c_0_5078,plain,
ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3321]) ).
cnf(c_0_5079,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3322]) ).
cnf(c_0_5080,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_5081,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3324]) ).
cnf(c_0_5082,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_3325]) ).
cnf(c_0_5083,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_3326]) ).
cnf(c_0_5084,plain,
ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
inference(split_conjunct,[status(thm)],[c_0_3327]) ).
cnf(c_0_5085,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_3328]) ).
cnf(c_0_5086,plain,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(split_conjunct,[status(thm)],[c_0_3329]) ).
cnf(c_0_5087,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_3330]) ).
cnf(c_0_5088,plain,
( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3281]) ).
cnf(c_0_5089,plain,
( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3282]) ).
cnf(c_0_5090,plain,
hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_3331]) ).
cnf(c_0_5091,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_3332]) ).
cnf(c_0_5092,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_3333]) ).
cnf(c_0_5093,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ finite_finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3334]) ).
cnf(c_0_5094,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ finite_finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3335]) ).
cnf(c_0_5095,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_3336]) ).
cnf(c_0_5096,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_3337]) ).
cnf(c_0_5097,plain,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),comp(X1,X2,X3)) = comp(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_3338]) ).
cnf(c_0_5098,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_3339]) ).
cnf(c_0_5099,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_3340]) ).
cnf(c_0_5100,plain,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3341]) ).
cnf(c_0_5101,plain,
( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_5102,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
inference(split_conjunct,[status(thm)],[c_0_3342]) ).
cnf(c_0_5103,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
inference(split_conjunct,[status(thm)],[c_0_3343]) ).
cnf(c_0_5104,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[c_0_3344]) ).
cnf(c_0_5105,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[c_0_3345]) ).
cnf(c_0_5106,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3346]) ).
cnf(c_0_5107,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3347]) ).
cnf(c_0_5108,plain,
zero_zero(nat) != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[c_0_3348]) ).
cnf(c_0_5109,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3349]) ).
cnf(c_0_5110,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_3350]) ).
cnf(c_0_5111,plain,
ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3351]) ).
cnf(c_0_5112,plain,
X1 != hAPP(nat,nat,suc,X1),
inference(split_conjunct,[status(thm)],[c_0_3352]) ).
cnf(c_0_5113,plain,
hAPP(nat,nat,suc,X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_3353]) ).
cnf(c_0_5114,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3354]) ).
cnf(c_0_5115,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_3355]) ).
cnf(c_0_5116,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_3356]) ).
cnf(c_0_5117,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_3357]) ).
cnf(c_0_5118,plain,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
inference(split_conjunct,[status(thm)],[c_0_3358]) ).
cnf(c_0_5119,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_3359]) ).
cnf(c_0_5120,plain,
( hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2)
| ~ top(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3360]) ).
cnf(c_0_5121,plain,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
inference(split_conjunct,[status(thm)],[c_0_3361]) ).
cnf(c_0_5122,plain,
ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
inference(split_conjunct,[status(thm)],[c_0_3362]) ).
cnf(c_0_5123,plain,
( ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2)
| ~ comm_monoid_add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3363]) ).
cnf(c_0_5124,plain,
ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
inference(split_conjunct,[status(thm)],[c_0_3364]) ).
cnf(c_0_5125,plain,
ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3365]) ).
cnf(c_0_5126,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_3366]) ).
cnf(c_0_5127,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3367]) ).
cnf(c_0_5128,plain,
( X1 = hAPP(nat,nat,suc,esk97_1(X1))
| X1 = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3368]) ).
cnf(c_0_5129,plain,
( X1 = hAPP(nat,nat,suc,esk96_1(X1))
| X1 = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_3369]) ).
cnf(c_0_5130,plain,
hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3370]) ).
cnf(c_0_5131,plain,
hAPP(nat,nat,size_size(nat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_3371]) ).
cnf(c_0_5132,plain,
hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3372]) ).
cnf(c_0_5133,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[c_0_3373]) ).
cnf(c_0_5134,plain,
ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
inference(split_conjunct,[status(thm)],[c_0_3374]) ).
cnf(c_0_5135,plain,
hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3375]) ).
cnf(c_0_5136,plain,
hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3376]) ).
cnf(c_0_5137,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_3377]) ).
cnf(c_0_5138,plain,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
inference(split_conjunct,[status(thm)],[c_0_3378]) ).
cnf(c_0_5139,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3379]) ).
cnf(c_0_5140,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3380]) ).
cnf(c_0_5141,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3381]) ).
cnf(c_0_5142,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3382]) ).
cnf(c_0_5143,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(split_conjunct,[status(thm)],[c_0_3383]) ).
cnf(c_0_5144,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
inference(split_conjunct,[status(thm)],[c_0_3384]) ).
cnf(c_0_5145,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(split_conjunct,[status(thm)],[c_0_3385]) ).
cnf(c_0_5146,plain,
ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3386]) ).
cnf(c_0_5147,plain,
( ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1)
| ~ semilattice_sup(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3387]) ).
cnf(c_0_5148,plain,
( ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1)
| ~ semilattice_inf(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3388]) ).
cnf(c_0_5149,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ no_zero_divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3389]) ).
cnf(c_0_5150,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ mult_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3390]) ).
cnf(c_0_5151,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ ab_semigroup_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3391]) ).
cnf(c_0_5152,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3392]) ).
cnf(c_0_5153,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3393]) ).
cnf(c_0_5154,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3394]) ).
cnf(c_0_5155,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3395]) ).
cnf(c_0_5156,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3396]) ).
cnf(c_0_5157,plain,
( ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3397]) ).
cnf(c_0_5158,plain,
( ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3398]) ).
cnf(c_0_5159,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3399]) ).
cnf(c_0_5160,plain,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3400]) ).
cnf(c_0_5161,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(split_conjunct,[status(thm)],[c_0_3401]) ).
cnf(c_0_5162,plain,
ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
inference(split_conjunct,[status(thm)],[c_0_3402]) ).
cnf(c_0_5163,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(split_conjunct,[status(thm)],[c_0_3403]) ).
cnf(c_0_5164,plain,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
inference(split_conjunct,[status(thm)],[c_0_3404]) ).
cnf(c_0_5165,plain,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
inference(split_conjunct,[status(thm)],[c_0_3405]) ).
cnf(c_0_5166,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(split_conjunct,[status(thm)],[c_0_3406]) ).
cnf(c_0_5167,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(split_conjunct,[status(thm)],[c_0_3407]) ).
cnf(c_0_5168,plain,
( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
| ~ ring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3408]) ).
cnf(c_0_5169,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| zero_zero(X1) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3409]) ).
cnf(c_0_5170,plain,
( zero_zero(X1) = ti(X1,X2)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3409]) ).
cnf(c_0_5171,plain,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| one_one(X1) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3410]) ).
cnf(c_0_5172,plain,
( one_one(X1) = ti(X1,X2)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3410]) ).
cnf(c_0_5173,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_3411]) ).
cnf(c_0_5174,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(split_conjunct,[status(thm)],[c_0_3412]) ).
cnf(c_0_5175,plain,
( finite_finite(product_prod(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3413]) ).
cnf(c_0_5176,plain,
( finite_finite(sum_sum(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3414]) ).
cnf(c_0_5177,plain,
( finite_finite(fun(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3415]) ).
cnf(c_0_5178,plain,
ti(fun(nat,nat),size_size(nat)) = size_size(nat),
inference(split_conjunct,[status(thm)],[c_0_3416]) ).
cnf(c_0_5179,plain,
( ord(fun(X1,X2))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3417]) ).
cnf(c_0_5180,plain,
( top(fun(X1,X2))
| ~ top(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3418]) ).
cnf(c_0_5181,plain,
( order(fun(X1,X2))
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3419]) ).
cnf(c_0_5182,plain,
( lattice(fun(X1,X2))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3420]) ).
cnf(c_0_5183,plain,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3421]) ).
cnf(c_0_5184,plain,
( distrib_lattice(fun(X1,X2))
| ~ distrib_lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3422]) ).
cnf(c_0_5185,plain,
( semilattice_inf(fun(X1,X2))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3423]) ).
cnf(c_0_5186,plain,
( semilattice_sup(fun(X1,X2))
| ~ lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3424]) ).
cnf(c_0_5187,plain,
( bounded_lattice_top(fun(X1,X2))
| ~ bounded_lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3425]) ).
cnf(c_0_5188,plain,
( bounded_lattice(fun(X1,X2))
| ~ bounded_lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3426]) ).
cnf(c_0_5189,plain,
ti(fun(arrow_1998540521e_indi,nat),h) = h,
inference(split_conjunct,[status(thm)],[c_0_3427]) ).
cnf(c_0_5190,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(split_conjunct,[status(thm)],[c_0_3428]) ).
cnf(c_0_5191,plain,
ti(fun(nat,nat),nat_size) = nat_size,
inference(split_conjunct,[status(thm)],[c_0_3429]) ).
cnf(c_0_5192,plain,
ti(fun(nat,nat),suc) = suc,
inference(split_conjunct,[status(thm)],[c_0_3430]) ).
cnf(c_0_5193,plain,
ti(fun(bool,nat),bool_size) = bool_size,
inference(split_conjunct,[status(thm)],[c_0_3431]) ).
cnf(c_0_5194,plain,
( ti(X1,top_top(X1)) = top_top(X1)
| ~ top(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3432]) ).
cnf(c_0_5195,plain,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3433]) ).
cnf(c_0_5196,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3434]) ).
cnf(c_0_5197,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_3435]) ).
cnf(c_0_5198,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_3436]) ).
cnf(c_0_5199,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_3437]) ).
cnf(c_0_5200,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[c_0_3438]) ).
cnf(c_0_5201,plain,
( one_one(X1) != zero_zero(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3439]) ).
cnf(c_0_5202,plain,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3440]) ).
cnf(c_0_5203,plain,
( finite_finite(option(X1))
| ~ finite_finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3441]) ).
cnf(c_0_5204,plain,
ti(nat,n) = n,
inference(split_conjunct,[status(thm)],[c_0_3442]) ).
cnf(c_0_5205,plain,
ti(arrow_2142409994le_alt,e) = e,
inference(split_conjunct,[status(thm)],[c_0_3443]) ).
cnf(c_0_5206,plain,
ti(arrow_2142409994le_alt,b) = b,
inference(split_conjunct,[status(thm)],[c_0_3444]) ).
cnf(c_0_5207,plain,
ti(arrow_2142409994le_alt,a) = a,
inference(split_conjunct,[status(thm)],[c_0_3445]) ).
cnf(c_0_5208,plain,
ti(bool,fTrue) = fTrue,
inference(split_conjunct,[status(thm)],[c_0_3446]) ).
cnf(c_0_5209,plain,
ti(bool,fFalse) = fFalse,
inference(split_conjunct,[status(thm)],[c_0_3447]) ).
cnf(c_0_5210,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[c_0_3448]) ).
cnf(c_0_5211,plain,
hBOOL(fTrue),
inference(split_conjunct,[status(thm)],[c_0_3449]) ).
cnf(c_0_5212,plain,
finite_finite(product_unit),
inference(split_conjunct,[status(thm)],[c_0_3450]) ).
cnf(c_0_5213,plain,
ord(bool),
inference(split_conjunct,[status(thm)],[c_0_3451]) ).
cnf(c_0_5214,plain,
top(bool),
inference(split_conjunct,[status(thm)],[c_0_3452]) ).
cnf(c_0_5215,plain,
order(bool),
inference(split_conjunct,[status(thm)],[c_0_3453]) ).
cnf(c_0_5216,plain,
lattice(bool),
inference(split_conjunct,[status(thm)],[c_0_3454]) ).
cnf(c_0_5217,plain,
finite_finite(bool),
inference(split_conjunct,[status(thm)],[c_0_3455]) ).
cnf(c_0_5218,plain,
preorder(bool),
inference(split_conjunct,[status(thm)],[c_0_3456]) ).
cnf(c_0_5219,plain,
distrib_lattice(bool),
inference(split_conjunct,[status(thm)],[c_0_3457]) ).
cnf(c_0_5220,plain,
semilattice_inf(bool),
inference(split_conjunct,[status(thm)],[c_0_3458]) ).
cnf(c_0_5221,plain,
semilattice_sup(bool),
inference(split_conjunct,[status(thm)],[c_0_3459]) ).
cnf(c_0_5222,plain,
bounded_lattice_top(bool),
inference(split_conjunct,[status(thm)],[c_0_3460]) ).
cnf(c_0_5223,plain,
one(nat),
inference(split_conjunct,[status(thm)],[c_0_3461]) ).
cnf(c_0_5224,plain,
zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3462]) ).
cnf(c_0_5225,plain,
ord(nat),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_5226,plain,
semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_3464]) ).
cnf(c_0_5227,plain,
order(nat),
inference(split_conjunct,[status(thm)],[c_0_3465]) ).
cnf(c_0_5228,plain,
mult_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_3466]) ).
cnf(c_0_5229,plain,
lattice(nat),
inference(split_conjunct,[status(thm)],[c_0_3467]) ).
cnf(c_0_5230,plain,
semiring_0(nat),
inference(split_conjunct,[status(thm)],[c_0_3468]) ).
cnf(c_0_5231,plain,
monoid_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3469]) ).
cnf(c_0_5232,plain,
monoid_mult(nat),
inference(split_conjunct,[status(thm)],[c_0_3470]) ).
cnf(c_0_5233,plain,
linorder(nat),
inference(split_conjunct,[status(thm)],[c_0_3471]) ).
cnf(c_0_5234,plain,
preorder(nat),
inference(split_conjunct,[status(thm)],[c_0_3472]) ).
cnf(c_0_5235,plain,
zero_neq_one(nat),
inference(split_conjunct,[status(thm)],[c_0_3473]) ).
cnf(c_0_5236,plain,
comm_semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_3474]) ).
cnf(c_0_5237,plain,
comm_semiring_1(nat),
inference(split_conjunct,[status(thm)],[c_0_3475]) ).
cnf(c_0_5238,plain,
comm_monoid_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3476]) ).
cnf(c_0_5239,plain,
no_zero_divisors(nat),
inference(split_conjunct,[status(thm)],[c_0_3477]) ).
cnf(c_0_5240,plain,
ordered_semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_3478]) ).
cnf(c_0_5241,plain,
ab_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3479]) ).
cnf(c_0_5242,plain,
comm_monoid_mult(nat),
inference(split_conjunct,[status(thm)],[c_0_3480]) ).
cnf(c_0_5243,plain,
ab_semigroup_mult(nat),
inference(split_conjunct,[status(thm)],[c_0_3481]) ).
cnf(c_0_5244,plain,
distrib_lattice(nat),
inference(split_conjunct,[status(thm)],[c_0_3482]) ).
cnf(c_0_5245,plain,
semilattice_inf(nat),
inference(split_conjunct,[status(thm)],[c_0_3483]) ).
cnf(c_0_5246,plain,
semilattice_sup(nat),
inference(split_conjunct,[status(thm)],[c_0_3484]) ).
cnf(c_0_5247,plain,
linordered_semidom(nat),
inference(split_conjunct,[status(thm)],[c_0_3485]) ).
cnf(c_0_5248,plain,
linordered_semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_3486]) ).
cnf(c_0_5249,plain,
cancel_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3487]) ).
cnf(c_0_5250,plain,
ordere1490568538miring(nat),
inference(split_conjunct,[status(thm)],[c_0_3488]) ).
cnf(c_0_5251,plain,
ordere453448008miring(nat),
inference(split_conjunct,[status(thm)],[c_0_3489]) ).
cnf(c_0_5252,plain,
cancel146912293up_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3490]) ).
cnf(c_0_5253,plain,
ordere216010020id_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3491]) ).
cnf(c_0_5254,plain,
ordere779506340up_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3492]) ).
cnf(c_0_5255,plain,
linord20386208strict(nat),
inference(split_conjunct,[status(thm)],[c_0_3493]) ).
cnf(c_0_5256,plain,
linord893533164strict(nat),
inference(split_conjunct,[status(thm)],[c_0_3494]) ).
cnf(c_0_5257,plain,
ordere236663937imp_le(nat),
inference(split_conjunct,[status(thm)],[c_0_3495]) ).
cnf(c_0_5258,plain,
ordere223160158up_add(nat),
inference(split_conjunct,[status(thm)],[c_0_3496]) ).
cnf(c_0_5259,plain,
semiri456707255roduct(nat),
inference(split_conjunct,[status(thm)],[c_0_3497]) ).
cnf(c_0_5260,plain,
bounded_lattice(bool),
inference(split_conjunct,[status(thm)],[c_0_3498]) ).
cnf(c_0_5261,plain,
a != b,
inference(split_conjunct,[status(thm)],[c_0_3499]) ).
cnf(c_0_5262,plain,
c != d,
inference(split_conjunct,[status(thm)],[c_0_3500]) ).
cnf(c_0_5263,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
c_0_3501,
[final] ).
cnf(c_0_5264,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
c_0_3502,
[final] ).
cnf(c_0_5265,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
c_0_3503,
[final] ).
cnf(c_0_5266,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
c_0_3504,
[final] ).
cnf(c_0_5267,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
c_0_3505,
[final] ).
cnf(c_0_5268,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
c_0_3506,
[final] ).
cnf(c_0_5269,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
c_0_3507,
[final] ).
cnf(c_0_5270,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
c_0_3508,
[final] ).
cnf(c_0_5271,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
c_0_3509,
[final] ).
cnf(c_0_5272,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
c_0_3510,
[final] ).
cnf(c_0_5273,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
c_0_3511,
[final] ).
cnf(c_0_5274,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
c_0_3512,
[final] ).
cnf(c_0_5275,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_214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),
c_0_3513,
[final] ).
cnf(c_0_5276,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
c_0_3514,
[final] ).
cnf(c_0_5277,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
c_0_3515,
[final] ).
cnf(c_0_5278,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
c_0_3516,
[final] ).
cnf(c_0_5279,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
c_0_3517,
[final] ).
cnf(c_0_5280,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
c_0_3518,
[final] ).
cnf(c_0_5281,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_3519,
[final] ).
cnf(c_0_5282,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_3520,
[final] ).
cnf(c_0_5283,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
c_0_3521,
[final] ).
cnf(c_0_5284,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
c_0_3522,
[final] ).
cnf(c_0_5285,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
c_0_3523,
[final] ).
cnf(c_0_5286,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
c_0_3524,
[final] ).
cnf(c_0_5287,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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X5),X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X5)),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)))),X6)),X3),X4)) ),
c_0_3525,
[final] ).
cnf(c_0_5288,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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X5),X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X5)),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)))),X6)),X3),X4)) ),
c_0_3526,
[final] ).
cnf(c_0_5289,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6))
| ~ 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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_inf_inf(fun(product_prod(X2,X1),bool)),X3),X4))) ),
c_0_3527,
[final] ).
cnf(c_0_5290,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6))
| ~ 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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_sup_sup(fun(product_prod(X2,X1),bool)),X3),X4))) ),
c_0_3528,
[final] ).
cnf(c_0_5291,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk140_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
c_0_3529,
[final] ).
cnf(c_0_5292,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk29_0),one_one(nat))))),lab)),lba)))),
c_0_3530,
[final] ).
cnf(c_0_5293,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_3531,
[final] ).
cnf(c_0_5294,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
c_0_3532,
[final] ).
cnf(c_0_5295,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk29_0)) ),
c_0_3533,
[final] ).
cnf(c_0_5296,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_3534,
[final] ).
cnf(c_0_5297,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_3535,
[final] ).
cnf(c_0_5298,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_301600364e_Prof)),
c_0_3536,
[final] ).
cnf(c_0_5299,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk140_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
c_0_3537,
[final] ).
cnf(c_0_5300,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_3538,
[final] ).
cnf(c_0_5301,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_3539,
[final] ).
cnf(c_0_5302,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
c_0_3540,
[final] ).
cnf(c_0_5303,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk139_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
c_0_3541,
[final] ).
cnf(c_0_5304,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,fun(X3,bool)),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,bool)),fun(X1,X2)),combs(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),collect(X3)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),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),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)),X5)))),X6)))),X7) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combs(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X7)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),X6))))),X5)
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ comm_monoid_add(X2) ),
c_0_3542,
[final] ).
cnf(c_0_5305,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
c_0_3543,
[final] ).
cnf(c_0_5306,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X5,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X5,bool),X1)),fun(fun(X5,bool),fun(X2,X1)),combc(X2,fun(X5,bool),X1),hAPP(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1)),hAPP(fun(fun(X5,X1),fun(fun(X5,bool),X1)),fun(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1))),combb(fun(X5,X1),fun(fun(X5,bool),X1),X2),big_co1399186613setsum(X5,X1)),hAPP(fun(X5,X1),fun(X2,fun(X5,X1)),hAPP(fun(X2,fun(fun(X5,X1),fun(X5,X1))),fun(fun(X5,X1),fun(X2,fun(X5,X1))),combc(X2,fun(X5,X1),fun(X5,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1))),hAPP(fun(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1)))),combb(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1)),X2),combb(X1,X1,X5)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3))),X6))),X7)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X5,bool),X1,hAPP(fun(X5,X1),fun(fun(X5,bool),X1),big_co1399186613setsum(X5,X1),X6),X7))
| ~ semiring_0(X1) ),
c_0_3544,
[final] ).
cnf(c_0_5307,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) != hAPP(X1,X2,X8,esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) ),
c_0_3545,
[final] ).
cnf(c_0_5308,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_3546,
[final] ).
cnf(c_0_5309,plain,
( hAPP(fun(X5,bool),X2,hAPP(fun(X5,X2),fun(fun(X5,bool),X2),big_co1399186613setsum(X5,X2),hAPP(fun(X5,fun(X1,bool)),fun(X5,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X5,fun(X1,bool)),fun(X5,X2)),combb(fun(X1,bool),X2,X5),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),collect(X1)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),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),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)),X4)))),hAPP(fun(X1,fun(X5,bool)),fun(X5,fun(X1,bool)),combc(X1,X5,bool),hAPP(fun(X1,X5),fun(X1,fun(X5,bool)),hAPP(fun(X5,fun(X5,bool)),fun(fun(X1,X5),fun(X1,fun(X5,bool))),combb(X5,fun(X5,bool),X1),fequal(X5)),X6)))))),hAPP(fun(X1,bool),fun(X5,bool),hAPP(fun(X1,X5),fun(fun(X1,bool),fun(X5,bool)),image(X1,X5),X6),X4)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_3547,
[final] ).
cnf(c_0_5310,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk138_7(X4,X1,X5,X6,X7,X2,X3)),esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
c_0_3548,
[final] ).
cnf(c_0_5311,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk139_7(X4,X1,X5,X6,X7,X2,X3)),esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
c_0_3549,
[final] ).
cnf(c_0_5312,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),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)),X5)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_3550,
[final] ).
cnf(c_0_5313,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ 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),X4),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),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(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,esk117_4(X3,X1,X4,X2))))))) ),
c_0_3551,
[final] ).
cnf(c_0_5314,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_3552,
[final] ).
cnf(c_0_5315,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_3553,
[final] ).
cnf(c_0_5316,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
c_0_3554,
[final] ).
cnf(c_0_5317,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
c_0_3555,
[final] ).
cnf(c_0_5318,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),X5))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X5)),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_3556,
[final] ).
cnf(c_0_5319,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,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X3)),X4)),X5)),X6) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),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),X3))))),
c_0_3557,
[final] ).
cnf(c_0_5320,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
c_0_3558,
[final] ).
cnf(c_0_5321,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
c_0_3559,
[final] ).
cnf(c_0_5322,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,esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk55_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_3560,
[final] ).
cnf(c_0_5323,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,esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk53_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_3561,
[final] ).
cnf(c_0_5324,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,esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk46_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_3562,
[final] ).
cnf(c_0_5325,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,esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk44_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_3563,
[final] ).
cnf(c_0_5326,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,esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk51_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_3564,
[final] ).
cnf(c_0_5327,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,esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk49_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_3565,
[final] ).
cnf(c_0_5328,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,esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk41_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_3566,
[final] ).
cnf(c_0_5329,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,esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk39_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_3567,
[final] ).
cnf(c_0_5330,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2)))) ),
c_0_3568,
[final] ).
cnf(c_0_5331,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3569,
[final] ).
cnf(c_0_5332,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
c_0_3570,
[final] ).
cnf(c_0_5333,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3571,
[final] ).
cnf(c_0_5334,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
c_0_3572,
[final] ).
cnf(c_0_5335,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3573,
[final] ).
cnf(c_0_5336,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3574,
[final] ).
cnf(c_0_5337,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
c_0_3575,
[final] ).
cnf(c_0_5338,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3576,
[final] ).
cnf(c_0_5339,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
c_0_3577,
[final] ).
cnf(c_0_5340,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_3578,
[final] ).
cnf(c_0_5341,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3579,
[final] ).
cnf(c_0_5342,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X3)),X4)),one_one(X2)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),one_one(X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_mult(X2) ),
c_0_3580,
[final] ).
cnf(c_0_5343,plain,
( hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X1,bool),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X1,bool),fun(X3,X2)),combc(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),X6)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X3,bool),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X3,bool),fun(X1,X2)),combc(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),X5)),X6)
| ~ comm_monoid_add(X2) ),
c_0_3581,
[final] ).
cnf(c_0_5344,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X2,X1)),esk26_2(X2,X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk24_2(X2,X1)))) ),
c_0_3582,
[final] ).
cnf(c_0_5345,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3583,
[final] ).
cnf(c_0_5346,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3584,
[final] ).
cnf(c_0_5347,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3585,
[final] ).
cnf(c_0_5348,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3586,
[final] ).
cnf(c_0_5349,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_mult(X1) ),
c_0_3587,
[final] ).
cnf(c_0_5350,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X2,X1)),esk26_2(X2,X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk24_2(X2,X1),X2)))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
c_0_3588,
[final] ).
cnf(c_0_5351,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk24_2(X2,X1)),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
c_0_3589,
[final] ).
cnf(c_0_5352,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
c_0_3590,
[final] ).
cnf(c_0_5353,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
c_0_3591,
[final] ).
cnf(c_0_5354,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
c_0_3592,
[final] ).
cnf(c_0_5355,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3593,
[final] ).
cnf(c_0_5356,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| ti(arrow_2142409994le_alt,esk26_2(X2,X1)) != ti(arrow_2142409994le_alt,esk25_2(X2,X1)) ),
c_0_3594,
[final] ).
cnf(c_0_5357,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3595,
[final] ).
cnf(c_0_5358,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3596,
[final] ).
cnf(c_0_5359,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_3597,
[final] ).
cnf(c_0_5360,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_3598,
[final] ).
cnf(c_0_5361,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3599,
[final] ).
cnf(c_0_5362,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3600,
[final] ).
cnf(c_0_5363,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3601,
[final] ).
cnf(c_0_5364,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3602,
[final] ).
cnf(c_0_5365,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3603,
[final] ).
cnf(c_0_5366,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3604,
[final] ).
cnf(c_0_5367,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3605,
[final] ).
cnf(c_0_5368,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3606,
[final] ).
cnf(c_0_5369,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
c_0_3607,
[final] ).
cnf(c_0_5370,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
c_0_3608,
[final] ).
cnf(c_0_5371,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
c_0_3609,
[final] ).
cnf(c_0_5372,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
c_0_3610,
[final] ).
cnf(c_0_5373,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
c_0_3611,
[final] ).
cnf(c_0_5374,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
c_0_3612,
[final] ).
cnf(c_0_5375,plain,
( hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),hAPP(fun(X1,X6),fun(X1,X2),hAPP(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2))),compose(X1,X6,X2),X4),X7),X8)) = hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3))),compose(X1,X6,X3),X4),hAPP(fun(X6,X2),fun(X6,X3),hAPP(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3)),hAPP(fun(X6,bool),fun(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3))),compose(X6,X2,X3),X9),X5),X7)),X8)
| ~ hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X5),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X10),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X11))))
| ~ hBOOL(hAPP(fun(fun(X6,X2),bool),bool,hAPP(fun(X6,X2),fun(fun(fun(X6,X2),bool),bool),member(fun(X6,X2)),X7),hAPP(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool)),pi(X6,X2),X9),hAPP(fun(X2,bool),fun(X6,fun(X2,bool)),combk(fun(X2,bool),X6),X10))))
| ~ hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),X8),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X9)))) ),
c_0_3613,
[final] ).
cnf(c_0_5376,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),esk54_6(X1,X2,X5,X6,X3,X4)),esk55_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_3614,
[final] ).
cnf(c_0_5377,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),esk52_6(X1,X2,X5,X6,X3,X4)),esk53_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_3615,
[final] ).
cnf(c_0_5378,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),esk47_6(X1,X2,X6,X3,X4,X5)),esk46_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_3616,
[final] ).
cnf(c_0_5379,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),esk45_6(X1,X2,X6,X3,X4,X5)),esk44_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_3617,
[final] ).
cnf(c_0_5380,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),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),X7))))
| ~ hBOOL(hAPP(fun(fun(X3,X2),bool),bool,hAPP(fun(X3,X2),fun(fun(fun(X3,X2),bool),bool),member(fun(X3,X2)),X5),hAPP(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool)),pi(X3,X2),X8),hAPP(fun(X2,bool),fun(X3,fun(X2,bool)),combk(fun(X2,bool),X3),X7))))
| ~ 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),X4),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X8)))) ),
c_0_3618,
[final] ).
cnf(c_0_5381,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
c_0_3619,
[final] ).
cnf(c_0_5382,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_3620,
[final] ).
cnf(c_0_5383,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),esk50_6(X1,X2,X6,X3,X4,X5)),esk51_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_3621,
[final] ).
cnf(c_0_5384,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),esk48_6(X1,X2,X6,X3,X4,X5)),esk49_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_3622,
[final] ).
cnf(c_0_5385,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),esk42_6(X1,X2,X5,X6,X3,X4)),esk41_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_3623,
[final] ).
cnf(c_0_5386,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),esk40_6(X1,X2,X5,X6,X3,X4)),esk39_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_3624,
[final] ).
cnf(c_0_5387,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3625,
[final] ).
cnf(c_0_5388,plain,
( hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),the_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
c_0_3626,
[final] ).
cnf(c_0_5389,plain,
( hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),hilbert_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = 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),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
c_0_3627,
[final] ).
cnf(c_0_5390,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3628,
[final] ).
cnf(c_0_5391,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3629,
[final] ).
cnf(c_0_5392,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X3)),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)),X4)),X2)) ),
c_0_3630,
[final] ).
cnf(c_0_5393,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X3)),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)),X4)),X2)) ),
c_0_3631,
[final] ).
cnf(c_0_5394,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3632,
[final] ).
cnf(c_0_5395,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
c_0_3633,
[final] ).
cnf(c_0_5396,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
c_0_3634,
[final] ).
cnf(c_0_5397,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3635,
[final] ).
cnf(c_0_5398,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3636,
[final] ).
cnf(c_0_5399,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,esk59_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,esk59_5(X2,X1,X4,X5,X3)))) ),
c_0_3637,
[final] ).
cnf(c_0_5400,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3638,
[final] ).
cnf(c_0_5401,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3639,
[final] ).
cnf(c_0_5402,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
c_0_3640,
[final] ).
cnf(c_0_5403,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
c_0_3641,
[final] ).
cnf(c_0_5404,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),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linordered_ring(X1) ),
c_0_3642,
[final] ).
cnf(c_0_5405,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_3643,
[final] ).
cnf(c_0_5406,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_3644,
[final] ).
cnf(c_0_5407,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3645,
[final] ).
cnf(c_0_5408,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)),
c_0_3646,
[final] ).
cnf(c_0_5409,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3647,
[final] ).
cnf(c_0_5410,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk132_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,esk132_5(X2,X1,X3,X5,X4)))) ),
c_0_3648,
[final] ).
cnf(c_0_5411,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(X2,X1,X5,esk173_5(X2,X1,X5,X4,X3)) != one_one(X1) ),
c_0_3649,
[final] ).
cnf(c_0_5412,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_3650,
[final] ).
cnf(c_0_5413,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3651,
[final] ).
cnf(c_0_5414,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),esk22_4(X1,X2,X4,X3)),esk23_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),esk22_4(X1,X2,X4,X3)),esk23_4(X1,X2,X4,X3))),X3)) ),
c_0_3652,
[final] ).
cnf(c_0_5415,plain,
hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
c_0_3653,
[final] ).
cnf(c_0_5416,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3654,
[final] ).
cnf(c_0_5417,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3655,
[final] ).
cnf(c_0_5418,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3656,
[final] ).
cnf(c_0_5419,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk137_6(X2,X1,X5,X4,X6,X3)),X3))
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
c_0_3657,
[final] ).
cnf(c_0_5420,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_3658,
[final] ).
cnf(c_0_5421,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_3659,
[final] ).
cnf(c_0_5422,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),esk75_2(X2,X1)),hAPP(nat,nat,X1,esk75_2(X2,X1)))) ),
c_0_3660,
[final] ).
cnf(c_0_5423,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),X4),X5)),X6)),X7) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X4,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X5),X7)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X6),X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X4),X8),X3)) ),
c_0_3661,
[final] ).
cnf(c_0_5424,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3662,
[final] ).
cnf(c_0_5425,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_3663,
[final] ).
cnf(c_0_5426,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_3664,
[final] ).
cnf(c_0_5427,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_3665,
[final] ).
cnf(c_0_5428,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_3666,
[final] ).
cnf(c_0_5429,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),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)))),
c_0_3667,
[final] ).
cnf(c_0_5430,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3668,
[final] ).
cnf(c_0_5431,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3669,
[final] ).
cnf(c_0_5432,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3670,
[final] ).
cnf(c_0_5433,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3671,
[final] ).
cnf(c_0_5434,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3672,
[final] ).
cnf(c_0_5435,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3673,
[final] ).
cnf(c_0_5436,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3674,
[final] ).
cnf(c_0_5437,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3675,
[final] ).
cnf(c_0_5438,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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)),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),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X3))))
| hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3) != ti(fun(X1,bool),X5) ),
c_0_3676,
[final] ).
cnf(c_0_5439,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3677,
[final] ).
cnf(c_0_5440,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3678,
[final] ).
cnf(c_0_5441,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_3679,
[final] ).
cnf(c_0_5442,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
c_0_3680,
[final] ).
cnf(c_0_5443,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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
c_0_3681,
[final] ).
cnf(c_0_5444,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),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,esk133_5(X2,X1,X3,X5,X4))),X5)) ),
c_0_3682,
[final] ).
cnf(c_0_5445,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,esk137_6(X2,X1,X5,X4,X6,X3)) != hAPP(X2,X1,X6,esk137_6(X2,X1,X5,X4,X6,X3)) ),
c_0_3683,
[final] ).
cnf(c_0_5446,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3684,
[final] ).
cnf(c_0_5447,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3685,
[final] ).
cnf(c_0_5448,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))))
| ~ lattice(X1) ),
c_0_3686,
[final] ).
cnf(c_0_5449,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3687,
[final] ).
cnf(c_0_5450,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3688,
[final] ).
cnf(c_0_5451,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) ),
c_0_3689,
[final] ).
cnf(c_0_5452,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
c_0_3690,
[final] ).
cnf(c_0_5453,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3691,
[final] ).
cnf(c_0_5454,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3692,
[final] ).
cnf(c_0_5455,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3693,
[final] ).
cnf(c_0_5456,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
c_0_3694,
[final] ).
cnf(c_0_5457,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
c_0_3695,
[final] ).
cnf(c_0_5458,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3696,
[final] ).
cnf(c_0_5459,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3697,
[final] ).
cnf(c_0_5460,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
c_0_3698,
[final] ).
cnf(c_0_5461,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
c_0_3699,
[final] ).
cnf(c_0_5462,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
c_0_3700,
[final] ).
cnf(c_0_5463,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
c_0_3701,
[final] ).
cnf(c_0_5464,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3702,
[final] ).
cnf(c_0_5465,plain,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk147_6(X4,X1,X5,X6,X2,X3)),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
c_0_3703,
[final] ).
cnf(c_0_5466,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3704,
[final] ).
cnf(c_0_5467,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3705,
[final] ).
cnf(c_0_5468,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3706,
[final] ).
cnf(c_0_5469,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3707,
[final] ).
cnf(c_0_5470,plain,
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),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))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),
c_0_3708,
[final] ).
cnf(c_0_5471,plain,
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),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))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),
c_0_3709,
[final] ).
cnf(c_0_5472,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3710,
[final] ).
cnf(c_0_5473,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3711,
[final] ).
cnf(c_0_5474,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))))
| ~ comm_monoid_add(X1) ),
c_0_3712,
[final] ).
cnf(c_0_5475,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3713,
[final] ).
cnf(c_0_5476,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_3714,
[final] ).
cnf(c_0_5477,plain,
( hAPP(fun(X1,bool),X2,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X6,hAPP(fun(X1,bool),X2,X3,X4)),hAPP(fun(X1,bool),X2,X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X6),X7),X8),X3)) ),
c_0_3715,
[final] ).
cnf(c_0_5478,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_3716,
[final] ).
cnf(c_0_5479,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_3717,
[final] ).
cnf(c_0_5480,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3718,
[final] ).
cnf(c_0_5481,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3719,
[final] ).
cnf(c_0_5482,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_3720,
[final] ).
cnf(c_0_5483,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(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk131_5(X1,X2,X3,X5,X4))),X5)) ),
c_0_3721,
[final] ).
cnf(c_0_5484,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3722,
[final] ).
cnf(c_0_5485,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3723,
[final] ).
cnf(c_0_5486,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3724,
[final] ).
cnf(c_0_5487,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_3725,
[final] ).
cnf(c_0_5488,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3726,
[final] ).
cnf(c_0_5489,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3727,
[final] ).
cnf(c_0_5490,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3728,
[final] ).
cnf(c_0_5491,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3729,
[final] ).
cnf(c_0_5492,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3730,
[final] ).
cnf(c_0_5493,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3731,
[final] ).
cnf(c_0_5494,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3732,
[final] ).
cnf(c_0_5495,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3733,
[final] ).
cnf(c_0_5496,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3734,
[final] ).
cnf(c_0_5497,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3735,
[final] ).
cnf(c_0_5498,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3736,
[final] ).
cnf(c_0_5499,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
c_0_3737,
[final] ).
cnf(c_0_5500,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
c_0_3738,
[final] ).
cnf(c_0_5501,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
c_0_3739,
[final] ).
cnf(c_0_5502,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
c_0_3740,
[final] ).
cnf(c_0_5503,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
c_0_3741,
[final] ).
cnf(c_0_5504,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),esk22_4(X1,X2,X4,X3)),esk23_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),esk22_4(X1,X2,X4,X3)),esk23_4(X1,X2,X4,X3))),X3)) ),
c_0_3742,
[final] ).
cnf(c_0_5505,plain,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3743,
[final] ).
cnf(c_0_5506,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk14_4(X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3)) ),
c_0_3744,
[final] ).
cnf(c_0_5507,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3745,
[final] ).
cnf(c_0_5508,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
c_0_3746,
[final] ).
cnf(c_0_5509,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
c_0_3747,
[final] ).
cnf(c_0_5510,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3748,
[final] ).
cnf(c_0_5511,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(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),X5),X4)),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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
c_0_3749,
[final] ).
cnf(c_0_5512,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))))
| ~ lattice(X1) ),
c_0_3750,
[final] ).
cnf(c_0_5513,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
c_0_3751,
[final] ).
cnf(c_0_5514,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_3752,
[final] ).
cnf(c_0_5515,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3753,
[final] ).
cnf(c_0_5516,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3754,
[final] ).
cnf(c_0_5517,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ comm_monoid_add(X2) ),
c_0_3755,
[final] ).
cnf(c_0_5518,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
c_0_3756,
[final] ).
cnf(c_0_5519,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3757,
[final] ).
cnf(c_0_5520,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,esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
c_0_3758,
[final] ).
cnf(c_0_5521,plain,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hAPP(X1,X4,X5,esk147_6(X4,X1,X5,X6,X2,X3)) != hAPP(X1,X4,X6,esk147_6(X4,X1,X5,X6,X2,X3)) ),
c_0_3759,
[final] ).
cnf(c_0_5522,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
c_0_3760,
[final] ).
cnf(c_0_5523,plain,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
c_0_3761,
[final] ).
cnf(c_0_5524,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3762,
[final] ).
cnf(c_0_5525,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3)),X5)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),X5)
| ~ semiring_0(X1) ),
c_0_3763,
[final] ).
cnf(c_0_5526,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_3764,
[final] ).
cnf(c_0_5527,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_3765,
[final] ).
cnf(c_0_5528,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X1),X2),X3)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
c_0_3766,
[final] ).
cnf(c_0_5529,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X1),X2),X3)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
c_0_3767,
[final] ).
cnf(c_0_5530,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_3768,
[final] ).
cnf(c_0_5531,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)),the_inv_into(X1,X2),X3),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X6))
| ~ 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(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X3)) ),
c_0_3769,
[final] ).
cnf(c_0_5532,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk11_1(X1))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk10_1(X1)))) ),
c_0_3770,
[final] ).
cnf(c_0_5533,plain,
( ~ linord581940658strict(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
c_0_3771,
[final] ).
cnf(c_0_5534,plain,
( hBOOL(hAPP(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(X1,bool,X4,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),top_top(fun(X1,bool))),X3),esk108_5(X1,X2,X5,X4,X3)))) ),
c_0_3772,
[final] ).
cnf(c_0_5535,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),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2))) ),
c_0_3773,
[final] ).
cnf(c_0_5536,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),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2))) ),
c_0_3774,
[final] ).
cnf(c_0_5537,plain,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1)) ),
c_0_3775,
[final] ).
cnf(c_0_5538,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
c_0_3776,
[final] ).
cnf(c_0_5539,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_3777,
[final] ).
cnf(c_0_5540,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X4),X5)),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X3)) ),
c_0_3778,
[final] ).
cnf(c_0_5541,plain,
hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
c_0_3779,
[final] ).
cnf(c_0_5542,plain,
( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X3),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X4)),X5) = ti(fun(X1,X2),X5)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X4)))) ),
c_0_3780,
[final] ).
cnf(c_0_5543,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_3781,
[final] ).
cnf(c_0_5544,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),hAPP(fun(X5,bool),fun(X1,bool),hAPP(fun(X5,X1),fun(fun(X5,bool),fun(X1,bool)),image(X5,X1),X6),X7)) = hAPP(fun(X5,bool),X2,hAPP(X2,fun(fun(X5,bool),X2),hAPP(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2))),finite_fold_image(X2,X5),times_times(X2)),hAPP(fun(X5,X1),fun(X5,X2),hAPP(fun(X1,X2),fun(fun(X5,X1),fun(X5,X2)),comp(X1,X2,X5),X3),X6)),X4),X7)
| ~ hBOOL(hAPP(fun(X5,bool),bool,hAPP(fun(X5,X1),fun(fun(X5,bool),bool),inj_on(X5,X1),X6),X7))
| ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),X7))
| ~ ab_semigroup_mult(X2) ),
c_0_3782,
[final] ).
cnf(c_0_5545,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),esk59_5(X2,X1,X4,X5,X3)),X3)) ),
c_0_3783,
[final] ).
cnf(c_0_5546,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3784,
[final] ).
cnf(c_0_5547,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(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
c_0_3785,
[final] ).
cnf(c_0_5548,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X6),X4),X7),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X3)) ),
c_0_3786,
[final] ).
cnf(c_0_5549,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),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),esk133_5(X2,X1,X3,X5,X4)),X4)) ),
c_0_3787,
[final] ).
cnf(c_0_5550,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
c_0_3788,
[final] ).
cnf(c_0_5551,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
c_0_3789,
[final] ).
cnf(c_0_5552,plain,
( hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X3),X4),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)) = ti(fun(X1,X2),X4)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
c_0_3790,
[final] ).
cnf(c_0_5553,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3791,
[final] ).
cnf(c_0_5554,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_3792,
[final] ).
cnf(c_0_5555,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_3793,
[final] ).
cnf(c_0_5556,plain,
( hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
c_0_3794,
[final] ).
cnf(c_0_5557,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
c_0_3795,
[final] ).
cnf(c_0_5558,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
c_0_3796,
[final] ).
cnf(c_0_5559,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_3797,
[final] ).
cnf(c_0_5560,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_3798,
[final] ).
cnf(c_0_5561,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3799,
[final] ).
cnf(c_0_5562,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3800,
[final] ).
cnf(c_0_5563,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
c_0_3801,
[final] ).
cnf(c_0_5564,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
c_0_3802,
[final] ).
cnf(c_0_5565,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
c_0_3803,
[final] ).
cnf(c_0_5566,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
c_0_3804,
[final] ).
cnf(c_0_5567,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X1),X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X1),X2))) ),
c_0_3805,
[final] ).
cnf(c_0_5568,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X1),X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X1),X2))) ),
c_0_3806,
[final] ).
cnf(c_0_5569,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
c_0_3807,
[final] ).
cnf(c_0_5570,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
c_0_3808,
[final] ).
cnf(c_0_5571,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
c_0_3809,
[final] ).
cnf(c_0_5572,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
c_0_3810,
[final] ).
cnf(c_0_5573,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(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
c_0_3811,
[final] ).
cnf(c_0_5574,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_3812,
[final] ).
cnf(c_0_5575,plain,
( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk132_5(X2,X1,X3,X5,X4)),X4)) ),
c_0_3813,
[final] ).
cnf(c_0_5576,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,esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk92_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
c_0_3814,
[final] ).
cnf(c_0_5577,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_3815,
[final] ).
cnf(c_0_5578,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,esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk90_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
c_0_3816,
[final] ).
cnf(c_0_5579,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
c_0_3817,
[final] ).
cnf(c_0_5580,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
c_0_3818,
[final] ).
cnf(c_0_5581,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
c_0_3819,
[final] ).
cnf(c_0_5582,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
c_0_3820,
[final] ).
cnf(c_0_5583,plain,
( hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_3821,
[final] ).
cnf(c_0_5584,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3822,
[final] ).
cnf(c_0_5585,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)),X5)
| ~ semiring(X1) ),
c_0_3823,
[final] ).
cnf(c_0_5586,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_3824,
[final] ).
cnf(c_0_5587,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X6),X4),X5)) ),
c_0_3825,
[final] ).
cnf(c_0_5588,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
c_0_3826,
[final] ).
cnf(c_0_5589,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
c_0_3827,
[final] ).
cnf(c_0_5590,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
c_0_3828,
[final] ).
cnf(c_0_5591,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_3829,
[final] ).
cnf(c_0_5592,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),esk107_4(X3,X1,X4,X2)),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),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))) ),
c_0_3830,
[final] ).
cnf(c_0_5593,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)),X4),
c_0_3831,
[final] ).
cnf(c_0_5594,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_3832,
[final] ).
cnf(c_0_5595,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(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
c_0_3833,
[final] ).
cnf(c_0_5596,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_3834,
[final] ).
cnf(c_0_5597,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_3835,
[final] ).
cnf(c_0_5598,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
c_0_3836,
[final] ).
cnf(c_0_5599,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk125_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
c_0_3837,
[final] ).
cnf(c_0_5600,plain,
( 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),X4),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_3838,
[final] ).
cnf(c_0_5601,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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
c_0_3839,
[final] ).
cnf(c_0_5602,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_3840,
[final] ).
cnf(c_0_5603,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X2),fun(fun(X4,bool),bool),inj_on(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)) ),
c_0_3841,
[final] ).
cnf(c_0_5604,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_3842,
[final] ).
cnf(c_0_5605,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),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(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),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_3843,
[final] ).
cnf(c_0_5606,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6)) ),
c_0_3844,
[final] ).
cnf(c_0_5607,plain,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
c_0_3845,
[final] ).
cnf(c_0_5608,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3846,
[final] ).
cnf(c_0_5609,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_3847,
[final] ).
cnf(c_0_5610,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk11_1(X1))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk10_1(X1)))) ),
c_0_3848,
[final] ).
cnf(c_0_5611,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X4),X5))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
c_0_3849,
[final] ).
cnf(c_0_5612,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_3850,
[final] ).
cnf(c_0_5613,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_3851,
[final] ).
cnf(c_0_5614,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
c_0_3852,
[final] ).
cnf(c_0_5615,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_3853,
[final] ).
cnf(c_0_5616,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_3854,
[final] ).
cnf(c_0_5617,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_atLeastAtMost(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_eq(X1),X2),X3)) ),
c_0_3855,
[final] ).
cnf(c_0_5618,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_atLeastAtMost(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_eq(X1),X2),X3)) ),
c_0_3856,
[final] ).
cnf(c_0_5619,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_3857,
[final] ).
cnf(c_0_5620,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_3858,
[final] ).
cnf(c_0_5621,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_3859,
[final] ).
cnf(c_0_5622,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_3860,
[final] ).
cnf(c_0_5623,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_3861,
[final] ).
cnf(c_0_5624,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_3862,
[final] ).
cnf(c_0_5625,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_3863,
[final] ).
cnf(c_0_5626,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_3864,
[final] ).
cnf(c_0_5627,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr676655987ssThan(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)) ),
c_0_3865,
[final] ).
cnf(c_0_5628,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(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)) ),
c_0_3866,
[final] ).
cnf(c_0_5629,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr1471790799AtMost(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)) ),
c_0_3867,
[final] ).
cnf(c_0_5630,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(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)) ),
c_0_3868,
[final] ).
cnf(c_0_5631,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk145_5(X1,X2,X5,X3,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
c_0_3869,
[final] ).
cnf(c_0_5632,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
c_0_3870,
[final] ).
cnf(c_0_5633,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_3871,
[final] ).
cnf(c_0_5634,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk125_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_3872,
[final] ).
cnf(c_0_5635,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3873,
[final] ).
cnf(c_0_5636,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
c_0_3874,
[final] ).
cnf(c_0_5637,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
c_0_3875,
[final] ).
cnf(c_0_5638,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linordered_ring(X1) ),
c_0_3876,
[final] ).
cnf(c_0_5639,plain,
( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
| ~ 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)) ),
c_0_3877,
[final] ).
cnf(c_0_5640,plain,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
c_0_3878,
[final] ).
cnf(c_0_5641,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_3879,
[final] ).
cnf(c_0_5642,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_3880,
[final] ).
cnf(c_0_5643,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_3881,
[final] ).
cnf(c_0_5644,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_3882,
[final] ).
cnf(c_0_5645,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
c_0_3883,
[final] ).
cnf(c_0_5646,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
c_0_3884,
[final] ).
cnf(c_0_5647,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
c_0_3885,
[final] ).
cnf(c_0_5648,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
c_0_3886,
[final] ).
cnf(c_0_5649,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
c_0_3887,
[final] ).
cnf(c_0_5650,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
c_0_3888,
[final] ).
cnf(c_0_5651,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X2))) ),
c_0_3889,
[final] ).
cnf(c_0_5652,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk111_5(X3,X1,X4,X5,X2)),X5))
| ~ 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),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_3890,
[final] ).
cnf(c_0_5653,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| ~ 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_3891,
[final] ).
cnf(c_0_5654,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| ~ 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_3892,
[final] ).
cnf(c_0_5655,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_3893,
[final] ).
cnf(c_0_5656,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(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk131_5(X1,X2,X3,X5,X4)),X4)) ),
c_0_3894,
[final] ).
cnf(c_0_5657,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3895,
[final] ).
cnf(c_0_5658,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
c_0_3896,
[final] ).
cnf(c_0_5659,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_3897,
[final] ).
cnf(c_0_5660,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
c_0_3898,
[final] ).
cnf(c_0_5661,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_3899,
[final] ).
cnf(c_0_5662,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_3900,
[final] ).
cnf(c_0_5663,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_3901,
[final] ).
cnf(c_0_5664,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_3902,
[final] ).
cnf(c_0_5665,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_3903,
[final] ).
cnf(c_0_5666,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)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
c_0_3904,
[final] ).
cnf(c_0_5667,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)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
c_0_3905,
[final] ).
cnf(c_0_5668,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
c_0_3906,
[final] ).
cnf(c_0_5669,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
c_0_3907,
[final] ).
cnf(c_0_5670,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
c_0_3908,
[final] ).
cnf(c_0_5671,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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
c_0_3909,
[final] ).
cnf(c_0_5672,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_3910,
[final] ).
cnf(c_0_5673,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_3911,
[final] ).
cnf(c_0_5674,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
c_0_3912,
[final] ).
cnf(c_0_5675,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
c_0_3913,
[final] ).
cnf(c_0_5676,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,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
c_0_3914,
[final] ).
cnf(c_0_5677,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3))) ),
c_0_3915,
[final] ).
cnf(c_0_5678,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hAPP(X1,X2,X3,esk145_5(X1,X2,X5,X3,X4)) != hAPP(X1,X2,X5,esk145_5(X1,X2,X5,X3,X4)) ),
c_0_3916,
[final] ).
cnf(c_0_5679,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk109_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_3917,
[final] ).
cnf(c_0_5680,plain,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk103_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_3918,
[final] ).
cnf(c_0_5681,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
c_0_3919,
[final] ).
cnf(c_0_5682,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
c_0_3920,
[final] ).
cnf(c_0_5683,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
c_0_3921,
[final] ).
cnf(c_0_5684,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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)),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),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_3922,
[final] ).
cnf(c_0_5685,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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)),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),X2),X4))
| ~ ordered_semiring(X1) ),
c_0_3923,
[final] ).
cnf(c_0_5686,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ ordered_semiring(X1) ),
c_0_3924,
[final] ).
cnf(c_0_5687,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_3925,
[final] ).
cnf(c_0_5688,plain,
( 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),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
c_0_3926,
[final] ).
cnf(c_0_5689,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(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
c_0_3927,
[final] ).
cnf(c_0_5690,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),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
c_0_3928,
[final] ).
cnf(c_0_5691,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),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3))) ),
c_0_3929,
[final] ).
cnf(c_0_5692,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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_3930,
[final] ).
cnf(c_0_5693,plain,
( 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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_3931,
[final] ).
cnf(c_0_5694,plain,
( 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),X3),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
c_0_3932,
[final] ).
cnf(c_0_5695,plain,
( 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),X4),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_3933,
[final] ).
cnf(c_0_5696,plain,
( 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),X4),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
c_0_3934,
[final] ).
cnf(c_0_5697,plain,
( 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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_3935,
[final] ).
cnf(c_0_5698,plain,
( 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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
c_0_3936,
[final] ).
cnf(c_0_5699,plain,
( 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),X4),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_3937,
[final] ).
cnf(c_0_5700,plain,
( 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),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
c_0_3938,
[final] ).
cnf(c_0_5701,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_3939,
[final] ).
cnf(c_0_5702,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)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),X4) = ti(fun(X2,bool),X7)
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X5),X8) != ti(fun(X2,bool),X7)
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X4) != ti(fun(X3,bool),X8) ),
c_0_3940,
[final] ).
cnf(c_0_5703,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_3941,
[final] ).
cnf(c_0_5704,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_3942,
[final] ).
cnf(c_0_5705,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_3943,
[final] ).
cnf(c_0_5706,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_3944,
[final] ).
cnf(c_0_5707,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_3945,
[final] ).
cnf(c_0_5708,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_3946,
[final] ).
cnf(c_0_5709,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3))
| ~ comm_monoid_add(X1) ),
c_0_3947,
[final] ).
cnf(c_0_5710,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3948,
[final] ).
cnf(c_0_5711,plain,
( hBOOL(hAPP(X1,bool,X4,X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk108_5(X1,X2,X5,X4,X3)),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)))))
| ~ 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_3949,
[final] ).
cnf(c_0_5712,plain,
( hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X4),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))),X5))),X5) = ti(fun(X1,X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),top_top(fun(X1,bool)))) ),
c_0_3950,
[final] ).
cnf(c_0_5713,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk15_1(X1)))) ),
c_0_3951,
[final] ).
cnf(c_0_5714,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
c_0_3952,
[final] ).
cnf(c_0_5715,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
c_0_3953,
[final] ).
cnf(c_0_5716,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
c_0_3954,
[final] ).
cnf(c_0_5717,plain,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
c_0_3955,
[final] ).
cnf(c_0_5718,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X1),X2)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
c_0_3956,
[final] ).
cnf(c_0_5719,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X1),X2)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
c_0_3957,
[final] ).
cnf(c_0_5720,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,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4)) ),
c_0_3958,
[final] ).
cnf(c_0_5721,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
c_0_3959,
[final] ).
cnf(c_0_5722,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X4),top_top(fun(X3,bool)))) ),
c_0_3960,
[final] ).
cnf(c_0_5723,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_3961,
[final] ).
cnf(c_0_5724,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_3962,
[final] ).
cnf(c_0_5725,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_3963,
[final] ).
cnf(c_0_5726,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_3964,
[final] ).
cnf(c_0_5727,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_3965,
[final] ).
cnf(c_0_5728,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_3966,
[final] ).
cnf(c_0_5729,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_3967,
[final] ).
cnf(c_0_5730,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_3968,
[final] ).
cnf(c_0_5731,plain,
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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
c_0_3969,
[final] ).
cnf(c_0_5732,plain,
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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
c_0_3970,
[final] ).
cnf(c_0_5733,plain,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
c_0_3971,
[final] ).
cnf(c_0_5734,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_3972,
[final] ).
cnf(c_0_5735,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),X3)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
c_0_3973,
[final] ).
cnf(c_0_5736,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
c_0_3974,
[final] ).
cnf(c_0_5737,plain,
( 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
c_0_3975,
[final] ).
cnf(c_0_5738,plain,
( 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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
c_0_3976,
[final] ).
cnf(c_0_5739,plain,
( 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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
c_0_3977,
[final] ).
cnf(c_0_5740,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_3978,
[final] ).
cnf(c_0_5741,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_3979,
[final] ).
cnf(c_0_5742,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,esk43_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,esk43_4(X1,X2,X3,X4))))
| ~ ord(X2) ),
c_0_3980,
[final] ).
cnf(c_0_5743,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,esk30_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk30_4(X2,X1,X3,X4)))) ),
c_0_3981,
[final] ).
cnf(c_0_5744,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk166_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk167_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
c_0_3982,
[final] ).
cnf(c_0_5745,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)),the_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)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
c_0_3983,
[final] ).
cnf(c_0_5746,plain,
( hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X3),X4),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X5),X4)),X3)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)
| hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5) != ti(fun(X1,bool),X3) ),
c_0_3984,
[final] ).
cnf(c_0_5747,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
c_0_3985,
[final] ).
cnf(c_0_5748,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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_3986,
[final] ).
cnf(c_0_5749,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_3987,
[final] ).
cnf(c_0_5750,plain,
( 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_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
c_0_3988,
[final] ).
cnf(c_0_5751,plain,
( 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| ~ 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),X4),X2)) ),
c_0_3989,
[final] ).
cnf(c_0_5752,plain,
( 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X4),X2)) ),
c_0_3990,
[final] ).
cnf(c_0_5753,plain,
( 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
c_0_3991,
[final] ).
cnf(c_0_5754,plain,
( 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
c_0_3992,
[final] ).
cnf(c_0_5755,plain,
( 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
c_0_3993,
[final] ).
cnf(c_0_5756,plain,
( 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| ~ 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),X4),X2)) ),
c_0_3994,
[final] ).
cnf(c_0_5757,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ 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_3995,
[final] ).
cnf(c_0_5758,plain,
( ti(X1,X3) = ti(X1,X5)
| ti(X1,X2) = ti(X1,X4)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
c_0_3996,
[final] ).
cnf(c_0_5759,plain,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X4) = ti(X1,X5)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)) ),
c_0_3997,
[final] ).
cnf(c_0_5760,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),X4),X3)),X5)) = ti(fun(X2,bool),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X6) ),
c_0_3998,
[final] ).
cnf(c_0_5761,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
c_0_3999,
[final] ).
cnf(c_0_5762,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
c_0_4000,
[final] ).
cnf(c_0_5763,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(nat,X1,X2,X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ comm_monoid_add(X1) ),
c_0_4001,
[final] ).
cnf(c_0_5764,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X1)),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
c_0_4002,
[final] ).
cnf(c_0_5765,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_4003,
[final] ).
cnf(c_0_5766,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| 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),X4),X5)) ),
c_0_4004,
[final] ).
cnf(c_0_5767,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk135_3(X1,X2,X3)),X2)),X3)) ),
c_0_4005,
[final] ).
cnf(c_0_5768,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk170_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk171_4(X1,X2,X4,X5))) ),
c_0_4006,
[final] ).
cnf(c_0_5769,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk170_4(X1,X2,X4,X5))) ),
c_0_4007,
[final] ).
cnf(c_0_5770,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)) ),
c_0_4008,
[final] ).
cnf(c_0_5771,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk79_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_4009,
[final] ).
cnf(c_0_5772,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk79_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_4010,
[final] ).
cnf(c_0_5773,plain,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),esk111_5(X3,X1,X4,X5,X2)))
| ~ 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),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_4011,
[final] ).
cnf(c_0_5774,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
c_0_4012,
[final] ).
cnf(c_0_5775,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
c_0_4013,
[final] ).
cnf(c_0_5776,plain,
( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,X3)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X3)) ),
c_0_4014,
[final] ).
cnf(c_0_5777,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
c_0_4015,
[final] ).
cnf(c_0_5778,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ linord893533164strict(X1) ),
c_0_4016,
[final] ).
cnf(c_0_5779,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ linord20386208strict(X1) ),
c_0_4017,
[final] ).
cnf(c_0_5780,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_4018,
[final] ).
cnf(c_0_5781,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
c_0_4019,
[final] ).
cnf(c_0_5782,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
c_0_4020,
[final] ).
cnf(c_0_5783,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X3)) ),
c_0_4021,
[final] ).
cnf(c_0_5784,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ ordere1490568538miring(X1) ),
c_0_4022,
[final] ).
cnf(c_0_5785,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ ordered_semiring(X1) ),
c_0_4023,
[final] ).
cnf(c_0_5786,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X2),X4))
| ~ ordered_semiring(X1) ),
c_0_4024,
[final] ).
cnf(c_0_5787,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4),X3)) ),
c_0_4025,
[final] ).
cnf(c_0_5788,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3))
| ~ linord581940658strict(X1) ),
c_0_4026,
[final] ).
cnf(c_0_5789,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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),X4),X2))
| ~ linord581940658strict(X1) ),
c_0_4027,
[final] ).
cnf(c_0_5790,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4),X3)) ),
c_0_4028,
[final] ).
cnf(c_0_5791,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1))) ),
c_0_4029,
[final] ).
cnf(c_0_5792,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
c_0_4030,
[final] ).
cnf(c_0_5793,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3))
| ~ ordered_ring(X1) ),
c_0_4031,
[final] ).
cnf(c_0_5794,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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),X4),X2))
| ~ ordered_ring(X1) ),
c_0_4032,
[final] ).
cnf(c_0_5795,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk166_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,esk167_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
c_0_4033,
[final] ).
cnf(c_0_5796,plain,
( hBOOL(hAPP(X1,bool,X2,esk166_4(X1,X2,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk167_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
c_0_4034,
[final] ).
cnf(c_0_5797,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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))
| ~ semilattice_inf(X1) ),
c_0_4035,
[final] ).
cnf(c_0_5798,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(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))
| ~ semilattice_sup(X1) ),
c_0_4036,
[final] ).
cnf(c_0_5799,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_4037,
[final] ).
cnf(c_0_5800,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_4038,
[final] ).
cnf(c_0_5801,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_4039,
[final] ).
cnf(c_0_5802,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_4040,
[final] ).
cnf(c_0_5803,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_4041,
[final] ).
cnf(c_0_5804,plain,
( 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))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
c_0_4042,
[final] ).
cnf(c_0_5805,plain,
( 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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
c_0_4043,
[final] ).
cnf(c_0_5806,plain,
( 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),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
c_0_4044,
[final] ).
cnf(c_0_5807,plain,
( 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)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
c_0_4045,
[final] ).
cnf(c_0_5808,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
c_0_4046,
[final] ).
cnf(c_0_5809,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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_eq(nat),X2),X3)) ),
c_0_4047,
[final] ).
cnf(c_0_5810,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),zero_zero(nat)),X1)) ),
c_0_4048,
[final] ).
cnf(c_0_5811,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ 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),zero_zero(nat)),X2)) ),
c_0_4049,
[final] ).
cnf(c_0_5812,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ 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),X1),X3)) ),
c_0_4050,
[final] ).
cnf(c_0_5813,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
c_0_4051,
[final] ).
cnf(c_0_5814,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_4052,
[final] ).
cnf(c_0_5815,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_4053,
[final] ).
cnf(c_0_5816,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_4054,
[final] ).
cnf(c_0_5817,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
c_0_4055,
[final] ).
cnf(c_0_5818,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
c_0_4056,
[final] ).
cnf(c_0_5819,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
c_0_4057,
[final] ).
cnf(c_0_5820,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(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))
| ~ linordered_idom(X1) ),
c_0_4058,
[final] ).
cnf(c_0_5821,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(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))
| ~ linordered_idom(X1) ),
c_0_4059,
[final] ).
cnf(c_0_5822,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_4060,
[final] ).
cnf(c_0_5823,plain,
( hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk154_1(X1)),X2)) = hAPP(nat,nat,X1,esk154_1(X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,hAPP(nat,nat,suc,esk153_1(X1)))),hAPP(nat,nat,X1,esk153_1(X1)))) ),
c_0_4061,
[final] ).
cnf(c_0_5824,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,esk171_4(X1,X2,X4,X5))) ),
c_0_4062,
[final] ).
cnf(c_0_5825,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
c_0_4063,
[final] ).
cnf(c_0_5826,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
c_0_4064,
[final] ).
cnf(c_0_5827,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_4065,
[final] ).
cnf(c_0_5828,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_4066,
[final] ).
cnf(c_0_5829,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
c_0_4067,
[final] ).
cnf(c_0_5830,plain,
( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk111_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2)
| ~ 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),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_4068,
[final] ).
cnf(c_0_5831,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
c_0_4069,
[final] ).
cnf(c_0_5832,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
c_0_4070,
[final] ).
cnf(c_0_5833,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
c_0_4071,
[final] ).
cnf(c_0_5834,plain,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
c_0_4072,
[final] ).
cnf(c_0_5835,plain,
( 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_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
c_0_4073,
[final] ).
cnf(c_0_5836,plain,
( 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_atLeastAtMost(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_eq(X1),X2),X3))
| ~ dense_linorder(X1) ),
c_0_4074,
[final] ).
cnf(c_0_5837,plain,
( 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_4075,
[final] ).
cnf(c_0_5838,plain,
( 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
c_0_4076,
[final] ).
cnf(c_0_5839,plain,
( 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
c_0_4077,
[final] ).
cnf(c_0_5840,plain,
( 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_gr676655987ssThan(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))
| ~ dense_linorder(X1) ),
c_0_4078,
[final] ).
cnf(c_0_5841,plain,
( 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_gr1471790799AtMost(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))
| ~ dense_linorder(X1) ),
c_0_4079,
[final] ).
cnf(c_0_5842,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)))) ),
c_0_4080,
[final] ).
cnf(c_0_5843,plain,
( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)) = hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)
| ~ hBOOL(hAPP(fun(fun(X3,bool),fun(X2,X2)),bool,hAPP(fun(X3,fun(X2,X2)),fun(fun(fun(X3,bool),fun(X2,X2)),bool),finite_folding_idem(X3,X2),X4),X7)) ),
c_0_4081,
[final] ).
cnf(c_0_5844,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
| hAPP(X2,X1,X5,hAPP(X1,X2,X3,esk69_5(X2,X1,X5,X3,X4))) != ti(X1,esk69_5(X2,X1,X5,X3,X4)) ),
c_0_4082,
[final] ).
cnf(c_0_5845,plain,
( ti(X1,X5) = ti(X1,esk104_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))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
c_0_4083,
[final] ).
cnf(c_0_5846,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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(X1,fun(fun(X1,bool),bool),member(X1),X4),X5)) ),
c_0_4084,
[final] ).
cnf(c_0_5847,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X5))
| ~ comm_semiring_1(X1) ),
c_0_4085,
[final] ).
cnf(c_0_5848,plain,
( hBOOL(hAPP(X1,bool,X4,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
c_0_4086,
[final] ).
cnf(c_0_5849,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5)) = ti(fun(X2,bool),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),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_4087,
[final] ).
cnf(c_0_5850,plain,
( hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)),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),X3))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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_4088,
[final] ).
cnf(c_0_5851,plain,
( hAPP(X1,X2,X3,esk104_4(X1,X2,X4,X3)) = ti(X2,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))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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))))) ),
c_0_4089,
[final] ).
cnf(c_0_5852,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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)) ),
c_0_4090,
[final] ).
cnf(c_0_5853,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_4091,
[final] ).
cnf(c_0_5854,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_4092,
[final] ).
cnf(c_0_5855,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_4093,
[final] ).
cnf(c_0_5856,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
c_0_4094,
[final] ).
cnf(c_0_5857,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
c_0_4095,
[final] ).
cnf(c_0_5858,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
c_0_4096,
[final] ).
cnf(c_0_5859,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
c_0_4097,
[final] ).
cnf(c_0_5860,plain,
( ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5) ),
c_0_4098,
[final] ).
cnf(c_0_5861,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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(X2,X4) != hAPP(X1,X2,X3,X5)
| ti(X1,esk105_5(X1,X2,X4,X3,X5)) != ti(X1,X5) ),
c_0_4099,
[final] ).
cnf(c_0_5862,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_4100,
[final] ).
cnf(c_0_5863,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_4101,
[final] ).
cnf(c_0_5864,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4),
c_0_4102,
[final] ).
cnf(c_0_5865,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4),
c_0_4103,
[final] ).
cnf(c_0_5866,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)),top_top(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),top_top(fun(X2,bool))) != top_top(fun(X1,bool)) ),
c_0_4104,
[final] ).
cnf(c_0_5867,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4105,
[final] ).
cnf(c_0_5868,plain,
( hBOOL(hAPP(X1,bool,X2,esk166_4(X1,X2,X4,X5)))
| hBOOL(hAPP(X1,bool,X2,esk167_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
c_0_4106,
[final] ).
cnf(c_0_5869,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
c_0_4107,
[final] ).
cnf(c_0_5870,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
c_0_4108,
[final] ).
cnf(c_0_5871,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
c_0_4109,
[final] ).
cnf(c_0_5872,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_4110,
[final] ).
cnf(c_0_5873,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_4111,
[final] ).
cnf(c_0_5874,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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
c_0_4112,
[final] ).
cnf(c_0_5875,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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
c_0_4113,
[final] ).
cnf(c_0_5876,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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1)),X2)) ),
c_0_4114,
[final] ).
cnf(c_0_5877,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_4115,
[final] ).
cnf(c_0_5878,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_4116,
[final] ).
cnf(c_0_5879,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_4117,
[final] ).
cnf(c_0_5880,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_4118,
[final] ).
cnf(c_0_5881,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_4119,
[final] ).
cnf(c_0_5882,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_4120,
[final] ).
cnf(c_0_5883,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_4121,
[final] ).
cnf(c_0_5884,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_4122,
[final] ).
cnf(c_0_5885,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_4123,
[final] ).
cnf(c_0_5886,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_4124,
[final] ).
cnf(c_0_5887,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_4125,
[final] ).
cnf(c_0_5888,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_4126,
[final] ).
cnf(c_0_5889,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_4127,
[final] ).
cnf(c_0_5890,plain,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk134_5(X2,X1,X3,X5,X4)),X4)) ),
c_0_4128,
[final] ).
cnf(c_0_5891,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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(X1,fun(fun(X1,bool),bool),member(X1),esk172_3(X1,X3,X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)) ),
c_0_4129,
[final] ).
cnf(c_0_5892,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X3),X4)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
c_0_4130,
[final] ).
cnf(c_0_5893,plain,
( hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X3,X1),fun(X3,X1),hAPP(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),combb(X1,X1,X3),hAPP(X1,fun(X1,X1),times_times(X1),X2)),X4)),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X4),X5))
| ~ semiring_0(X1) ),
c_0_4131,
[final] ).
cnf(c_0_5894,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk136_4(X2,X1,X4,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
c_0_4132,
[final] ).
cnf(c_0_5895,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,esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk79_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_4133,
[final] ).
cnf(c_0_5896,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,esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk79_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_4134,
[final] ).
cnf(c_0_5897,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_5(X2,X1,X5,X3,X4)),X4)) ),
c_0_4135,
[final] ).
cnf(c_0_5898,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4)))
| ~ comm_monoid_add(X1) ),
c_0_4136,
[final] ).
cnf(c_0_5899,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4)))
| ~ comm_monoid_add(X1) ),
c_0_4137,
[final] ).
cnf(c_0_5900,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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)),X2),X3)) ),
c_0_4138,
[final] ).
cnf(c_0_5901,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_4139,
[final] ).
cnf(c_0_5902,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_4140,
[final] ).
cnf(c_0_5903,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_4141,
[final] ).
cnf(c_0_5904,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_4142,
[final] ).
cnf(c_0_5905,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_4143,
[final] ).
cnf(c_0_5906,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_4144,
[final] ).
cnf(c_0_5907,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_4145,
[final] ).
cnf(c_0_5908,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_4146,
[final] ).
cnf(c_0_5909,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),esk107_4(X3,X1,X4,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),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))) ),
c_0_4147,
[final] ).
cnf(c_0_5910,plain,
hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
c_0_4148,
[final] ).
cnf(c_0_5911,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_4149,
[final] ).
cnf(c_0_5912,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
c_0_4150,
[final] ).
cnf(c_0_5913,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
c_0_4151,
[final] ).
cnf(c_0_5914,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
c_0_4152,
[final] ).
cnf(c_0_5915,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
| ~ linord20386208strict(X1) ),
c_0_4153,
[final] ).
cnf(c_0_5916,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2))
| ~ linord20386208strict(X1) ),
c_0_4154,
[final] ).
cnf(c_0_5917,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(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),zero_zero(X1)),X2)) ),
c_0_4155,
[final] ).
cnf(c_0_5918,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(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),zero_zero(X1))) ),
c_0_4156,
[final] ).
cnf(c_0_5919,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),X2),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
c_0_4157,
[final] ).
cnf(c_0_5920,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1) ),
c_0_4158,
[final] ).
cnf(c_0_5921,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2))
| ~ ordere453448008miring(X1) ),
c_0_4159,
[final] ).
cnf(c_0_5922,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
c_0_4160,
[final] ).
cnf(c_0_5923,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1))) ),
c_0_4161,
[final] ).
cnf(c_0_5924,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_4162,
[final] ).
cnf(c_0_5925,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_4163,
[final] ).
cnf(c_0_5926,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_4164,
[final] ).
cnf(c_0_5927,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_4165,
[final] ).
cnf(c_0_5928,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4))
| ~ semilattice_sup(X1) ),
c_0_4166,
[final] ).
cnf(c_0_5929,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4))
| ~ semilattice_sup(X1) ),
c_0_4167,
[final] ).
cnf(c_0_5930,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(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),X2),X4)) ),
c_0_4168,
[final] ).
cnf(c_0_5931,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
c_0_4169,
[final] ).
cnf(c_0_5932,plain,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| hAPP(X1,X2,X3,esk105_5(X1,X2,X4,X3,X5)) = ti(X2,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))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
c_0_4170,
[final] ).
cnf(c_0_5933,plain,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
c_0_4171,
[final] ).
cnf(c_0_5934,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(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),X2,hAPP(fun(X4,X2),fun(fun(X4,bool),X2),big_co1399186613setsum(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
| ~ comm_monoid_add(X2) ),
c_0_4172,
[final] ).
cnf(c_0_5935,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))
| ~ 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_4173,
[final] ).
cnf(c_0_5936,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),zero_zero(X1)))
| ~ linordered_ring(X1) ),
c_0_4174,
[final] ).
cnf(c_0_5937,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ 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_eq(X1),X2),X3))
| ~ linorder(X1) ),
c_0_4175,
[final] ).
cnf(c_0_5938,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ 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))
| ~ linorder(X1) ),
c_0_4176,
[final] ).
cnf(c_0_5939,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
c_0_4177,
[final] ).
cnf(c_0_5940,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
c_0_4178,
[final] ).
cnf(c_0_5941,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
c_0_4179,
[final] ).
cnf(c_0_5942,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
c_0_4180,
[final] ).
cnf(c_0_5943,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ 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_eq(X1),X2),X3))
| ~ linorder(X1) ),
c_0_4181,
[final] ).
cnf(c_0_5944,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ 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))
| ~ linorder(X1) ),
c_0_4182,
[final] ).
cnf(c_0_5945,plain,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(fun(X2,bool),fun(X1,X1),X3,X5)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X6),X3)) ),
c_0_4183,
[final] ).
cnf(c_0_5946,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk15_1(X1),X2))) ),
c_0_4184,
[final] ).
cnf(c_0_5947,plain,
( hAPP(X3,X1,X4,esk109_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_4185,
[final] ).
cnf(c_0_5948,plain,
( hAPP(X3,X1,X4,esk103_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_4186,
[final] ).
cnf(c_0_5949,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4))))
| ~ hBOOL(hAPP(X1,bool,X4,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
c_0_4187,
[final] ).
cnf(c_0_5950,plain,
( hAPP(fun(X1,bool),fun(X2,X2),X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X3,X4)),hAPP(fun(X1,bool),fun(X2,X2),X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X6),X3)) ),
c_0_4188,
[final] ).
cnf(c_0_5951,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X3),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
c_0_4189,
[final] ).
cnf(c_0_5952,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_4190,
[final] ).
cnf(c_0_5953,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
c_0_4191,
[final] ).
cnf(c_0_5954,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_4192,
[final] ).
cnf(c_0_5955,plain,
( 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),esk117_4(X3,X1,X4,X2)),X2))
| ~ 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),X4),X2))) ),
c_0_4193,
[final] ).
cnf(c_0_5956,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_4194,
[final] ).
cnf(c_0_5957,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_4195,
[final] ).
cnf(c_0_5958,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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)) ),
c_0_4196,
[final] ).
cnf(c_0_5959,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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)) ),
c_0_4197,
[final] ).
cnf(c_0_5960,plain,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X5,X6)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X5),X3)) ),
c_0_4198,
[final] ).
cnf(c_0_5961,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk168_4(X1,X2,X4,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
c_0_4199,
[final] ).
cnf(c_0_5962,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk168_4(X1,X2,X5,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
c_0_4200,
[final] ).
cnf(c_0_5963,plain,
( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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_4201,
[final] ).
cnf(c_0_5964,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
c_0_4202,
[final] ).
cnf(c_0_5965,plain,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
c_0_4203,
[final] ).
cnf(c_0_5966,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
c_0_4204,
[final] ).
cnf(c_0_5967,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X3))) ),
c_0_4205,
[final] ).
cnf(c_0_5968,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
c_0_4206,
[final] ).
cnf(c_0_5969,plain,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
c_0_4207,
[final] ).
cnf(c_0_5970,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_4208,
[final] ).
cnf(c_0_5971,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_4209,
[final] ).
cnf(c_0_5972,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_4210,
[final] ).
cnf(c_0_5973,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
c_0_4211,
[final] ).
cnf(c_0_5974,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
c_0_4212,
[final] ).
cnf(c_0_5975,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),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,finite_finite_1(X3),X5)) ),
c_0_4213,
[final] ).
cnf(c_0_5976,plain,
( 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),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
c_0_4214,
[final] ).
cnf(c_0_5977,plain,
( 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),times_times(X1),X3),X2)))
| ~ linord20386208strict(X1) ),
c_0_4215,
[final] ).
cnf(c_0_5978,plain,
( hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6),X7) = hAPP(X3,X2,X5,hAPP(X1,X3,X6,X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X4)) ),
c_0_4216,
[final] ).
cnf(c_0_5979,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),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_4217,
[final] ).
cnf(c_0_5980,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),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_4218,
[final] ).
cnf(c_0_5981,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_4219,
[final] ).
cnf(c_0_5982,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
c_0_4220,
[final] ).
cnf(c_0_5983,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
c_0_4221,
[final] ).
cnf(c_0_5984,plain,
( 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))
| ~ 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),X4),X2))) ),
c_0_4222,
[final] ).
cnf(c_0_5985,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_4223,
[final] ).
cnf(c_0_5986,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X2)),
c_0_4224,
[final] ).
cnf(c_0_5987,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X3)),
c_0_4225,
[final] ).
cnf(c_0_5988,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(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_4226,
[final] ).
cnf(c_0_5989,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_4227,
[final] ).
cnf(c_0_5990,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_4228,
[final] ).
cnf(c_0_5991,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X4) ),
c_0_4229,
[final] ).
cnf(c_0_5992,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X5) ),
c_0_4230,
[final] ).
cnf(c_0_5993,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X4) ),
c_0_4231,
[final] ).
cnf(c_0_5994,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X5) ),
c_0_4232,
[final] ).
cnf(c_0_5995,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5))
| ~ comm_semiring_1(X1) ),
c_0_4233,
[final] ).
cnf(c_0_5996,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ comm_semiring_1(X1) ),
c_0_4234,
[final] ).
cnf(c_0_5997,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_4235,
[final] ).
cnf(c_0_5998,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_4236,
[final] ).
cnf(c_0_5999,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),X3)) = ti(fun(X2,bool),X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
c_0_4237,
[final] ).
cnf(c_0_6000,plain,
( hAPP(X3,X1,X4,esk116_4(X1,X3,X2,X4)) = 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),top_top(fun(X3,bool))))) ),
c_0_4238,
[final] ).
cnf(c_0_6001,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,esk136_4(X2,X1,X4,X3)) != one_one(X1) ),
c_0_4239,
[final] ).
cnf(c_0_6002,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
c_0_4240,
[final] ).
cnf(c_0_6003,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
c_0_4241,
[final] ).
cnf(c_0_6004,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
c_0_4242,
[final] ).
cnf(c_0_6005,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk163_2(X1,X3)),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
c_0_4243,
[final] ).
cnf(c_0_6006,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk115_2(X1,X3)),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
c_0_4244,
[final] ).
cnf(c_0_6007,plain,
( 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),X2),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
c_0_4245,
[final] ).
cnf(c_0_6008,plain,
( 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),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
c_0_4246,
[final] ).
cnf(c_0_6009,plain,
( 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),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
c_0_4247,
[final] ).
cnf(c_0_6010,plain,
( 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),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
c_0_4248,
[final] ).
cnf(c_0_6011,plain,
( 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(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),top_top(fun(X1,bool))),X3),esk106_3(X1,X2,X3))) != ti(X2,esk106_3(X1,X2,X3)) ),
c_0_4249,
[final] ).
cnf(c_0_6012,plain,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X3),zero_zero(X2)),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_4250,
[final] ).
cnf(c_0_6013,plain,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),plus_plus(X1)),X3),zero_zero(X1)),X4) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
c_0_4251,
[final] ).
cnf(c_0_6014,plain,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4)
| hAPP(X1,X2,X3,esk134_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X5,esk134_5(X2,X1,X3,X5,X4)) ),
c_0_4252,
[final] ).
cnf(c_0_6015,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_4253,
[final] ).
cnf(c_0_6016,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_4254,
[final] ).
cnf(c_0_6017,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_4255,
[final] ).
cnf(c_0_6018,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk164_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
c_0_4256,
[final] ).
cnf(c_0_6019,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk112_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
c_0_4257,
[final] ).
cnf(c_0_6020,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ semilattice_inf(X1) ),
c_0_4258,
[final] ).
cnf(c_0_6021,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ semilattice_inf(X1) ),
c_0_4259,
[final] ).
cnf(c_0_6022,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1) ),
c_0_4260,
[final] ).
cnf(c_0_6023,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_inf(X1) ),
c_0_4261,
[final] ).
cnf(c_0_6024,plain,
hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),hAPP(fun(X1,X5),fun(X1,X2),hAPP(fun(X5,X2),fun(fun(X1,X5),fun(X1,X2)),comp(X5,X2,X1),X6),X7)) = hAPP(fun(X1,X5),fun(X1,X3),hAPP(fun(X5,X3),fun(fun(X1,X5),fun(X1,X3)),comp(X5,X3,X1),hAPP(fun(X5,X2),fun(X5,X3),hAPP(fun(X2,X3),fun(fun(X5,X2),fun(X5,X3)),comp(X2,X3,X5),X4),X6)),X7),
c_0_4262,
[final] ).
cnf(c_0_6025,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_4263,
[final] ).
cnf(c_0_6026,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_4264,
[final] ).
cnf(c_0_6027,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_4265,
[final] ).
cnf(c_0_6028,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_4266,
[final] ).
cnf(c_0_6029,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_4267,
[final] ).
cnf(c_0_6030,plain,
hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),X6) = hAPP(fun(X1,bool),fun(X1,X3),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X1,X3)),restrict(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X5),X6)),X4),
c_0_4268,
[final] ).
cnf(c_0_6031,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,esk57_4(X2,X1,X4,X3)),esk58_4(X2,X1,X4,X3))) ),
c_0_4269,
[final] ).
cnf(c_0_6032,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)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),top_top(fun(X3,bool))) != top_top(fun(X2,bool))
| 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))) != top_top(fun(X3,bool)) ),
c_0_4270,
[final] ).
cnf(c_0_6033,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(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),ord_atLeast(X1),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
c_0_4271,
[final] ).
cnf(c_0_6034,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ 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),ord_greaterThan(X1),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
c_0_4272,
[final] ).
cnf(c_0_6035,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk18_2(X1,X2)),arrow_301600364e_Prof)) ),
c_0_4273,
[final] ).
cnf(c_0_6036,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_4274,
[final] ).
cnf(c_0_6037,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ linord20386208strict(X1) ),
c_0_4275,
[final] ).
cnf(c_0_6038,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),times_times(X1),X2),X3)))
| ~ ordered_ring(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)) ),
c_0_4276,
[final] ).
cnf(c_0_6039,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),times_times(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))
| ~ ordere453448008miring(X1) ),
c_0_4277,
[final] ).
cnf(c_0_6040,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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)) ),
c_0_4278,
[final] ).
cnf(c_0_6041,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_4279,
[final] ).
cnf(c_0_6042,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_4280,
[final] ).
cnf(c_0_6043,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_4281,
[final] ).
cnf(c_0_6044,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_4282,
[final] ).
cnf(c_0_6045,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_4283,
[final] ).
cnf(c_0_6046,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ 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)))
| ~ linord581940658strict(X1) ),
c_0_4284,
[final] ).
cnf(c_0_6047,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),times_times(X1),X2),X3)))
| ~ ordered_ring(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))) ),
c_0_4285,
[final] ).
cnf(c_0_6048,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),times_times(X1),X2),X3)))
| ~ 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)))
| ~ ordered_ring(X1) ),
c_0_4286,
[final] ).
cnf(c_0_6049,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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))) ),
c_0_4287,
[final] ).
cnf(c_0_6050,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),esk27_2(X1,X2))) ),
c_0_4288,
[final] ).
cnf(c_0_6051,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_4289,
[final] ).
cnf(c_0_6052,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_4290,
[final] ).
cnf(c_0_6053,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_4291,
[final] ).
cnf(c_0_6054,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_4292,
[final] ).
cnf(c_0_6055,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_4293,
[final] ).
cnf(c_0_6056,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(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),X2),X3)) ),
c_0_4294,
[final] ).
cnf(c_0_6057,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3))
| ~ semilattice_inf(X1) ),
c_0_4295,
[final] ).
cnf(c_0_6058,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3))
| ~ semilattice_inf(X1) ),
c_0_4296,
[final] ).
cnf(c_0_6059,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),esk100_3(X1,X2,X3)))) ),
c_0_4297,
[final] ).
cnf(c_0_6060,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),esk20_0)),
c_0_4298,
[final] ).
cnf(c_0_6061,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),esk19_0)),
c_0_4299,
[final] ).
cnf(c_0_6062,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
c_0_4300,
[final] ).
cnf(c_0_6063,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
c_0_4301,
[final] ).
cnf(c_0_6064,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)),comp(X3,X2,X1),X4),X5)),X6) = 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),X6)),
c_0_4302,
[final] ).
cnf(c_0_6065,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_4303,
[final] ).
cnf(c_0_6066,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk164_2(X1,X3))) ),
c_0_4304,
[final] ).
cnf(c_0_6067,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,esk112_2(X1,X3))) ),
c_0_4305,
[final] ).
cnf(c_0_6068,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_4306,
[final] ).
cnf(c_0_6069,plain,
( hBOOL(hAPP(nat,bool,X1,esk163_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
c_0_4307,
[final] ).
cnf(c_0_6070,plain,
( hBOOL(hAPP(nat,bool,X1,esk115_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
c_0_4308,
[final] ).
cnf(c_0_6071,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_4309,
[final] ).
cnf(c_0_6072,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_4310,
[final] ).
cnf(c_0_6073,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_4311,
[final] ).
cnf(c_0_6074,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_4312,
[final] ).
cnf(c_0_6075,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)
| ~ distrib_lattice(X1) ),
c_0_4313,
[final] ).
cnf(c_0_6076,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4)
| ~ distrib_lattice(X1) ),
c_0_4314,
[final] ).
cnf(c_0_6077,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
| ~ comm_semiring(X1) ),
c_0_4315,
[final] ).
cnf(c_0_6078,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
| ~ comm_semiring_1(X1) ),
c_0_4316,
[final] ).
cnf(c_0_6079,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
c_0_4317,
[final] ).
cnf(c_0_6080,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ 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)) ),
c_0_4318,
[final] ).
cnf(c_0_6081,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_4319,
[final] ).
cnf(c_0_6082,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_4320,
[final] ).
cnf(c_0_6083,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_4321,
[final] ).
cnf(c_0_6084,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk176_4(X1,X3,X2,X4)),X2))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat)) ),
c_0_4322,
[final] ).
cnf(c_0_6085,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_4323,
[final] ).
cnf(c_0_6086,plain,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| ~ 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_4324,
[final] ).
cnf(c_0_6087,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_4325,
[final] ).
cnf(c_0_6088,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_4326,
[final] ).
cnf(c_0_6089,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
c_0_4327,
[final] ).
cnf(c_0_6090,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
c_0_4328,
[final] ).
cnf(c_0_6091,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_4329,
[final] ).
cnf(c_0_6092,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
c_0_4330,
[final] ).
cnf(c_0_6093,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
c_0_4331,
[final] ).
cnf(c_0_6094,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
c_0_4332,
[final] ).
cnf(c_0_6095,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
c_0_4333,
[final] ).
cnf(c_0_6096,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3),
c_0_4334,
[final] ).
cnf(c_0_6097,plain,
( 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)))
| ~ ring_char_0(X1) ),
c_0_4335,
[final] ).
cnf(c_0_6098,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3)) ),
c_0_4336,
[final] ).
cnf(c_0_6099,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_4337,
[final] ).
cnf(c_0_6100,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_4338,
[final] ).
cnf(c_0_6101,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
c_0_4339,
[final] ).
cnf(c_0_6102,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
c_0_4340,
[final] ).
cnf(c_0_6103,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
c_0_4341,
[final] ).
cnf(c_0_6104,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
c_0_4342,
[final] ).
cnf(c_0_6105,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_4343,
[final] ).
cnf(c_0_6106,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X4,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3)) ),
c_0_4344,
[final] ).
cnf(c_0_6107,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_4345,
[final] ).
cnf(c_0_6108,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_4346,
[final] ).
cnf(c_0_6109,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_4347,
[final] ).
cnf(c_0_6110,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_4348,
[final] ).
cnf(c_0_6111,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_4349,
[final] ).
cnf(c_0_6112,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_4350,
[final] ).
cnf(c_0_6113,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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))
| hAPP(X2,X1,X4,X6) != ti(X1,X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
c_0_4351,
[final] ).
cnf(c_0_6114,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_4352,
[final] ).
cnf(c_0_6115,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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
c_0_4353,
[final] ).
cnf(c_0_6116,plain,
( 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),times_times(nat),X1),X2))) ),
c_0_4354,
[final] ).
cnf(c_0_6117,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk178_4(X1,X3,X2,X4)),X2))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat) ),
c_0_4355,
[final] ).
cnf(c_0_6118,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
c_0_4356,
[final] ).
cnf(c_0_6119,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
c_0_4357,
[final] ).
cnf(c_0_6120,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_4358,
[final] ).
cnf(c_0_6121,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
c_0_4359,
[final] ).
cnf(c_0_6122,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
c_0_4360,
[final] ).
cnf(c_0_6123,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_4361,
[final] ).
cnf(c_0_6124,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_4362,
[final] ).
cnf(c_0_6125,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_4363,
[final] ).
cnf(c_0_6126,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_4364,
[final] ).
cnf(c_0_6127,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_4365,
[final] ).
cnf(c_0_6128,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_4366,
[final] ).
cnf(c_0_6129,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk162_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_4367,
[final] ).
cnf(c_0_6130,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk114_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
c_0_4368,
[final] ).
cnf(c_0_6131,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4),X3)) ),
c_0_4369,
[final] ).
cnf(c_0_6132,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2),X3)) ),
c_0_4370,
[final] ).
cnf(c_0_6133,plain,
( hBOOL(hAPP(X1,bool,X2,X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
c_0_4371,
[final] ).
cnf(c_0_6134,plain,
( hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
c_0_4372,
[final] ).
cnf(c_0_6135,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_4373,
[final] ).
cnf(c_0_6136,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_4374,
[final] ).
cnf(c_0_6137,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_4375,
[final] ).
cnf(c_0_6138,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_4376,
[final] ).
cnf(c_0_6139,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_4377,
[final] ).
cnf(c_0_6140,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_4378,
[final] ).
cnf(c_0_6141,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk165_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_4379,
[final] ).
cnf(c_0_6142,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk113_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
c_0_4380,
[final] ).
cnf(c_0_6143,plain,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(X2,fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X3,X4)) = hAPP(X2,fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X3),X5)) ),
c_0_4381,
[final] ).
cnf(c_0_6144,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
c_0_4382,
[final] ).
cnf(c_0_6145,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
c_0_4383,
[final] ).
cnf(c_0_6146,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
c_0_4384,
[final] ).
cnf(c_0_6147,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
c_0_4385,
[final] ).
cnf(c_0_6148,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_4386,
[final] ).
cnf(c_0_6149,plain,
( hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X7,X2,hAPP(fun(X7,X8),fun(X7,X2),hAPP(fun(X8,X2),fun(fun(X7,X8),fun(X7,X2)),comp(X8,X2,X7),X9),X10),X11)
| hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)) != hAPP(X8,X2,X9,hAPP(X7,X8,X10,X11)) ),
c_0_4387,
[final] ).
cnf(c_0_6150,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))),X3)
| ~ comm_semiring_1(X1) ),
c_0_4388,
[final] ).
cnf(c_0_6151,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ distrib_lattice(X1) ),
c_0_4389,
[final] ).
cnf(c_0_6152,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ distrib_lattice(X1) ),
c_0_4390,
[final] ).
cnf(c_0_6153,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
c_0_4391,
[final] ).
cnf(c_0_6154,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
c_0_4392,
[final] ).
cnf(c_0_6155,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_4393,
[final] ).
cnf(c_0_6156,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
| ~ lattice(X1) ),
c_0_4394,
[final] ).
cnf(c_0_6157,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
| ~ semilattice_inf(X1) ),
c_0_4395,
[final] ).
cnf(c_0_6158,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
| ~ lattice(X1) ),
c_0_4396,
[final] ).
cnf(c_0_6159,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
| ~ semilattice_inf(X1) ),
c_0_4397,
[final] ).
cnf(c_0_6160,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_4398,
[final] ).
cnf(c_0_6161,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_4399,
[final] ).
cnf(c_0_6162,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_4400,
[final] ).
cnf(c_0_6163,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_4401,
[final] ).
cnf(c_0_6164,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_4402,
[final] ).
cnf(c_0_6165,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_4403,
[final] ).
cnf(c_0_6166,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_4404,
[final] ).
cnf(c_0_6167,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_4405,
[final] ).
cnf(c_0_6168,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_4406,
[final] ).
cnf(c_0_6169,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk15_1(X1)),arrow_301600364e_Prof)) ),
c_0_4407,
[final] ).
cnf(c_0_6170,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk10_1(X1)),arrow_301600364e_Prof)) ),
c_0_4408,
[final] ).
cnf(c_0_6171,plain,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk11_1(X1)),arrow_301600364e_Prof)) ),
c_0_4409,
[final] ).
cnf(c_0_6172,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_4410,
[final] ).
cnf(c_0_6173,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_4411,
[final] ).
cnf(c_0_6174,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_4412,
[final] ).
cnf(c_0_6175,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_4413,
[final] ).
cnf(c_0_6176,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_4414,
[final] ).
cnf(c_0_6177,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_4415,
[final] ).
cnf(c_0_6178,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_4416,
[final] ).
cnf(c_0_6179,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_4417,
[final] ).
cnf(c_0_6180,plain,
( 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),ord_atLeast(X1),X2)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
c_0_4418,
[final] ).
cnf(c_0_6181,plain,
( 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),ord_greaterThan(X1),X2)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
c_0_4419,
[final] ).
cnf(c_0_6182,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X3)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))
| hAPP(nat,X1,X2,zero_zero(nat)) != zero_zero(X1)
| ~ comm_monoid_add(X1) ),
c_0_4420,
[final] ).
cnf(c_0_6183,plain,
( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2))
| hAPP(nat,nat,X1,zero_zero(nat)) != zero_zero(nat) ),
c_0_4421,
[final] ).
cnf(c_0_6184,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
c_0_4422,
[final] ).
cnf(c_0_6185,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_4423,
[final] ).
cnf(c_0_6186,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,esk57_4(X2,X1,X4,X3)),esk58_4(X2,X1,X4,X3))) ),
c_0_4424,
[final] ).
cnf(c_0_6187,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_4425,
[final] ).
cnf(c_0_6188,plain,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = ti(fun(X1,X2),X3)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
c_0_4426,
[final] ).
cnf(c_0_6189,plain,
( ti(X1,X4) = ti(X1,X6)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X2) != ti(X1,X5)
| ~ semiri456707255roduct(X1) ),
c_0_4427,
[final] ).
cnf(c_0_6190,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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,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_4428,
[final] ).
cnf(c_0_6191,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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,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_4429,
[final] ).
cnf(c_0_6192,plain,
( hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2)))) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4430,
[final] ).
cnf(c_0_6193,plain,
( hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk119_2(X1,X2)),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)),esk118_2(X1,X2)))) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4431,
[final] ).
cnf(c_0_6194,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_4432,
[final] ).
cnf(c_0_6195,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_4433,
[final] ).
cnf(c_0_6196,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ semilattice_sup(X1) ),
c_0_4434,
[final] ).
cnf(c_0_6197,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ semilattice_sup(X1) ),
c_0_4435,
[final] ).
cnf(c_0_6198,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1) ),
c_0_4436,
[final] ).
cnf(c_0_6199,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1) ),
c_0_4437,
[final] ).
cnf(c_0_6200,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_4438,
[final] ).
cnf(c_0_6201,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_4439,
[final] ).
cnf(c_0_6202,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_4440,
[final] ).
cnf(c_0_6203,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_4441,
[final] ).
cnf(c_0_6204,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_4442,
[final] ).
cnf(c_0_6205,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_4443,
[final] ).
cnf(c_0_6206,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_4444,
[final] ).
cnf(c_0_6207,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_4445,
[final] ).
cnf(c_0_6208,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_4446,
[final] ).
cnf(c_0_6209,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_4447,
[final] ).
cnf(c_0_6210,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_4448,
[final] ).
cnf(c_0_6211,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_4449,
[final] ).
cnf(c_0_6212,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_4450,
[final] ).
cnf(c_0_6213,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_4451,
[final] ).
cnf(c_0_6214,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_4452,
[final] ).
cnf(c_0_6215,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk95_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
c_0_4453,
[final] ).
cnf(c_0_6216,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_4454,
[final] ).
cnf(c_0_6217,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_4455,
[final] ).
cnf(c_0_6218,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_4456,
[final] ).
cnf(c_0_6219,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_4457,
[final] ).
cnf(c_0_6220,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_4458,
[final] ).
cnf(c_0_6221,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),
c_0_4459,
[final] ).
cnf(c_0_6222,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),
c_0_4460,
[final] ).
cnf(c_0_6223,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)) ),
c_0_4461,
[final] ).
cnf(c_0_6224,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)) ),
c_0_4462,
[final] ).
cnf(c_0_6225,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_4463,
[final] ).
cnf(c_0_6226,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_4464,
[final] ).
cnf(c_0_6227,plain,
( ti(fun(X1,bool),X4) = ti(fun(X1,bool),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(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_4465,
[final] ).
cnf(c_0_6228,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_4466,
[final] ).
cnf(c_0_6229,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_4467,
[final] ).
cnf(c_0_6230,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_4468,
[final] ).
cnf(c_0_6231,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,esk176_4(X1,X3,X2,X4)) != zero_zero(nat) ),
c_0_4469,
[final] ).
cnf(c_0_6232,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,esk146_3(X1,X4,X2))),hAPP(X1,nat,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
c_0_4470,
[final] ).
cnf(c_0_6233,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_4471,
[final] ).
cnf(c_0_6234,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_4472,
[final] ).
cnf(c_0_6235,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,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4) = 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_4473,
[final] ).
cnf(c_0_6236,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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,X3,esk150_3(X1,X3,X2))) ),
c_0_4474,
[final] ).
cnf(c_0_6237,plain,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| zero_zero(nat) != one_one(nat) ),
c_0_4475,
[final] ).
cnf(c_0_6238,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2))),
c_0_4476,
[final] ).
cnf(c_0_6239,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),
c_0_4477,
[final] ).
cnf(c_0_6240,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
c_0_4478,
[final] ).
cnf(c_0_6241,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(X2,X1,X4,hAPP(X1,X2,X3,esk110_4(X1,X2,X4,X3))) != ti(X1,esk110_4(X1,X2,X4,X3))
| 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_4479,
[final] ).
cnf(c_0_6242,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_4480,
[final] ).
cnf(c_0_6243,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_4481,
[final] ).
cnf(c_0_6244,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_4482,
[final] ).
cnf(c_0_6245,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_4483,
[final] ).
cnf(c_0_6246,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_4484,
[final] ).
cnf(c_0_6247,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_4485,
[final] ).
cnf(c_0_6248,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_4486,
[final] ).
cnf(c_0_6249,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_4487,
[final] ).
cnf(c_0_6250,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_4488,
[final] ).
cnf(c_0_6251,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_4489,
[final] ).
cnf(c_0_6252,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_4490,
[final] ).
cnf(c_0_6253,plain,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_4491,
[final] ).
cnf(c_0_6254,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_4492,
[final] ).
cnf(c_0_6255,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ti(X1,esk176_4(X1,X3,X2,X4)) != ti(X1,X4) ),
c_0_4493,
[final] ).
cnf(c_0_6256,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
c_0_4494,
[final] ).
cnf(c_0_6257,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_4495,
[final] ).
cnf(c_0_6258,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_4496,
[final] ).
cnf(c_0_6259,plain,
hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)) = arrow_301600364e_Prof,
c_0_4497,
[final] ).
cnf(c_0_6260,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_4498,
[final] ).
cnf(c_0_6261,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
c_0_4499,
[final] ).
cnf(c_0_6262,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ semilattice_inf(X1) ),
c_0_4500,
[final] ).
cnf(c_0_6263,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ lattice(X1) ),
c_0_4501,
[final] ).
cnf(c_0_6264,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ semilattice_inf(X1) ),
c_0_4502,
[final] ).
cnf(c_0_6265,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ semilattice_sup(X1) ),
c_0_4503,
[final] ).
cnf(c_0_6266,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ lattice(X1) ),
c_0_4504,
[final] ).
cnf(c_0_6267,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ semilattice_sup(X1) ),
c_0_4505,
[final] ).
cnf(c_0_6268,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ ab_semigroup_mult(X1) ),
c_0_4506,
[final] ).
cnf(c_0_6269,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
c_0_4507,
[final] ).
cnf(c_0_6270,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
c_0_4508,
[final] ).
cnf(c_0_6271,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_4509,
[final] ).
cnf(c_0_6272,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_4510,
[final] ).
cnf(c_0_6273,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_4511,
[final] ).
cnf(c_0_6274,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_4512,
[final] ).
cnf(c_0_6275,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_4513,
[final] ).
cnf(c_0_6276,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_4514,
[final] ).
cnf(c_0_6277,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_4515,
[final] ).
cnf(c_0_6278,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_4516,
[final] ).
cnf(c_0_6279,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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| hBOOL(hAPP(X1,bool,X2,esk150_3(X1,X3,X2))) ),
c_0_4517,
[final] ).
cnf(c_0_6280,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| hAPP(X1,nat,X3,esk178_4(X1,X3,X2,X4)) != zero_zero(nat) ),
c_0_4518,
[final] ).
cnf(c_0_6281,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
c_0_4519,
[final] ).
cnf(c_0_6282,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_4520,
[final] ).
cnf(c_0_6283,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
c_0_4521,
[final] ).
cnf(c_0_6284,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
c_0_4522,
[final] ).
cnf(c_0_6285,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_4523,
[final] ).
cnf(c_0_6286,plain,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
c_0_4524,
[final] ).
cnf(c_0_6287,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4525,
[final] ).
cnf(c_0_6288,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
c_0_4526,
[final] ).
cnf(c_0_6289,plain,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ti(X1,esk175_3(X1,X3,X2)) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
c_0_4527,
[final] ).
cnf(c_0_6290,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_4528,
[final] ).
cnf(c_0_6291,plain,
( 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,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X4)) ),
c_0_4529,
[final] ).
cnf(c_0_6292,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_4530,
[final] ).
cnf(c_0_6293,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_4531,
[final] ).
cnf(c_0_6294,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_4532,
[final] ).
cnf(c_0_6295,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
c_0_4533,
[final] ).
cnf(c_0_6296,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
c_0_4534,
[final] ).
cnf(c_0_6297,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
c_0_4535,
[final] ).
cnf(c_0_6298,plain,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
c_0_4536,
[final] ).
cnf(c_0_6299,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ti(X1,esk178_4(X1,X3,X2,X4)) != ti(X1,X4) ),
c_0_4537,
[final] ).
cnf(c_0_6300,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_4538,
[final] ).
cnf(c_0_6301,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_4539,
[final] ).
cnf(c_0_6302,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),esk77_4(X2,X1,X3,X4)),X4)) ),
c_0_4540,
[final] ).
cnf(c_0_6303,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),esk78_4(X2,X1,X3,X4)),X4)) ),
c_0_4541,
[final] ).
cnf(c_0_6304,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_4542,
[final] ).
cnf(c_0_6305,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),esk32_4(X1,X2,X3,X4)),X4)) ),
c_0_4543,
[final] ).
cnf(c_0_6306,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_4544,
[final] ).
cnf(c_0_6307,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_4545,
[final] ).
cnf(c_0_6308,plain,
( hAPP(nat,nat,suc,esk95_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
c_0_4546,
[final] ).
cnf(c_0_6309,plain,
( hAPP(nat,nat,suc,esk93_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_4547,
[final] ).
cnf(c_0_6310,plain,
( hBOOL(hAPP(nat,bool,X3,X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk87_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_4548,
[final] ).
cnf(c_0_6311,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_4549,
[final] ).
cnf(c_0_6312,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_4550,
[final] ).
cnf(c_0_6313,plain,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,esk169_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
c_0_4551,
[final] ).
cnf(c_0_6314,plain,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,esk169_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
c_0_4552,
[final] ).
cnf(c_0_6315,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_4553,
[final] ).
cnf(c_0_6316,plain,
( 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))))
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
c_0_4554,
[final] ).
cnf(c_0_6317,plain,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ti(X1,esk177_3(X1,X3,X2)) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
c_0_4555,
[final] ).
cnf(c_0_6318,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_4556,
[final] ).
cnf(c_0_6319,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),esk60_3(X1,X3,X2)),X3)) ),
c_0_4557,
[final] ).
cnf(c_0_6320,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_4558,
[final] ).
cnf(c_0_6321,plain,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6))
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9) ),
c_0_4559,
[final] ).
cnf(c_0_6322,plain,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6))
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9) ),
c_0_4560,
[final] ).
cnf(c_0_6323,plain,
( hBOOL(hAPP(nat,bool,X3,X1))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,esk87_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_4561,
[final] ).
cnf(c_0_6324,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_4562,
[final] ).
cnf(c_0_6325,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_4563,
[final] ).
cnf(c_0_6326,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_4564,
[final] ).
cnf(c_0_6327,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_4565,
[final] ).
cnf(c_0_6328,plain,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ 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),X4),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != zero_zero(nat) ),
c_0_4566,
[final] ).
cnf(c_0_6329,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_4567,
[final] ).
cnf(c_0_6330,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_4568,
[final] ).
cnf(c_0_6331,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_4569,
[final] ).
cnf(c_0_6332,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_4570,
[final] ).
cnf(c_0_6333,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_4571,
[final] ).
cnf(c_0_6334,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
c_0_4572,
[final] ).
cnf(c_0_6335,plain,
( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2) ),
c_0_4573,
[final] ).
cnf(c_0_6336,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_4574,
[final] ).
cnf(c_0_6337,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_4575,
[final] ).
cnf(c_0_6338,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
c_0_4576,
[final] ).
cnf(c_0_6339,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
c_0_4577,
[final] ).
cnf(c_0_6340,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_4578,
[final] ).
cnf(c_0_6341,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_4579,
[final] ).
cnf(c_0_6342,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_4580,
[final] ).
cnf(c_0_6343,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_4581,
[final] ).
cnf(c_0_6344,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X4)),X5),X6) = ti(X2,X4),
c_0_4582,
[final] ).
cnf(c_0_6345,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_4583,
[final] ).
cnf(c_0_6346,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk71_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_4584,
[final] ).
cnf(c_0_6347,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
c_0_4585,
[final] ).
cnf(c_0_6348,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
c_0_4586,
[final] ).
cnf(c_0_6349,plain,
( hBOOL(hAPP(X1,bool,X2,esk168_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
c_0_4587,
[final] ).
cnf(c_0_6350,plain,
( hBOOL(hAPP(X1,bool,X2,esk168_4(X1,X2,X5,X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
c_0_4588,
[final] ).
cnf(c_0_6351,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),esk80_2(X2,X1)),one_one(nat))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_4589,
[final] ).
cnf(c_0_6352,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_4590,
[final] ).
cnf(c_0_6353,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk175_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
c_0_4591,
[final] ).
cnf(c_0_6354,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_4592,
[final] ).
cnf(c_0_6355,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_4593,
[final] ).
cnf(c_0_6356,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_4594,
[final] ).
cnf(c_0_6357,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_4595,
[final] ).
cnf(c_0_6358,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_4596,
[final] ).
cnf(c_0_6359,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_4597,
[final] ).
cnf(c_0_6360,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_4598,
[final] ).
cnf(c_0_6361,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_4599,
[final] ).
cnf(c_0_6362,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_4600,
[final] ).
cnf(c_0_6363,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_4601,
[final] ).
cnf(c_0_6364,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_4602,
[final] ).
cnf(c_0_6365,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_4603,
[final] ).
cnf(c_0_6366,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_4604,
[final] ).
cnf(c_0_6367,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_4605,
[final] ).
cnf(c_0_6368,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_4606,
[final] ).
cnf(c_0_6369,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_4607,
[final] ).
cnf(c_0_6370,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_4608,
[final] ).
cnf(c_0_6371,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_4609,
[final] ).
cnf(c_0_6372,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_4610,
[final] ).
cnf(c_0_6373,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_4611,
[final] ).
cnf(c_0_6374,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_4612,
[final] ).
cnf(c_0_6375,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_4613,
[final] ).
cnf(c_0_6376,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_4614,
[final] ).
cnf(c_0_6377,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_4615,
[final] ).
cnf(c_0_6378,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
c_0_4616,
[final] ).
cnf(c_0_6379,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
c_0_4617,
[final] ).
cnf(c_0_6380,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
c_0_4618,
[final] ).
cnf(c_0_6381,plain,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
c_0_4619,
[final] ).
cnf(c_0_6382,plain,
( X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
c_0_4620,
[final] ).
cnf(c_0_6383,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_4621,
[final] ).
cnf(c_0_6384,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_4622,
[final] ).
cnf(c_0_6385,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
c_0_4623,
[final] ).
cnf(c_0_6386,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),times_times(X1),X2),X2)))
| ~ linordered_ring(X1) ),
c_0_4624,
[final] ).
cnf(c_0_6387,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_4625,
[final] ).
cnf(c_0_6388,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ semilattice_inf(X1) ),
c_0_4626,
[final] ).
cnf(c_0_6389,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ lattice(X1) ),
c_0_4627,
[final] ).
cnf(c_0_6390,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ semilattice_inf(X1) ),
c_0_4628,
[final] ).
cnf(c_0_6391,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ semilattice_sup(X1) ),
c_0_4629,
[final] ).
cnf(c_0_6392,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ lattice(X1) ),
c_0_4630,
[final] ).
cnf(c_0_6393,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ semilattice_sup(X1) ),
c_0_4631,
[final] ).
cnf(c_0_6394,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
c_0_4632,
[final] ).
cnf(c_0_6395,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_4633,
[final] ).
cnf(c_0_6396,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,esk87_3(X3,X1,X2))) ),
c_0_4634,
[final] ).
cnf(c_0_6397,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
| ~ semilattice_sup(X1) ),
c_0_4635,
[final] ).
cnf(c_0_6398,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
| ~ lattice(X1) ),
c_0_4636,
[final] ).
cnf(c_0_6399,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
| ~ semilattice_sup(X1) ),
c_0_4637,
[final] ).
cnf(c_0_6400,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
| ~ lattice(X1) ),
c_0_4638,
[final] ).
cnf(c_0_6401,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_4639,
[final] ).
cnf(c_0_6402,plain,
( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),esk122_2(X1,X2)),X2) = 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)),esk123_2(X1,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4640,
[final] ).
cnf(c_0_6403,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_4641,
[final] ).
cnf(c_0_6404,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_4642,
[final] ).
cnf(c_0_6405,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_4643,
[final] ).
cnf(c_0_6406,plain,
( 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(X1,X2,X3,hAPP(X2,X1,X4,esk128_4(X1,X2,X3,X4))) != ti(X2,esk128_4(X1,X2,X3,X4)) ),
c_0_4644,
[final] ).
cnf(c_0_6407,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk177_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
c_0_4645,
[final] ).
cnf(c_0_6408,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),
c_0_4646,
[final] ).
cnf(c_0_6409,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),
c_0_4647,
[final] ).
cnf(c_0_6410,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1))),
c_0_4648,
[final] ).
cnf(c_0_6411,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_4649,
[final] ).
cnf(c_0_6412,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_4650,
[final] ).
cnf(c_0_6413,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_4651,
[final] ).
cnf(c_0_6414,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_4652,
[final] ).
cnf(c_0_6415,plain,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk18_2(X1,X2)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk18_2(X1,X2),X2) ),
c_0_4653,
[final] ).
cnf(c_0_6416,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),esk82_2(X2,X1))) ),
c_0_4654,
[final] ).
cnf(c_0_6417,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),esk80_2(X2,X1))) ),
c_0_4655,
[final] ).
cnf(c_0_6418,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_4656,
[final] ).
cnf(c_0_6419,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_4657,
[final] ).
cnf(c_0_6420,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),esk70_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4658,
[final] ).
cnf(c_0_6421,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),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)) ),
c_0_4659,
[final] ).
cnf(c_0_6422,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),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)),X3),X2)) ),
c_0_4660,
[final] ).
cnf(c_0_6423,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),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)),X3),X2)) ),
c_0_4661,
[final] ).
cnf(c_0_6424,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
c_0_4662,
[final] ).
cnf(c_0_6425,plain,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
c_0_4663,
[final] ).
cnf(c_0_6426,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_4664,
[final] ).
cnf(c_0_6427,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_4665,
[final] ).
cnf(c_0_6428,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),esk60_3(X1,X3,X2)),X2)) ),
c_0_4666,
[final] ).
cnf(c_0_6429,plain,
( X2 = hAPP(nat,nat,suc,X1)
| 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),X1),X2)) ),
c_0_4667,
[final] ).
cnf(c_0_6430,plain,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk88_2(X2,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_4668,
[final] ).
cnf(c_0_6431,plain,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk86_2(X2,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_4669,
[final] ).
cnf(c_0_6432,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_4670,
[final] ).
cnf(c_0_6433,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_4671,
[final] ).
cnf(c_0_6434,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_4672,
[final] ).
cnf(c_0_6435,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_4673,
[final] ).
cnf(c_0_6436,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_4674,
[final] ).
cnf(c_0_6437,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_4675,
[final] ).
cnf(c_0_6438,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_4676,
[final] ).
cnf(c_0_6439,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_4677,
[final] ).
cnf(c_0_6440,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_4678,
[final] ).
cnf(c_0_6441,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_4679,
[final] ).
cnf(c_0_6442,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_4680,
[final] ).
cnf(c_0_6443,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_4681,
[final] ).
cnf(c_0_6444,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_4682,
[final] ).
cnf(c_0_6445,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_4683,
[final] ).
cnf(c_0_6446,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_4684,
[final] ).
cnf(c_0_6447,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_4685,
[final] ).
cnf(c_0_6448,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_4686,
[final] ).
cnf(c_0_6449,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_4687,
[final] ).
cnf(c_0_6450,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_4688,
[final] ).
cnf(c_0_6451,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_4689,
[final] ).
cnf(c_0_6452,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_4690,
[final] ).
cnf(c_0_6453,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_4691,
[final] ).
cnf(c_0_6454,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_4692,
[final] ).
cnf(c_0_6455,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk174_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4693,
[final] ).
cnf(c_0_6456,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_4694,
[final] ).
cnf(c_0_6457,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_4695,
[final] ).
cnf(c_0_6458,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_4696,
[final] ).
cnf(c_0_6459,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_4697,
[final] ).
cnf(c_0_6460,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_4698,
[final] ).
cnf(c_0_6461,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_4699,
[final] ).
cnf(c_0_6462,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2),
c_0_4700,
[final] ).
cnf(c_0_6463,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2))),
c_0_4701,
[final] ).
cnf(c_0_6464,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2))),
c_0_4702,
[final] ).
cnf(c_0_6465,plain,
hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2))),
c_0_4703,
[final] ).
cnf(c_0_6466,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_4704,
[final] ).
cnf(c_0_6467,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk83_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_4705,
[final] ).
cnf(c_0_6468,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 != X3 ),
c_0_4706,
[final] ).
cnf(c_0_6469,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_4707,
[final] ).
cnf(c_0_6470,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_4708,
[final] ).
cnf(c_0_6471,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_4709,
[final] ).
cnf(c_0_6472,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_4710,
[final] ).
cnf(c_0_6473,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_4711,
[final] ).
cnf(c_0_6474,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_4712,
[final] ).
cnf(c_0_6475,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_4713,
[final] ).
cnf(c_0_6476,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_4714,
[final] ).
cnf(c_0_6477,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_4715,
[final] ).
cnf(c_0_6478,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_4716,
[final] ).
cnf(c_0_6479,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) != ti(fun(X1,bool),X3) ),
c_0_4717,
[final] ).
cnf(c_0_6480,plain,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk27_2(X1,X2)),arrow_1568854078le_Lin)) ),
c_0_4718,
[final] ).
cnf(c_0_6481,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_4719,
[final] ).
cnf(c_0_6482,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_4720,
[final] ).
cnf(c_0_6483,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk66_0),arrow_1568854078le_Lin)),
c_0_4721,
[final] ).
cnf(c_0_6484,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk20_0),arrow_1568854078le_Lin)),
c_0_4722,
[final] ).
cnf(c_0_6485,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk19_0),arrow_1568854078le_Lin)),
c_0_4723,
[final] ).
cnf(c_0_6486,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
c_0_4724,
[final] ).
cnf(c_0_6487,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
c_0_4725,
[final] ).
cnf(c_0_6488,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,esk165_2(X1,X3))) ),
c_0_4726,
[final] ).
cnf(c_0_6489,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,esk113_2(X1,X3))) ),
c_0_4727,
[final] ).
cnf(c_0_6490,plain,
( hBOOL(hAPP(nat,bool,X1,esk162_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_4728,
[final] ).
cnf(c_0_6491,plain,
( hBOOL(hAPP(nat,bool,X1,esk114_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
c_0_4729,
[final] ).
cnf(c_0_6492,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_4730,
[final] ).
cnf(c_0_6493,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk99_2(X2,X1)))) ),
c_0_4731,
[final] ).
cnf(c_0_6494,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_4732,
[final] ).
cnf(c_0_6495,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_4733,
[final] ).
cnf(c_0_6496,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),esk135_3(X1,X2,X3)),one_one(X1)))
| ~ linord1117847801e_zero(X1) ),
c_0_4734,
[final] ).
cnf(c_0_6497,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_4735,
[final] ).
cnf(c_0_6498,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_4736,
[final] ).
cnf(c_0_6499,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_4737,
[final] ).
cnf(c_0_6500,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
c_0_4738,
[final] ).
cnf(c_0_6501,plain,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
c_0_4739,
[final] ).
cnf(c_0_6502,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,suc,X2)),
c_0_4740,
[final] ).
cnf(c_0_6503,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
| ti(X1,esk78_4(X2,X1,X3,X4)) != ti(X1,esk77_4(X2,X1,X3,X4)) ),
c_0_4741,
[final] ).
cnf(c_0_6504,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
| ti(X1,esk32_4(X1,X2,X3,X4)) != ti(X1,esk31_4(X1,X2,X3,X4)) ),
c_0_4742,
[final] ).
cnf(c_0_6505,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_4743,
[final] ).
cnf(c_0_6506,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)
| X2 != X3 ),
c_0_4744,
[final] ).
cnf(c_0_6507,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,esk78_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,esk77_4(X2,X1,X3,X4)) ),
c_0_4745,
[final] ).
cnf(c_0_6508,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,esk32_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,esk31_4(X1,X2,X3,X4)) ),
c_0_4746,
[final] ).
cnf(c_0_6509,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)),esk135_3(X1,X2,X3)))
| ~ linord1117847801e_zero(X1) ),
c_0_4747,
[final] ).
cnf(c_0_6510,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)),esk100_3(X1,X2,X3)))
| ~ linordered_field(X1) ),
c_0_4748,
[final] ).
cnf(c_0_6511,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_4749,
[final] ).
cnf(c_0_6512,plain,
( hAPP(X1,nat,X3,esk175_3(X1,X3,X2)) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
c_0_4750,
[final] ).
cnf(c_0_6513,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_4751,
[final] ).
cnf(c_0_6514,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_4752,
[final] ).
cnf(c_0_6515,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1) ),
c_0_4753,
[final] ).
cnf(c_0_6516,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ semilattice_inf(X1) ),
c_0_4754,
[final] ).
cnf(c_0_6517,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ semilattice_sup(X1) ),
c_0_4755,
[final] ).
cnf(c_0_6518,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1) ),
c_0_4756,
[final] ).
cnf(c_0_6519,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_4757,
[final] ).
cnf(c_0_6520,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk83_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_4758,
[final] ).
cnf(c_0_6521,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk56_2(X2,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_4759,
[final] ).
cnf(c_0_6522,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_4760,
[final] ).
cnf(c_0_6523,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_4761,
[final] ).
cnf(c_0_6524,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_4762,
[final] ).
cnf(c_0_6525,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_4763,
[final] ).
cnf(c_0_6526,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_4764,
[final] ).
cnf(c_0_6527,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_4765,
[final] ).
cnf(c_0_6528,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_4766,
[final] ).
cnf(c_0_6529,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_4767,
[final] ).
cnf(c_0_6530,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ semilattice_inf(X1) ),
c_0_4768,
[final] ).
cnf(c_0_6531,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ lattice(X1) ),
c_0_4769,
[final] ).
cnf(c_0_6532,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ semilattice_inf(X1) ),
c_0_4770,
[final] ).
cnf(c_0_6533,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ semilattice_sup(X1) ),
c_0_4771,
[final] ).
cnf(c_0_6534,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ lattice(X1) ),
c_0_4772,
[final] ).
cnf(c_0_6535,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ semilattice_sup(X1) ),
c_0_4773,
[final] ).
cnf(c_0_6536,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)
| ~ ab_sem1668676832m_mult(X1) ),
c_0_4774,
[final] ).
cnf(c_0_6537,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(X1,bool,X3,esk151_3(X1,X3,X2))) ),
c_0_4775,
[final] ).
cnf(c_0_6538,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_4776,
[final] ).
cnf(c_0_6539,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_4777,
[final] ).
cnf(c_0_6540,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_4778,
[final] ).
cnf(c_0_6541,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_4779,
[final] ).
cnf(c_0_6542,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_4780,
[final] ).
cnf(c_0_6543,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_4781,
[final] ).
cnf(c_0_6544,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_4782,
[final] ).
cnf(c_0_6545,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(X2,X1)),X2)) ),
c_0_4783,
[final] ).
cnf(c_0_6546,plain,
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk74_2(X1,X2)),X2)) ),
c_0_4784,
[final] ).
cnf(c_0_6547,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),esk72_2(X1,X2)),X2)) ),
c_0_4785,
[final] ).
cnf(c_0_6548,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_4786,
[final] ).
cnf(c_0_6549,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_4787,
[final] ).
cnf(c_0_6550,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_4788,
[final] ).
cnf(c_0_6551,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_4789,
[final] ).
cnf(c_0_6552,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_4790,
[final] ).
cnf(c_0_6553,plain,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X4,X2,X7,X6)
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != ti(fun(X4,X2),X7) ),
c_0_4791,
[final] ).
cnf(c_0_6554,plain,
( ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk149_2(X1,X2)),X2)) ),
c_0_4792,
[final] ).
cnf(c_0_6555,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_4793,
[final] ).
cnf(c_0_6556,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_4794,
[final] ).
cnf(c_0_6557,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_4795,
[final] ).
cnf(c_0_6558,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_4796,
[final] ).
cnf(c_0_6559,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),esk81_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4797,
[final] ).
cnf(c_0_6560,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_4798,
[final] ).
cnf(c_0_6561,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),hAPP(nat,nat,suc,X4)) = hAPP(nat,X1,X3,X4),
c_0_4799,
[final] ).
cnf(c_0_6562,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_4800,
[final] ).
cnf(c_0_6563,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X1)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X1)),
c_0_4801,
[final] ).
cnf(c_0_6564,plain,
( X2 = hAPP(nat,nat,suc,X1)
| hAPP(nat,nat,suc,esk94_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_4802,
[final] ).
cnf(c_0_6565,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X1)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X1)),
c_0_4803,
[final] ).
cnf(c_0_6566,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),esk122_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
c_0_4804,
[final] ).
cnf(c_0_6567,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk82_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_4805,
[final] ).
cnf(c_0_6568,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk80_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_4806,
[final] ).
cnf(c_0_6569,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_4807,
[final] ).
cnf(c_0_6570,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_4808,
[final] ).
cnf(c_0_6571,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != ti(X1,X2) ),
c_0_4809,
[final] ).
cnf(c_0_6572,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != ti(X1,X3) ),
c_0_4810,
[final] ).
cnf(c_0_6573,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_4811,
[final] ).
cnf(c_0_6574,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk29_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
c_0_4812,
[final] ).
cnf(c_0_6575,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
c_0_4813,
[final] ).
cnf(c_0_6576,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
c_0_4814,
[final] ).
cnf(c_0_6577,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(X1,bool,X2,esk151_3(X1,X3,X2))) ),
c_0_4815,
[final] ).
cnf(c_0_6578,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_4816,
[final] ).
cnf(c_0_6579,plain,
( hAPP(X1,nat,X3,esk177_3(X1,X3,X2)) = one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
c_0_4817,
[final] ).
cnf(c_0_6580,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_1(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_4818,
[final] ).
cnf(c_0_6581,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2),
c_0_4819,
[final] ).
cnf(c_0_6582,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2),
c_0_4820,
[final] ).
cnf(c_0_6583,plain,
( hAPP(nat,nat,suc,esk89_1(X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_4821,
[final] ).
cnf(c_0_6584,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_4822,
[final] ).
cnf(c_0_6585,plain,
( hAPP(X3,X1,X4,esk129_4(X3,X1,X4,X2)) = ti(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))) != top_top(fun(X1,bool)) ),
c_0_4823,
[final] ).
cnf(c_0_6586,plain,
( hAPP(X3,X1,X4,esk127_4(X3,X1,X2,X4)) = ti(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))) != top_top(fun(X1,bool)) ),
c_0_4824,
[final] ).
cnf(c_0_6587,plain,
( hAPP(X3,X1,X4,esk126_4(X3,X1,X2,X4)) = ti(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))) != top_top(fun(X1,bool)) ),
c_0_4825,
[final] ).
cnf(c_0_6588,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) = hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))),
c_0_4826,
[final] ).
cnf(c_0_6589,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) = hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))),
c_0_4827,
[final] ).
cnf(c_0_6590,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_4828,
[final] ).
cnf(c_0_6591,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_4829,
[final] ).
cnf(c_0_6592,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
c_0_4830,
[final] ).
cnf(c_0_6593,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_4831,
[final] ).
cnf(c_0_6594,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_4832,
[final] ).
cnf(c_0_6595,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_4833,
[final] ).
cnf(c_0_6596,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_4834,
[final] ).
cnf(c_0_6597,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_4835,
[final] ).
cnf(c_0_6598,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_4836,
[final] ).
cnf(c_0_6599,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_4837,
[final] ).
cnf(c_0_6600,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_4838,
[final] ).
cnf(c_0_6601,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_4839,
[final] ).
cnf(c_0_6602,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_4840,
[final] ).
cnf(c_0_6603,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_4841,
[final] ).
cnf(c_0_6604,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_4842,
[final] ).
cnf(c_0_6605,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_4843,
[final] ).
cnf(c_0_6606,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_4844,
[final] ).
cnf(c_0_6607,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_4845,
[final] ).
cnf(c_0_6608,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_4846,
[final] ).
cnf(c_0_6609,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X2))
| ~ top(X1) ),
c_0_4847,
[final] ).
cnf(c_0_6610,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_4848,
[final] ).
cnf(c_0_6611,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
c_0_4849,
[final] ).
cnf(c_0_6612,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
c_0_4850,
[final] ).
cnf(c_0_6613,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_4851,
[final] ).
cnf(c_0_6614,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
| X1 != X2 ),
c_0_4852,
[final] ).
cnf(c_0_6615,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
c_0_4853,
[final] ).
cnf(c_0_6616,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
| ~ preorder(X1) ),
c_0_4854,
[final] ).
cnf(c_0_6617,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_4855,
[final] ).
cnf(c_0_6618,plain,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_4856,
[final] ).
cnf(c_0_6619,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
c_0_4857,
[final] ).
cnf(c_0_6620,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
c_0_4858,
[final] ).
cnf(c_0_6621,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
c_0_4859,
[final] ).
cnf(c_0_6622,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
c_0_4860,
[final] ).
cnf(c_0_6623,plain,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_4861,
[final] ).
cnf(c_0_6624,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
c_0_4862,
[final] ).
cnf(c_0_6625,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_4863,
[final] ).
cnf(c_0_6626,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_4864,
[final] ).
cnf(c_0_6627,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_4865,
[final] ).
cnf(c_0_6628,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_4866,
[final] ).
cnf(c_0_6629,plain,
( X1 = X2
| X3 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
c_0_4867,
[final] ).
cnf(c_0_6630,plain,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
c_0_4868,
[final] ).
cnf(c_0_6631,plain,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) ),
c_0_4869,
[final] ).
cnf(c_0_6632,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
c_0_4870,
[final] ).
cnf(c_0_6633,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
c_0_4871,
[final] ).
cnf(c_0_6634,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_4872,
[final] ).
cnf(c_0_6635,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_4873,
[final] ).
cnf(c_0_6636,plain,
hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2),
c_0_4874,
[final] ).
cnf(c_0_6637,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
c_0_4875,
[final] ).
cnf(c_0_6638,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = ti(X1,X2)
| ~ lattice(X1) ),
c_0_4876,
[final] ).
cnf(c_0_6639,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = ti(X1,X2)
| ~ lattice(X1) ),
c_0_4877,
[final] ).
cnf(c_0_6640,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
c_0_4878,
[final] ).
cnf(c_0_6641,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
c_0_4879,
[final] ).
cnf(c_0_6642,plain,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,esk174_3(X1,X3,X2)) != zero_zero(nat) ),
c_0_4880,
[final] ).
cnf(c_0_6643,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(X2,X1)),X1)) ),
c_0_4881,
[final] ).
cnf(c_0_6644,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_4882,
[final] ).
cnf(c_0_6645,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),esk72_2(X1,X2)),X1)) ),
c_0_4883,
[final] ).
cnf(c_0_6646,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,esk21_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk21_4(X1,X2,X3,X4)) ),
c_0_4884,
[final] ).
cnf(c_0_6647,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2),
c_0_4885,
[final] ).
cnf(c_0_6648,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2),
c_0_4886,
[final] ).
cnf(c_0_6649,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_4887,
[final] ).
cnf(c_0_6650,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_4888,
[final] ).
cnf(c_0_6651,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_4889,
[final] ).
cnf(c_0_6652,plain,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = ti(X1,X2),
c_0_4890,
[final] ).
cnf(c_0_6653,plain,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2),
c_0_4891,
[final] ).
cnf(c_0_6654,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),zero_zero(X2))),X3) = zero_zero(X2)
| ~ comm_monoid_add(X2) ),
c_0_4892,
[final] ).
cnf(c_0_6655,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_4893,
[final] ).
cnf(c_0_6656,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_4894,
[final] ).
cnf(c_0_6657,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_4895,
[final] ).
cnf(c_0_6658,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_4896,
[final] ).
cnf(c_0_6659,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_4897,
[final] ).
cnf(c_0_6660,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_4898,
[final] ).
cnf(c_0_6661,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_4899,
[final] ).
cnf(c_0_6662,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_4900,
[final] ).
cnf(c_0_6663,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
c_0_4901,
[final] ).
cnf(c_0_6664,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_4902,
[final] ).
cnf(c_0_6665,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_4903,
[final] ).
cnf(c_0_6666,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_4904,
[final] ).
cnf(c_0_6667,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_4905,
[final] ).
cnf(c_0_6668,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_4906,
[final] ).
cnf(c_0_6669,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,esk98_1(X1))) ),
c_0_4907,
[final] ).
cnf(c_0_6670,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_4908,
[final] ).
cnf(c_0_6671,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_4909,
[final] ).
cnf(c_0_6672,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_4910,
[final] ).
cnf(c_0_6673,plain,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_4911,
[final] ).
cnf(c_0_6674,plain,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_4912,
[final] ).
cnf(c_0_6675,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_4913,
[final] ).
cnf(c_0_6676,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk148_1(X1)),top_top(fun(X1,bool)))),
c_0_4914,
[final] ).
cnf(c_0_6677,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_4915,
[final] ).
cnf(c_0_6678,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
c_0_4916,
[final] ).
cnf(c_0_6679,plain,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
c_0_4917,
[final] ).
cnf(c_0_6680,plain,
hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X1)),
c_0_4918,
[final] ).
cnf(c_0_6681,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_4919,
[final] ).
cnf(c_0_6682,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_4920,
[final] ).
cnf(c_0_6683,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_4921,
[final] ).
cnf(c_0_6684,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_4922,
[final] ).
cnf(c_0_6685,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_4923,
[final] ).
cnf(c_0_6686,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_4924,
[final] ).
cnf(c_0_6687,plain,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
c_0_4925,
[final] ).
cnf(c_0_6688,plain,
( X2 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
c_0_4926,
[final] ).
cnf(c_0_6689,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_4927,
[final] ).
cnf(c_0_6690,plain,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,esk99_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
c_0_4928,
[final] ).
cnf(c_0_6691,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,esk82_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_4929,
[final] ).
cnf(c_0_6692,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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)) ),
c_0_4930,
[final] ).
cnf(c_0_6693,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_4931,
[final] ).
cnf(c_0_6694,plain,
( 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))
| ti(X2,esk130_3(X1,X2,X3)) != hAPP(X1,X2,X3,X4) ),
c_0_4932,
[final] ).
cnf(c_0_6695,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_4933,
[final] ).
cnf(c_0_6696,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_4934,
[final] ).
cnf(c_0_6697,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_4935,
[final] ).
cnf(c_0_6698,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_4936,
[final] ).
cnf(c_0_6699,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_4937,
[final] ).
cnf(c_0_6700,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_4938,
[final] ).
cnf(c_0_6701,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
c_0_4939,
[final] ).
cnf(c_0_6702,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
c_0_4940,
[final] ).
cnf(c_0_6703,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_4941,
[final] ).
cnf(c_0_6704,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_4942,
[final] ).
cnf(c_0_6705,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_4943,
[final] ).
cnf(c_0_6706,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_4944,
[final] ).
cnf(c_0_6707,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ semilattice_inf(X1) ),
c_0_4945,
[final] ).
cnf(c_0_6708,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ lattice(X1) ),
c_0_4946,
[final] ).
cnf(c_0_6709,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ semilattice_inf(X1) ),
c_0_4947,
[final] ).
cnf(c_0_6710,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ semilattice_sup(X1) ),
c_0_4948,
[final] ).
cnf(c_0_6711,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ lattice(X1) ),
c_0_4949,
[final] ).
cnf(c_0_6712,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ semilattice_sup(X1) ),
c_0_4950,
[final] ).
cnf(c_0_6713,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)
| ~ comm_semiring_1(X1) ),
c_0_4951,
[final] ).
cnf(c_0_6714,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_4952,
[final] ).
cnf(c_0_6715,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),top_top(X1)))
| ~ top(X1) ),
c_0_4953,
[final] ).
cnf(c_0_6716,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_4954,
[final] ).
cnf(c_0_6717,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X2 != X3
| ~ preorder(X1) ),
c_0_4955,
[final] ).
cnf(c_0_6718,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
c_0_4956,
[final] ).
cnf(c_0_6719,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
c_0_4957,
[final] ).
cnf(c_0_6720,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
c_0_4958,
[final] ).
cnf(c_0_6721,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
c_0_4959,
[final] ).
cnf(c_0_6722,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
c_0_4960,
[final] ).
cnf(c_0_6723,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
| X1 != zero_zero(nat) ),
c_0_4961,
[final] ).
cnf(c_0_6724,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_4962,
[final] ).
cnf(c_0_6725,plain,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
c_0_4963,
[final] ).
cnf(c_0_6726,plain,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
c_0_4964,
[final] ).
cnf(c_0_6727,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
c_0_4965,
[final] ).
cnf(c_0_6728,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
c_0_4966,
[final] ).
cnf(c_0_6729,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X2 != zero_zero(nat) ),
c_0_4967,
[final] ).
cnf(c_0_6730,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_4968,
[final] ).
cnf(c_0_6731,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_4969,
[final] ).
cnf(c_0_6732,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_4970,
[final] ).
cnf(c_0_6733,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
c_0_4971,
[final] ).
cnf(c_0_6734,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
c_0_4972,
[final] ).
cnf(c_0_6735,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X1 != X3 ),
c_0_4973,
[final] ).
cnf(c_0_6736,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_4974,
[final] ).
cnf(c_0_6737,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_4975,
[final] ).
cnf(c_0_6738,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
c_0_4976,
[final] ).
cnf(c_0_6739,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1),
c_0_4977,
[final] ).
cnf(c_0_6740,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_4978,
[final] ).
cnf(c_0_6741,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
c_0_4979,
[final] ).
cnf(c_0_6742,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X2) ),
c_0_4980,
[final] ).
cnf(c_0_6743,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
c_0_4981,
[final] ).
cnf(c_0_6744,plain,
( hBOOL(hAPP(X1,bool,X2,esk146_3(X1,X4,X2)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
c_0_4982,
[final] ).
cnf(c_0_6745,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_4983,
[final] ).
cnf(c_0_6746,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_4984,
[final] ).
cnf(c_0_6747,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_4985,
[final] ).
cnf(c_0_6748,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_4986,
[final] ).
cnf(c_0_6749,plain,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)),
c_0_4987,
[final] ).
cnf(c_0_6750,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
c_0_4988,
[final] ).
cnf(c_0_6751,plain,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
c_0_4989,
[final] ).
cnf(c_0_6752,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1) ),
c_0_4990,
[final] ).
cnf(c_0_6753,plain,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
c_0_4991,
[final] ).
cnf(c_0_6754,plain,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
c_0_4992,
[final] ).
cnf(c_0_6755,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_4993,
[final] ).
cnf(c_0_6756,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X2) = ti(fun(X1,bool),X2),
c_0_4994,
[final] ).
cnf(c_0_6757,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X2) = top_top(fun(X1,bool)),
c_0_4995,
[final] ).
cnf(c_0_6758,plain,
( ti(X1,X2) = top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
c_0_4996,
[final] ).
cnf(c_0_6759,plain,
( ti(X1,X3) = top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
c_0_4997,
[final] ).
cnf(c_0_6760,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_4998,
[final] ).
cnf(c_0_6761,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_4999,
[final] ).
cnf(c_0_6762,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),top_top(fun(X1,bool))) = ti(fun(X1,bool),X2),
c_0_5000,
[final] ).
cnf(c_0_6763,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
c_0_5001,
[final] ).
cnf(c_0_6764,plain,
( X1 = zero_zero(nat)
| X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != zero_zero(nat) ),
c_0_5002,
[final] ).
cnf(c_0_6765,plain,
( X1 = zero_zero(nat)
| X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != X1 ),
c_0_5003,
[final] ).
cnf(c_0_6766,plain,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
c_0_5004,
[final] ).
cnf(c_0_6767,plain,
( X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
c_0_5005,
[final] ).
cnf(c_0_6768,plain,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
c_0_5006,
[final] ).
cnf(c_0_6769,plain,
( X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
c_0_5007,
[final] ).
cnf(c_0_6770,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
c_0_5008,
[final] ).
cnf(c_0_6771,plain,
( X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
c_0_5009,
[final] ).
cnf(c_0_6772,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != X2 ),
c_0_5010,
[final] ).
cnf(c_0_6773,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
c_0_5011,
[final] ).
cnf(c_0_6774,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
c_0_5012,
[final] ).
cnf(c_0_6775,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_5013,
[final] ).
cnf(c_0_6776,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_5014,
[final] ).
cnf(c_0_6777,plain,
ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
c_0_5015,
[final] ).
cnf(c_0_6778,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X1) = hAPP(nat,nat,suc,X1),
c_0_5016,
[final] ).
cnf(c_0_6779,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),one_one(nat)) = hAPP(nat,nat,suc,X1),
c_0_5017,
[final] ).
cnf(c_0_6780,plain,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X1),
c_0_5018,
[final] ).
cnf(c_0_6781,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_5019,
[final] ).
cnf(c_0_6782,plain,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
c_0_5020,
[final] ).
cnf(c_0_6783,plain,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
c_0_5021,
[final] ).
cnf(c_0_6784,plain,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
c_0_5022,
[final] ).
cnf(c_0_6785,plain,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
c_0_5023,
[final] ).
cnf(c_0_6786,plain,
ti(fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)))),compose(X1,X2,X3)) = compose(X1,X2,X3),
c_0_5024,
[final] ).
cnf(c_0_6787,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_5025,
[final] ).
cnf(c_0_6788,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3) ),
c_0_5026,
[final] ).
cnf(c_0_6789,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3) ),
c_0_5027,
[final] ).
cnf(c_0_6790,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
| ~ bounded_lattice_top(X1)
| ti(X1,X3) != top_top(X1)
| ti(X1,X2) != top_top(X1) ),
c_0_5028,
[final] ).
cnf(c_0_6791,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
c_0_5029,
[final] ).
cnf(c_0_6792,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_5030,
[final] ).
cnf(c_0_6793,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_5031,
[final] ).
cnf(c_0_6794,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X3) != zero_zero(X1) ),
c_0_5032,
[final] ).
cnf(c_0_6795,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_5033,
[final] ).
cnf(c_0_6796,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_5034,
[final] ).
cnf(c_0_6797,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X2) = ti(X1,X2)
| ~ bounded_lattice_top(X1) ),
c_0_5035,
[final] ).
cnf(c_0_6798,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
c_0_5036,
[final] ).
cnf(c_0_6799,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ monoid_mult(X1) ),
c_0_5037,
[final] ).
cnf(c_0_6800,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
c_0_5038,
[final] ).
cnf(c_0_6801,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_5039,
[final] ).
cnf(c_0_6802,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
| ~ monoid_add(X1) ),
c_0_5040,
[final] ).
cnf(c_0_6803,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_5041,
[final] ).
cnf(c_0_6804,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),top_top(X1)) = ti(X1,X2)
| ~ bounded_lattice_top(X1) ),
c_0_5042,
[final] ).
cnf(c_0_6805,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
c_0_5043,
[final] ).
cnf(c_0_6806,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
c_0_5044,
[final] ).
cnf(c_0_6807,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
c_0_5045,
[final] ).
cnf(c_0_6808,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_5046,
[final] ).
cnf(c_0_6809,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
| ~ monoid_add(X1) ),
c_0_5047,
[final] ).
cnf(c_0_6810,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_5048,
[final] ).
cnf(c_0_6811,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_5049,
[final] ).
cnf(c_0_6812,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_5050,
[final] ).
cnf(c_0_6813,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X2) = top_top(X1)
| ~ bounded_lattice_top(X1) ),
c_0_5051,
[final] ).
cnf(c_0_6814,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ mult_zero(X1) ),
c_0_5052,
[final] ).
cnf(c_0_6815,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
c_0_5053,
[final] ).
cnf(c_0_6816,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ lattice(X1) ),
c_0_5054,
[final] ).
cnf(c_0_6817,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ lattice(X1) ),
c_0_5055,
[final] ).
cnf(c_0_6818,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
c_0_5056,
[final] ).
cnf(c_0_6819,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
c_0_5057,
[final] ).
cnf(c_0_6820,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
c_0_5058,
[final] ).
cnf(c_0_6821,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
c_0_5059,
[final] ).
cnf(c_0_6822,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
c_0_5060,
[final] ).
cnf(c_0_6823,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
c_0_5061,
[final] ).
cnf(c_0_6824,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),top_top(X1)) = top_top(X1)
| ~ bounded_lattice_top(X1) ),
c_0_5062,
[final] ).
cnf(c_0_6825,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ mult_zero(X1) ),
c_0_5063,
[final] ).
cnf(c_0_6826,plain,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
c_0_5064,
[final] ).
cnf(c_0_6827,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
c_0_5065,
[final] ).
cnf(c_0_6828,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
c_0_5066,
[final] ).
cnf(c_0_6829,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X2 != one_one(nat)
| X1 != one_one(nat) ),
c_0_5067,
[final] ).
cnf(c_0_6830,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X2 != one_one(nat)
| X1 != one_one(nat) ),
c_0_5068,
[final] ).
cnf(c_0_6831,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_5069,
[final] ).
cnf(c_0_6832,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
c_0_5070,
[final] ).
cnf(c_0_6833,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X1 != zero_zero(nat) ),
c_0_5071,
[final] ).
cnf(c_0_6834,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X2 != zero_zero(nat) ),
c_0_5072,
[final] ).
cnf(c_0_6835,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X1) = X1,
c_0_5073,
[final] ).
cnf(c_0_6836,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
c_0_5074,
[final] ).
cnf(c_0_6837,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
c_0_5075,
[final] ).
cnf(c_0_6838,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),one_one(nat)) = X1,
c_0_5076,
[final] ).
cnf(c_0_6839,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
c_0_5077,
[final] ).
cnf(c_0_6840,plain,
ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
c_0_5078,
[final] ).
cnf(c_0_6841,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
c_0_5079,
[final] ).
cnf(c_0_6842,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
c_0_5080,
[final] ).
cnf(c_0_6843,plain,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
c_0_5081,
[final] ).
cnf(c_0_6844,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_5082,
[final] ).
cnf(c_0_6845,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
c_0_5083,
[final] ).
cnf(c_0_6846,plain,
ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
c_0_5084,
[final] ).
cnf(c_0_6847,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
| ~ finite_finite(X1) ),
c_0_5085,
[final] ).
cnf(c_0_6848,plain,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
c_0_5086,
[final] ).
cnf(c_0_6849,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_5087,
[final] ).
cnf(c_0_6850,plain,
( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
c_0_5088,
[final] ).
cnf(c_0_6851,plain,
( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
c_0_5089,
[final] ).
cnf(c_0_6852,plain,
hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
c_0_5090,
[final] ).
cnf(c_0_6853,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
c_0_5091,
[final] ).
cnf(c_0_6854,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_5092,
[final] ).
cnf(c_0_6855,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ finite_finite(X1) ),
c_0_5093,
[final] ).
cnf(c_0_6856,plain,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ finite_finite(X1) ),
c_0_5094,
[final] ).
cnf(c_0_6857,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
c_0_5095,
[final] ).
cnf(c_0_6858,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_5096,
[final] ).
cnf(c_0_6859,plain,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),comp(X1,X2,X3)) = comp(X1,X2,X3),
c_0_5097,
[final] ).
cnf(c_0_6860,plain,
ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
c_0_5098,
[final] ).
cnf(c_0_6861,plain,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
c_0_5099,
[final] ).
cnf(c_0_6862,plain,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
c_0_5100,
[final] ).
cnf(c_0_6863,plain,
( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
| X1 != X2 ),
c_0_5101,
[final] ).
cnf(c_0_6864,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
c_0_5102,
[final] ).
cnf(c_0_6865,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
c_0_5103,
[final] ).
cnf(c_0_6866,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
c_0_5104,
[final] ).
cnf(c_0_6867,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
c_0_5105,
[final] ).
cnf(c_0_6868,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
c_0_5106,
[final] ).
cnf(c_0_6869,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
c_0_5107,
[final] ).
cnf(c_0_6870,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
c_0_5108,
[final] ).
cnf(c_0_6871,plain,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
c_0_5109,
[final] ).
cnf(c_0_6872,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_5110,
[final] ).
cnf(c_0_6873,plain,
ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
c_0_5111,
[final] ).
cnf(c_0_6874,plain,
hAPP(nat,nat,suc,X1) != X1,
c_0_5112,
[final] ).
cnf(c_0_6875,plain,
hAPP(nat,nat,suc,X1) != X1,
c_0_5113,
[final] ).
cnf(c_0_6876,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
c_0_5114,
[final] ).
cnf(c_0_6877,plain,
ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
c_0_5115,
[final] ).
cnf(c_0_6878,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
c_0_5116,
[final] ).
cnf(c_0_6879,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
c_0_5117,
[final] ).
cnf(c_0_6880,plain,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
c_0_5118,
[final] ).
cnf(c_0_6881,plain,
hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
c_0_5119,
[final] ).
cnf(c_0_6882,plain,
( hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2)
| ~ top(X2) ),
c_0_5120,
[final] ).
cnf(c_0_6883,plain,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
c_0_5121,
[final] ).
cnf(c_0_6884,plain,
ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
c_0_5122,
[final] ).
cnf(c_0_6885,plain,
( ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2)
| ~ comm_monoid_add(X2) ),
c_0_5123,
[final] ).
cnf(c_0_6886,plain,
ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
c_0_5124,
[final] ).
cnf(c_0_6887,plain,
ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
c_0_5125,
[final] ).
cnf(c_0_6888,plain,
ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
c_0_5126,
[final] ).
cnf(c_0_6889,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
c_0_5127,
[final] ).
cnf(c_0_6890,plain,
( hAPP(nat,nat,suc,esk97_1(X1)) = X1
| X1 = zero_zero(nat) ),
c_0_5128,
[final] ).
cnf(c_0_6891,plain,
( hAPP(nat,nat,suc,esk96_1(X1)) = X1
| X1 = zero_zero(nat) ),
c_0_5129,
[final] ).
cnf(c_0_6892,plain,
hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
c_0_5130,
[final] ).
cnf(c_0_6893,plain,
hAPP(nat,nat,size_size(nat),X1) = X1,
c_0_5131,
[final] ).
cnf(c_0_6894,plain,
hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
c_0_5132,
[final] ).
cnf(c_0_6895,plain,
hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
c_0_5133,
[final] ).
cnf(c_0_6896,plain,
ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
c_0_5134,
[final] ).
cnf(c_0_6897,plain,
hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
c_0_5135,
[final] ).
cnf(c_0_6898,plain,
hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
c_0_5136,
[final] ).
cnf(c_0_6899,plain,
ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
c_0_5137,
[final] ).
cnf(c_0_6900,plain,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
c_0_5138,
[final] ).
cnf(c_0_6901,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1)
| ~ linorder(X1) ),
c_0_5139,
[final] ).
cnf(c_0_6902,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1)
| ~ linorder(X1) ),
c_0_5140,
[final] ).
cnf(c_0_6903,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
| ~ linorder(X1) ),
c_0_5141,
[final] ).
cnf(c_0_6904,plain,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1)
| ~ order(X1) ),
c_0_5142,
[final] ).
cnf(c_0_6905,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
c_0_5143,
[final] ).
cnf(c_0_6906,plain,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
c_0_5144,
[final] ).
cnf(c_0_6907,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
c_0_5145,
[final] ).
cnf(c_0_6908,plain,
ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
c_0_5146,
[final] ).
cnf(c_0_6909,plain,
( ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1)
| ~ semilattice_sup(X1) ),
c_0_5147,
[final] ).
cnf(c_0_6910,plain,
( ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1)
| ~ semilattice_inf(X1) ),
c_0_5148,
[final] ).
cnf(c_0_6911,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ no_zero_divisors(X1) ),
c_0_5149,
[final] ).
cnf(c_0_6912,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ mult_zero(X1) ),
c_0_5150,
[final] ).
cnf(c_0_6913,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ ab_semigroup_mult(X1) ),
c_0_5151,
[final] ).
cnf(c_0_6914,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ monoid_mult(X1) ),
c_0_5152,
[final] ).
cnf(c_0_6915,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ semiring(X1) ),
c_0_5153,
[final] ).
cnf(c_0_6916,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ cancel_semigroup_add(X1) ),
c_0_5154,
[final] ).
cnf(c_0_6917,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ ab_semigroup_add(X1) ),
c_0_5155,
[final] ).
cnf(c_0_6918,plain,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ monoid_add(X1) ),
c_0_5156,
[final] ).
cnf(c_0_6919,plain,
( ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1)
| ~ ord(X1) ),
c_0_5157,
[final] ).
cnf(c_0_6920,plain,
( ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1)
| ~ ord(X1) ),
c_0_5158,
[final] ).
cnf(c_0_6921,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
c_0_5159,
[final] ).
cnf(c_0_6922,plain,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
c_0_5160,
[final] ).
cnf(c_0_6923,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
c_0_5161,
[final] ).
cnf(c_0_6924,plain,
ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
c_0_5162,
[final] ).
cnf(c_0_6925,plain,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
c_0_5163,
[final] ).
cnf(c_0_6926,plain,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
c_0_5164,
[final] ).
cnf(c_0_6927,plain,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
c_0_5165,
[final] ).
cnf(c_0_6928,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
c_0_5166,
[final] ).
cnf(c_0_6929,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
c_0_5167,
[final] ).
cnf(c_0_6930,plain,
( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
| ~ ring_1(X1) ),
c_0_5168,
[final] ).
cnf(c_0_6931,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_5169,
[final] ).
cnf(c_0_6932,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_5170,
[final] ).
cnf(c_0_6933,plain,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
c_0_5171,
[final] ).
cnf(c_0_6934,plain,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
c_0_5172,
[final] ).
cnf(c_0_6935,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
c_0_5173,
[final] ).
cnf(c_0_6936,plain,
ti(fun(X1,X1),combi(X1)) = combi(X1),
c_0_5174,
[final] ).
cnf(c_0_6937,plain,
( finite_finite(product_prod(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
c_0_5175,
[final] ).
cnf(c_0_6938,plain,
( finite_finite(sum_sum(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
c_0_5176,
[final] ).
cnf(c_0_6939,plain,
( finite_finite(fun(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
c_0_5177,
[final] ).
cnf(c_0_6940,plain,
ti(fun(nat,nat),size_size(nat)) = size_size(nat),
c_0_5178,
[final] ).
cnf(c_0_6941,plain,
( ord(fun(X1,X2))
| ~ ord(X2) ),
c_0_5179,
[final] ).
cnf(c_0_6942,plain,
( top(fun(X1,X2))
| ~ top(X2) ),
c_0_5180,
[final] ).
cnf(c_0_6943,plain,
( order(fun(X1,X2))
| ~ order(X2) ),
c_0_5181,
[final] ).
cnf(c_0_6944,plain,
( lattice(fun(X1,X2))
| ~ lattice(X2) ),
c_0_5182,
[final] ).
cnf(c_0_6945,plain,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
c_0_5183,
[final] ).
cnf(c_0_6946,plain,
( distrib_lattice(fun(X1,X2))
| ~ distrib_lattice(X2) ),
c_0_5184,
[final] ).
cnf(c_0_6947,plain,
( semilattice_inf(fun(X1,X2))
| ~ lattice(X2) ),
c_0_5185,
[final] ).
cnf(c_0_6948,plain,
( semilattice_sup(fun(X1,X2))
| ~ lattice(X2) ),
c_0_5186,
[final] ).
cnf(c_0_6949,plain,
( bounded_lattice_top(fun(X1,X2))
| ~ bounded_lattice(X2) ),
c_0_5187,
[final] ).
cnf(c_0_6950,plain,
( bounded_lattice(fun(X1,X2))
| ~ bounded_lattice(X2) ),
c_0_5188,
[final] ).
cnf(c_0_6951,plain,
ti(fun(arrow_1998540521e_indi,nat),h) = h,
c_0_5189,
[final] ).
cnf(c_0_6952,plain,
ti(fun(bool,bool),fNot) = fNot,
c_0_5190,
[final] ).
cnf(c_0_6953,plain,
ti(fun(nat,nat),nat_size) = nat_size,
c_0_5191,
[final] ).
cnf(c_0_6954,plain,
ti(fun(nat,nat),suc) = suc,
c_0_5192,
[final] ).
cnf(c_0_6955,plain,
ti(fun(bool,nat),bool_size) = bool_size,
c_0_5193,
[final] ).
cnf(c_0_6956,plain,
( ti(X1,top_top(X1)) = top_top(X1)
| ~ top(X1) ),
c_0_5194,
[final] ).
cnf(c_0_6957,plain,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
c_0_5195,
[final] ).
cnf(c_0_6958,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
c_0_5196,
[final] ).
cnf(c_0_6959,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
c_0_5197,
[final] ).
cnf(c_0_6960,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
c_0_5198,
[final] ).
cnf(c_0_6961,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
c_0_5199,
[final] ).
cnf(c_0_6962,plain,
ti(X1,undefined(X1)) = undefined(X1),
c_0_5200,
[final] ).
cnf(c_0_6963,plain,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
c_0_5201,
[final] ).
cnf(c_0_6964,plain,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
c_0_5202,
[final] ).
cnf(c_0_6965,plain,
( finite_finite(option(X1))
| ~ finite_finite(X1) ),
c_0_5203,
[final] ).
cnf(c_0_6966,plain,
ti(nat,n) = n,
c_0_5204,
[final] ).
cnf(c_0_6967,plain,
ti(arrow_2142409994le_alt,e) = e,
c_0_5205,
[final] ).
cnf(c_0_6968,plain,
ti(arrow_2142409994le_alt,b) = b,
c_0_5206,
[final] ).
cnf(c_0_6969,plain,
ti(arrow_2142409994le_alt,a) = a,
c_0_5207,
[final] ).
cnf(c_0_6970,plain,
ti(bool,fTrue) = fTrue,
c_0_5208,
[final] ).
cnf(c_0_6971,plain,
ti(bool,fFalse) = fFalse,
c_0_5209,
[final] ).
cnf(c_0_6972,plain,
~ hBOOL(fFalse),
c_0_5210,
[final] ).
cnf(c_0_6973,plain,
hBOOL(fTrue),
c_0_5211,
[final] ).
cnf(c_0_6974,plain,
finite_finite(product_unit),
c_0_5212,
[final] ).
cnf(c_0_6975,plain,
ord(bool),
c_0_5213,
[final] ).
cnf(c_0_6976,plain,
top(bool),
c_0_5214,
[final] ).
cnf(c_0_6977,plain,
order(bool),
c_0_5215,
[final] ).
cnf(c_0_6978,plain,
lattice(bool),
c_0_5216,
[final] ).
cnf(c_0_6979,plain,
finite_finite(bool),
c_0_5217,
[final] ).
cnf(c_0_6980,plain,
preorder(bool),
c_0_5218,
[final] ).
cnf(c_0_6981,plain,
distrib_lattice(bool),
c_0_5219,
[final] ).
cnf(c_0_6982,plain,
semilattice_inf(bool),
c_0_5220,
[final] ).
cnf(c_0_6983,plain,
semilattice_sup(bool),
c_0_5221,
[final] ).
cnf(c_0_6984,plain,
bounded_lattice_top(bool),
c_0_5222,
[final] ).
cnf(c_0_6985,plain,
one(nat),
c_0_5223,
[final] ).
cnf(c_0_6986,plain,
zero(nat),
c_0_5224,
[final] ).
cnf(c_0_6987,plain,
ord(nat),
c_0_5225,
[final] ).
cnf(c_0_6988,plain,
semiring(nat),
c_0_5226,
[final] ).
cnf(c_0_6989,plain,
order(nat),
c_0_5227,
[final] ).
cnf(c_0_6990,plain,
mult_zero(nat),
c_0_5228,
[final] ).
cnf(c_0_6991,plain,
lattice(nat),
c_0_5229,
[final] ).
cnf(c_0_6992,plain,
semiring_0(nat),
c_0_5230,
[final] ).
cnf(c_0_6993,plain,
monoid_add(nat),
c_0_5231,
[final] ).
cnf(c_0_6994,plain,
monoid_mult(nat),
c_0_5232,
[final] ).
cnf(c_0_6995,plain,
linorder(nat),
c_0_5233,
[final] ).
cnf(c_0_6996,plain,
preorder(nat),
c_0_5234,
[final] ).
cnf(c_0_6997,plain,
zero_neq_one(nat),
c_0_5235,
[final] ).
cnf(c_0_6998,plain,
comm_semiring(nat),
c_0_5236,
[final] ).
cnf(c_0_6999,plain,
comm_semiring_1(nat),
c_0_5237,
[final] ).
cnf(c_0_7000,plain,
comm_monoid_add(nat),
c_0_5238,
[final] ).
cnf(c_0_7001,plain,
no_zero_divisors(nat),
c_0_5239,
[final] ).
cnf(c_0_7002,plain,
ordered_semiring(nat),
c_0_5240,
[final] ).
cnf(c_0_7003,plain,
ab_semigroup_add(nat),
c_0_5241,
[final] ).
cnf(c_0_7004,plain,
comm_monoid_mult(nat),
c_0_5242,
[final] ).
cnf(c_0_7005,plain,
ab_semigroup_mult(nat),
c_0_5243,
[final] ).
cnf(c_0_7006,plain,
distrib_lattice(nat),
c_0_5244,
[final] ).
cnf(c_0_7007,plain,
semilattice_inf(nat),
c_0_5245,
[final] ).
cnf(c_0_7008,plain,
semilattice_sup(nat),
c_0_5246,
[final] ).
cnf(c_0_7009,plain,
linordered_semidom(nat),
c_0_5247,
[final] ).
cnf(c_0_7010,plain,
linordered_semiring(nat),
c_0_5248,
[final] ).
cnf(c_0_7011,plain,
cancel_semigroup_add(nat),
c_0_5249,
[final] ).
cnf(c_0_7012,plain,
ordere1490568538miring(nat),
c_0_5250,
[final] ).
cnf(c_0_7013,plain,
ordere453448008miring(nat),
c_0_5251,
[final] ).
cnf(c_0_7014,plain,
cancel146912293up_add(nat),
c_0_5252,
[final] ).
cnf(c_0_7015,plain,
ordere216010020id_add(nat),
c_0_5253,
[final] ).
cnf(c_0_7016,plain,
ordere779506340up_add(nat),
c_0_5254,
[final] ).
cnf(c_0_7017,plain,
linord20386208strict(nat),
c_0_5255,
[final] ).
cnf(c_0_7018,plain,
linord893533164strict(nat),
c_0_5256,
[final] ).
cnf(c_0_7019,plain,
ordere236663937imp_le(nat),
c_0_5257,
[final] ).
cnf(c_0_7020,plain,
ordere223160158up_add(nat),
c_0_5258,
[final] ).
cnf(c_0_7021,plain,
semiri456707255roduct(nat),
c_0_5259,
[final] ).
cnf(c_0_7022,plain,
bounded_lattice(bool),
c_0_5260,
[final] ).
cnf(c_0_7023,plain,
b != a,
c_0_5261,
[final] ).
cnf(c_0_7024,plain,
d != c,
c_0_5262,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_5263_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_3,axiom,
( hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_5,axiom,
( hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_6,axiom,
( hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5263_7,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X11))
| hAPP(X1,X1,X8,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| hAPP(X1,X2,X9,hAPP(X1,X1,X7,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X10,sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11) ),
inference(literals_permutation,[status(thm)],[c_0_5263]) ).
cnf(c_0_5264_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_1,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_4,axiom,
( hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_5,axiom,
( hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5264_6,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))),X11))
| hAPP(X1,X1,X10,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| hAPP(X1,X2,X7,hAPP(X1,X1,X9,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))) != hAPP(X1,X2,X8,sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5264]) ).
cnf(c_0_5265_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_4,axiom,
( hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5265_5,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))),X6))
| hAPP(X1,X1,X7,hAPP(X1,X1,X8,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))) != ti(X1,sk1_esk155_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X9,X10,X7,X8,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X10),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X9),X11) ),
inference(literals_permutation,[status(thm)],[c_0_5265]) ).
cnf(c_0_5266_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_1,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_2,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5266_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk156_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X11)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk155_11(X1,X2,X7,X8,X9,X10,X11,X6,X3,X4,X5)),X11)) ),
inference(literals_permutation,[status(thm)],[c_0_5266]) ).
cnf(c_0_5267_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_1,axiom,
( ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_3,axiom,
( hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_4,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_5,axiom,
( hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_6,axiom,
( hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5267_7,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X10))
| hAPP(X4,X2,X6,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| hAPP(X4,X1,X8,hAPP(X2,X4,X5,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != hAPP(X2,X1,X9,sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10) ),
inference(literals_permutation,[status(thm)],[c_0_5267]) ).
cnf(c_0_5268_0,axiom,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_1,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_2,axiom,
( ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_4,axiom,
( hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_5,axiom,
( hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5268_6,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))),X10))
| hAPP(X4,X2,X9,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != ti(X2,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| hAPP(X4,X1,X6,hAPP(X2,X4,X8,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))) != hAPP(X2,X1,X7,sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5268]) ).
cnf(c_0_5269_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_2,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_4,axiom,
( hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5269_5,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))),X3))
| hAPP(X2,X4,X5,hAPP(X4,X2,X6,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))) != ti(X4,sk1_esk143_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X7,X8,X9,X5,X6,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X9),X7),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X8),X7),X10) ),
inference(literals_permutation,[status(thm)],[c_0_5269]) ).
cnf(c_0_5270_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_2,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5270_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9))) ),
inference(literals_permutation,[status(thm)],[c_0_5270]) ).
cnf(c_0_5271_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5271_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5271_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5271_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5271_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5271_5,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9))) ),
inference(literals_permutation,[status(thm)],[c_0_5271]) ).
cnf(c_0_5272_0,axiom,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5272]) ).
cnf(c_0_5272_1,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5272]) ).
cnf(c_0_5272_2,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5272]) ).
cnf(c_0_5272_3,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5272]) ).
cnf(c_0_5272_4,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk144_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X7),X5),X3) = hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X5),X10)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk143_10(X4,X2,X1,X5,X6,X7,X8,X9,X10,X3)),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_5272]) ).
cnf(c_0_5273_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(literals_permutation,[status(thm)],[c_0_5273]) ).
cnf(c_0_5273_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5273]) ).
cnf(c_0_5274_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(literals_permutation,[status(thm)],[c_0_5274]) ).
cnf(c_0_5274_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
inference(literals_permutation,[status(thm)],[c_0_5274]) ).
cnf(c_0_5275_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(literals_permutation,[status(thm)],[c_0_5275]) ).
cnf(c_0_5275_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
inference(literals_permutation,[status(thm)],[c_0_5275]) ).
cnf(c_0_5276_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5276]) ).
cnf(c_0_5276_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(literals_permutation,[status(thm)],[c_0_5276]) ).
cnf(c_0_5277_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
inference(literals_permutation,[status(thm)],[c_0_5277]) ).
cnf(c_0_5277_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(literals_permutation,[status(thm)],[c_0_5277]) ).
cnf(c_0_5278_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5278_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5278]) ).
cnf(c_0_5279_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5279]) ).
cnf(c_0_5279_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5279]) ).
cnf(c_0_5279_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5279]) ).
cnf(c_0_5279_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5279]) ).
cnf(c_0_5279_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5279]) ).
cnf(c_0_5279_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X1,X2,X7,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))),hAPP(X1,X2,X8,sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5279]) ).
cnf(c_0_5280_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
inference(literals_permutation,[status(thm)],[c_0_5280]) ).
cnf(c_0_5280_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
inference(literals_permutation,[status(thm)],[c_0_5280]) ).
cnf(c_0_5285_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5285_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5285_2,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5285_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5285_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5285_5,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk157_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk159_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5285]) ).
cnf(c_0_5286_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5286]) ).
cnf(c_0_5286_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5286]) ).
cnf(c_0_5286_2,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5286]) ).
cnf(c_0_5286_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5286]) ).
cnf(c_0_5286_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_5286]) ).
cnf(c_0_5286_5,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X9))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X4),X4))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk161_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),X9))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X9)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X9)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,sk1_esk158_9(X1,X2,X7,X8,X9,X6,X3,X4,X5)),sk1_esk160_9(X1,X2,X7,X8,X9,X6,X3,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5286]) ).
cnf(c_0_5287_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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X5),X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X5)),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)))),X6)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5287]) ).
cnf(c_0_5287_1,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X5)),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)))),X6)),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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X5),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5287]) ).
cnf(c_0_5288_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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X5),X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X5)),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)))),X6)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5288]) ).
cnf(c_0_5288_1,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X5)),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)))),X6)),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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X5),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5288]) ).
cnf(c_0_5289_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6))
| ~ 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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_inf_inf(fun(product_prod(X2,X1),bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5289]) ).
cnf(c_0_5289_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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_inf_inf(fun(product_prod(X2,X1),bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5289]) ).
cnf(c_0_5290_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6))
| ~ 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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_sup_sup(fun(product_prod(X2,X1),bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5290]) ).
cnf(c_0_5290_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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_sup_sup(fun(product_prod(X2,X1),bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5290]) ).
cnf(c_0_5291_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5291_1,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5291_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5291_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5291_4,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5291_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_5291]) ).
cnf(c_0_5295_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk29_0)) ),
inference(literals_permutation,[status(thm)],[c_0_5295]) ).
cnf(c_0_5295_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk29_0))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)))) ),
inference(literals_permutation,[status(thm)],[c_0_5295]) ).
cnf(c_0_5296_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5296]) ).
cnf(c_0_5296_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)))) ),
inference(literals_permutation,[status(thm)],[c_0_5296]) ).
cnf(c_0_5297_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5297]) ).
cnf(c_0_5297_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)))) ),
inference(literals_permutation,[status(thm)],[c_0_5297]) ).
cnf(c_0_5299_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_1,axiom,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_2,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5299_5,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_5299]) ).
cnf(c_0_5300_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_5300]) ).
cnf(c_0_5300_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_5300]) ).
cnf(c_0_5301_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_5301]) ).
cnf(c_0_5301_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_5301]) ).
cnf(c_0_5302_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_2,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_4,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5302_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5302]) ).
cnf(c_0_5303_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_2,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_4,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5303_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X4,X1,X5,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))),hAPP(X4,X1,X6,sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3))))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5303]) ).
cnf(c_0_5304_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,fun(X3,bool)),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,bool)),fun(X1,X2)),combs(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),collect(X3)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),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),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)),X5)))),X6)))),X7) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combs(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X7)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),X6))))),X5)
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5304]) ).
cnf(c_0_5304_1,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,fun(X3,bool)),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,bool)),fun(X1,X2)),combs(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),collect(X3)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),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),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)),X5)))),X6)))),X7) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combs(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X7)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),X6))))),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5304]) ).
cnf(c_0_5304_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,fun(X3,bool)),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,bool)),fun(X1,X2)),combs(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),collect(X3)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),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),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)),X5)))),X6)))),X7) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combs(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X7)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),X6))))),X5)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5304]) ).
cnf(c_0_5304_3,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,fun(X3,bool)),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,bool)),fun(X1,X2)),combs(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),collect(X3)),hAPP(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool)),hAPP(fun(fun(X3,bool),fun(X3,bool)),fun(fun(X1,fun(X3,bool)),fun(X1,fun(X3,bool))),combb(fun(X3,bool),fun(X3,bool),X1),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),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)),X5)))),X6)))),X7) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combs(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X7)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),X6))))),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5304]) ).
cnf(c_0_5305_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5305]) ).
cnf(c_0_5305_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5305]) ).
cnf(c_0_5305_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5305]) ).
cnf(c_0_5305_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5305]) ).
cnf(c_0_5306_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X5,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X5,bool),X1)),fun(fun(X5,bool),fun(X2,X1)),combc(X2,fun(X5,bool),X1),hAPP(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1)),hAPP(fun(fun(X5,X1),fun(fun(X5,bool),X1)),fun(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1))),combb(fun(X5,X1),fun(fun(X5,bool),X1),X2),big_co1399186613setsum(X5,X1)),hAPP(fun(X5,X1),fun(X2,fun(X5,X1)),hAPP(fun(X2,fun(fun(X5,X1),fun(X5,X1))),fun(fun(X5,X1),fun(X2,fun(X5,X1))),combc(X2,fun(X5,X1),fun(X5,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1))),hAPP(fun(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1)))),combb(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1)),X2),combb(X1,X1,X5)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3))),X6))),X7)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X5,bool),X1,hAPP(fun(X5,X1),fun(fun(X5,bool),X1),big_co1399186613setsum(X5,X1),X6),X7))
| ~ semiring_0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5306]) ).
cnf(c_0_5306_1,axiom,
( ~ semiring_0(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X5,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X5,bool),X1)),fun(fun(X5,bool),fun(X2,X1)),combc(X2,fun(X5,bool),X1),hAPP(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1)),hAPP(fun(fun(X5,X1),fun(fun(X5,bool),X1)),fun(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1))),combb(fun(X5,X1),fun(fun(X5,bool),X1),X2),big_co1399186613setsum(X5,X1)),hAPP(fun(X5,X1),fun(X2,fun(X5,X1)),hAPP(fun(X2,fun(fun(X5,X1),fun(X5,X1))),fun(fun(X5,X1),fun(X2,fun(X5,X1))),combc(X2,fun(X5,X1),fun(X5,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1))),hAPP(fun(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1)))),combb(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1)),X2),combb(X1,X1,X5)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3))),X6))),X7)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X5,bool),X1,hAPP(fun(X5,X1),fun(fun(X5,bool),X1),big_co1399186613setsum(X5,X1),X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5306]) ).
cnf(c_0_5307_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) != hAPP(X1,X2,X8,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5307]) ).
cnf(c_0_5307_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| hAPP(X1,X2,X7,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) != hAPP(X1,X2,X8,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5307]) ).
cnf(c_0_5307_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6)
| hAPP(X1,X2,X7,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) != hAPP(X1,X2,X8,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5307]) ).
cnf(c_0_5307_3,axiom,
( hAPP(X1,X2,X7,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5)) != hAPP(X1,X2,X8,sk1_esk152_8(X1,X2,X7,X8,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5307]) ).
cnf(c_0_5308_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_5308]) ).
cnf(c_0_5308_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_5308]) ).
cnf(c_0_5309_0,axiom,
( hAPP(fun(X5,bool),X2,hAPP(fun(X5,X2),fun(fun(X5,bool),X2),big_co1399186613setsum(X5,X2),hAPP(fun(X5,fun(X1,bool)),fun(X5,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X5,fun(X1,bool)),fun(X5,X2)),combb(fun(X1,bool),X2,X5),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),collect(X1)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),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),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)),X4)))),hAPP(fun(X1,fun(X5,bool)),fun(X5,fun(X1,bool)),combc(X1,X5,bool),hAPP(fun(X1,X5),fun(X1,fun(X5,bool)),hAPP(fun(X5,fun(X5,bool)),fun(fun(X1,X5),fun(X1,fun(X5,bool))),combb(X5,fun(X5,bool),X1),fequal(X5)),X6)))))),hAPP(fun(X1,bool),fun(X5,bool),hAPP(fun(X1,X5),fun(fun(X1,bool),fun(X5,bool)),image(X1,X5),X6),X4)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5309]) ).
cnf(c_0_5309_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X5,bool),X2,hAPP(fun(X5,X2),fun(fun(X5,bool),X2),big_co1399186613setsum(X5,X2),hAPP(fun(X5,fun(X1,bool)),fun(X5,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X5,fun(X1,bool)),fun(X5,X2)),combb(fun(X1,bool),X2,X5),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),collect(X1)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),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),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)),X4)))),hAPP(fun(X1,fun(X5,bool)),fun(X5,fun(X1,bool)),combc(X1,X5,bool),hAPP(fun(X1,X5),fun(X1,fun(X5,bool)),hAPP(fun(X5,fun(X5,bool)),fun(fun(X1,X5),fun(X1,fun(X5,bool))),combb(X5,fun(X5,bool),X1),fequal(X5)),X6)))))),hAPP(fun(X1,bool),fun(X5,bool),hAPP(fun(X1,X5),fun(fun(X1,bool),fun(X5,bool)),image(X1,X5),X6),X4)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5309]) ).
cnf(c_0_5309_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X5,bool),X2,hAPP(fun(X5,X2),fun(fun(X5,bool),X2),big_co1399186613setsum(X5,X2),hAPP(fun(X5,fun(X1,bool)),fun(X5,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X5,fun(X1,bool)),fun(X5,X2)),combb(fun(X1,bool),X2,X5),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),collect(X1)),hAPP(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X5,fun(X1,bool)),fun(X5,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X5),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),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)),X4)))),hAPP(fun(X1,fun(X5,bool)),fun(X5,fun(X1,bool)),combc(X1,X5,bool),hAPP(fun(X1,X5),fun(X1,fun(X5,bool)),hAPP(fun(X5,fun(X5,bool)),fun(fun(X1,X5),fun(X1,fun(X5,bool))),combb(X5,fun(X5,bool),X1),fequal(X5)),X6)))))),hAPP(fun(X1,bool),fun(X5,bool),hAPP(fun(X1,X5),fun(fun(X1,bool),fun(X5,bool)),image(X1,X5),X6),X4)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5309]) ).
cnf(c_0_5310_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5310_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5310_2,axiom,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5310_3,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5310_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5310_5,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk138_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk140_7(X4,X1,X5,X6,X7,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5310]) ).
cnf(c_0_5311_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5311_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5311_2,axiom,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5311_3,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5311_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5311_5,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X7))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X3),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),sk1_esk142_7(X4,X1,X5,X6,X7,X2,X3)),X7))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X5),X3),X7)),hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X3),X7)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,sk1_esk139_7(X4,X1,X5,X6,X7,X2,X3)),sk1_esk141_7(X4,X1,X5,X6,X7,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5311]) ).
cnf(c_0_5312_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),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)),X5)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5312]) ).
cnf(c_0_5312_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),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)),X5)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5312]) ).
cnf(c_0_5312_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),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)),X5)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5312]) ).
cnf(c_0_5313_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ 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),X4),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),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(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,sk1_esk117_4(X3,X1,X4,X2))))))) ),
inference(literals_permutation,[status(thm)],[c_0_5313]) ).
cnf(c_0_5313_1,axiom,
( ~ 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),X4),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(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),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(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,sk1_esk117_4(X3,X1,X4,X2))))))) ),
inference(literals_permutation,[status(thm)],[c_0_5313]) ).
cnf(c_0_5313_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(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),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(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,sk1_esk117_4(X3,X1,X4,X2)))))))
| ~ 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),X4),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5313]) ).
cnf(c_0_5314_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_5314]) ).
cnf(c_0_5314_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_5314]) ).
cnf(c_0_5315_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5315]) ).
cnf(c_0_5315_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5315]) ).
cnf(c_0_5315_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X5))),X3)),zero_zero(X2))),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5315]) ).
cnf(c_0_5316_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5316]) ).
cnf(c_0_5316_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5316]) ).
cnf(c_0_5316_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5316]) ).
cnf(c_0_5316_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5316]) ).
cnf(c_0_5317_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5317]) ).
cnf(c_0_5317_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5317]) ).
cnf(c_0_5317_2,axiom,
( ~ comm_monoid_add(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5317]) ).
cnf(c_0_5317_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_add(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),hAPP(fun(X2,fun(X2,bool)),fun(X2,fun(X2,bool)),combc(X2,X2,bool),fequal(X2)),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5317]) ).
cnf(c_0_5318_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),X5))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X5)),X3)),zero_zero(X2))),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5318]) ).
cnf(c_0_5318_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),X5))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X5)),X3)),zero_zero(X2))),X4)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5318]) ).
cnf(c_0_5318_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),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),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)),X4))),X5))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X5)),X3)),zero_zero(X2))),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5318]) ).
cnf(c_0_5320_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5320]) ).
cnf(c_0_5320_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5320]) ).
cnf(c_0_5320_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5320]) ).
cnf(c_0_5320_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = hAPP(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5320]) ).
cnf(c_0_5321_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5321]) ).
cnf(c_0_5321_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5321]) ).
cnf(c_0_5321_2,axiom,
( ~ comm_monoid_add(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5321]) ).
cnf(c_0_5321_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_add(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X3))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(X2,fun(X2,bool),fequal(X2),X4))),X5)),zero_zero(X1))),X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5321]) ).
cnf(c_0_5322_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_esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk55_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5322]) ).
cnf(c_0_5322_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_esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk55_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5322]) ).
cnf(c_0_5322_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_esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk55_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5322]) ).
cnf(c_0_5322_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_esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk55_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5322]) ).
cnf(c_0_5322_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_esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk55_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5322]) ).
cnf(c_0_5322_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk54_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk55_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_5322]) ).
cnf(c_0_5323_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_esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk53_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5323]) ).
cnf(c_0_5323_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_esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk53_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5323]) ).
cnf(c_0_5323_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_esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk53_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5323]) ).
cnf(c_0_5323_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_esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk53_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5323]) ).
cnf(c_0_5323_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_esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk53_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5323]) ).
cnf(c_0_5323_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk52_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk53_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_5323]) ).
cnf(c_0_5324_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_esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5324_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_esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5324_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_esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5324_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_esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5324_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_esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5324]) ).
cnf(c_0_5324_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk47_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk46_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_5324]) ).
cnf(c_0_5325_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_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5325_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_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5325_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_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5325_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_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5325_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_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5325]) ).
cnf(c_0_5325_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk44_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_5325]) ).
cnf(c_0_5326_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_esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk51_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_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_esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk51_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_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_esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk51_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_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_esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk51_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_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_esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk51_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5326]) ).
cnf(c_0_5326_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk50_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk51_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_5326]) ).
cnf(c_0_5327_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_esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk49_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_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_esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk49_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_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_esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk49_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_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_esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk49_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_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_esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk49_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5327]) ).
cnf(c_0_5327_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk48_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk49_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_5327]) ).
cnf(c_0_5328_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_esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk41_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_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_esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk41_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_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_esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk41_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_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_esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk41_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_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_esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk41_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5328]) ).
cnf(c_0_5328_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk42_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk41_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_5328]) ).
cnf(c_0_5329_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_esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk39_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_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_esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk39_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_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_esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk39_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_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_esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk39_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_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_esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk39_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5329]) ).
cnf(c_0_5329_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk40_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk39_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_5329]) ).
cnf(c_0_5330_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_3,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5330_9,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5330]) ).
cnf(c_0_5331_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_3,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5331_9,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5331]) ).
cnf(c_0_5332_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_3,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5332_9,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5332]) ).
cnf(c_0_5333_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5333_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5333]) ).
cnf(c_0_5334_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5334_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5334]) ).
cnf(c_0_5335_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_3,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_5,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_6,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_7,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_8,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5335_9,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5335]) ).
cnf(c_0_5336_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_3,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_5,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_6,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_7,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_8,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5336_9,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5336]) ).
cnf(c_0_5337_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_3,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_5,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_6,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_7,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_8,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5337_9,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5337]) ).
cnf(c_0_5338_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5338_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5338]) ).
cnf(c_0_5339_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_1,axiom,
( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5339_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
| ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5339]) ).
cnf(c_0_5340_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_5340]) ).
cnf(c_0_5340_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_5340]) ).
cnf(c_0_5341_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5341]) ).
cnf(c_0_5341_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5341]) ).
cnf(c_0_5341_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5341]) ).
cnf(c_0_5341_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5341]) ).
cnf(c_0_5341_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
inference(literals_permutation,[status(thm)],[c_0_5341]) ).
cnf(c_0_5342_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X3)),X4)),one_one(X2)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),one_one(X2)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5342]) ).
cnf(c_0_5342_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X3)),X4)),one_one(X2)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),one_one(X2)),X5))
| ~ comm_monoid_mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5342]) ).
cnf(c_0_5342_2,axiom,
( ~ comm_monoid_mult(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X3)),X4)),one_one(X2)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),one_one(X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5342]) ).
cnf(c_0_5343_0,axiom,
( hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X1,bool),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X1,bool),fun(X3,X2)),combc(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),X6)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X3,bool),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X3,bool),fun(X1,X2)),combc(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),X5)),X6)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5343]) ).
cnf(c_0_5343_1,axiom,
( ~ comm_monoid_add(X2)
| hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X1,bool),fun(X3,X2),hAPP(fun(X3,fun(fun(X1,bool),X2)),fun(fun(X1,bool),fun(X3,X2)),combc(X3,fun(X1,bool),X2),hAPP(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2)),hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),fun(fun(X3,fun(X1,X2)),fun(X3,fun(fun(X1,bool),X2))),combb(fun(X1,X2),fun(fun(X1,bool),X2),X3),big_co1399186613setsum(X1,X2)),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4))),X6)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X3,bool),fun(X1,X2),hAPP(fun(X1,fun(fun(X3,bool),X2)),fun(fun(X3,bool),fun(X1,X2)),combc(X1,fun(X3,bool),X2),hAPP(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2)),hAPP(fun(fun(X3,X2),fun(fun(X3,bool),X2)),fun(fun(X1,fun(X3,X2)),fun(X1,fun(fun(X3,bool),X2))),combb(fun(X3,X2),fun(fun(X3,bool),X2),X1),big_co1399186613setsum(X3,X2)),X4)),X5)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5343]) ).
cnf(c_0_5344_0,axiom,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk25_2(X2,X1)),sk1_esk26_2(X2,X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk24_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5344]) ).
cnf(c_0_5344_1,axiom,
( ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk25_2(X2,X1)),sk1_esk26_2(X2,X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk24_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5344]) ).
cnf(c_0_5344_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk25_2(X2,X1)),sk1_esk26_2(X2,X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk24_2(X2,X1))))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5344]) ).
cnf(c_0_5345_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5345]) ).
cnf(c_0_5345_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5345]) ).
cnf(c_0_5345_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5345]) ).
cnf(c_0_5345_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5345]) ).
cnf(c_0_5345_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5345]) ).
cnf(c_0_5346_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5346]) ).
cnf(c_0_5346_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5346]) ).
cnf(c_0_5346_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5346]) ).
cnf(c_0_5346_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5346]) ).
cnf(c_0_5346_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
inference(literals_permutation,[status(thm)],[c_0_5346]) ).
cnf(c_0_5347_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5347_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5347_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5347_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5347_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5347]) ).
cnf(c_0_5348_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5348]) ).
cnf(c_0_5348_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5348]) ).
cnf(c_0_5348_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5348]) ).
cnf(c_0_5348_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5348]) ).
cnf(c_0_5349_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5349]) ).
cnf(c_0_5349_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5349]) ).
cnf(c_0_5349_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X5))
| ~ comm_monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5349]) ).
cnf(c_0_5349_3,axiom,
( ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X4)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X3),one_one(X1)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5349]) ).
cnf(c_0_5350_0,axiom,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk25_2(X2,X1)),sk1_esk26_2(X2,X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk24_2(X2,X1),X2)))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
inference(literals_permutation,[status(thm)],[c_0_5350]) ).
cnf(c_0_5350_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk25_2(X2,X1)),sk1_esk26_2(X2,X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk24_2(X2,X1),X2)))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
inference(literals_permutation,[status(thm)],[c_0_5350]) ).
cnf(c_0_5350_2,axiom,
( ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk25_2(X2,X1)),sk1_esk26_2(X2,X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk24_2(X2,X1),X2)))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5350]) ).
cnf(c_0_5351_0,axiom,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk24_2(X2,X1)),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
inference(literals_permutation,[status(thm)],[c_0_5351]) ).
cnf(c_0_5351_1,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk24_2(X2,X1)),arrow_301600364e_Prof))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
inference(literals_permutation,[status(thm)],[c_0_5351]) ).
cnf(c_0_5351_2,axiom,
( ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk24_2(X2,X1)),arrow_301600364e_Prof))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5351]) ).
cnf(c_0_5352_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5352_1,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5352_2,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5352_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5352_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5352_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5352_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5352]) ).
cnf(c_0_5353_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5353_1,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5353_2,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5353_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5353_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5353_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5353_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5353]) ).
cnf(c_0_5354_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5354_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5354]) ).
cnf(c_0_5355_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_7,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5355_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5355]) ).
cnf(c_0_5356_0,axiom,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| ti(arrow_2142409994le_alt,sk1_esk26_2(X2,X1)) != ti(arrow_2142409994le_alt,sk1_esk25_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5356]) ).
cnf(c_0_5356_1,axiom,
( ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| ti(arrow_2142409994le_alt,sk1_esk26_2(X2,X1)) != ti(arrow_2142409994le_alt,sk1_esk25_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5356]) ).
cnf(c_0_5356_2,axiom,
( ti(arrow_2142409994le_alt,sk1_esk26_2(X2,X1)) != ti(arrow_2142409994le_alt,sk1_esk25_2(X2,X1))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X1),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5356]) ).
cnf(c_0_5357_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5357]) ).
cnf(c_0_5357_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5357]) ).
cnf(c_0_5357_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5357]) ).
cnf(c_0_5357_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5357]) ).
cnf(c_0_5357_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5357]) ).
cnf(c_0_5358_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5358]) ).
cnf(c_0_5358_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5358]) ).
cnf(c_0_5358_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5358]) ).
cnf(c_0_5358_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5358]) ).
cnf(c_0_5358_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
inference(literals_permutation,[status(thm)],[c_0_5358]) ).
cnf(c_0_5359_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_5359]) ).
cnf(c_0_5359_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_5359]) ).
cnf(c_0_5360_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_5360]) ).
cnf(c_0_5360_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_5360]) ).
cnf(c_0_5361_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5361_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5361_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5361_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5361_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5361]) ).
cnf(c_0_5362_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5362]) ).
cnf(c_0_5362_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5362]) ).
cnf(c_0_5362_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5362]) ).
cnf(c_0_5362_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5362]) ).
cnf(c_0_5362_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5362]) ).
cnf(c_0_5363_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5363_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5363_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5363_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5363_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5363]) ).
cnf(c_0_5364_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5364]) ).
cnf(c_0_5364_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5364]) ).
cnf(c_0_5364_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5364]) ).
cnf(c_0_5364_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5364]) ).
cnf(c_0_5364_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5364]) ).
cnf(c_0_5365_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5365]) ).
cnf(c_0_5365_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5365]) ).
cnf(c_0_5365_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5365]) ).
cnf(c_0_5365_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5365]) ).
cnf(c_0_5365_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
inference(literals_permutation,[status(thm)],[c_0_5365]) ).
cnf(c_0_5366_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5366]) ).
cnf(c_0_5366_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5366]) ).
cnf(c_0_5366_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5366]) ).
cnf(c_0_5366_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5366]) ).
cnf(c_0_5367_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5367_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5367_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5367_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5367_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5367]) ).
cnf(c_0_5368_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5368_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5368_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5368_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5368]) ).
cnf(c_0_5369_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5369_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5369]) ).
cnf(c_0_5370_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5370_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5370]) ).
cnf(c_0_5371_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_5,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_7,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5371_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5371]) ).
cnf(c_0_5372_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_4,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_5,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_6,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_7,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5372_8,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5372]) ).
cnf(c_0_5373_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5373_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5373_2,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5373_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5373_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5373_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5373_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5373]) ).
cnf(c_0_5374_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_2,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5374_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5374]) ).
cnf(c_0_5375_0,axiom,
( hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),hAPP(fun(X1,X6),fun(X1,X2),hAPP(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2))),compose(X1,X6,X2),X4),X7),X8)) = hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3))),compose(X1,X6,X3),X4),hAPP(fun(X6,X2),fun(X6,X3),hAPP(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3)),hAPP(fun(X6,bool),fun(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3))),compose(X6,X2,X3),X9),X5),X7)),X8)
| ~ hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X5),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X10),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X11))))
| ~ hBOOL(hAPP(fun(fun(X6,X2),bool),bool,hAPP(fun(X6,X2),fun(fun(fun(X6,X2),bool),bool),member(fun(X6,X2)),X7),hAPP(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool)),pi(X6,X2),X9),hAPP(fun(X2,bool),fun(X6,fun(X2,bool)),combk(fun(X2,bool),X6),X10))))
| ~ hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),X8),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X9)))) ),
inference(literals_permutation,[status(thm)],[c_0_5375]) ).
cnf(c_0_5375_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X5),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X10),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X11))))
| hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),hAPP(fun(X1,X6),fun(X1,X2),hAPP(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2))),compose(X1,X6,X2),X4),X7),X8)) = hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3))),compose(X1,X6,X3),X4),hAPP(fun(X6,X2),fun(X6,X3),hAPP(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3)),hAPP(fun(X6,bool),fun(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3))),compose(X6,X2,X3),X9),X5),X7)),X8)
| ~ hBOOL(hAPP(fun(fun(X6,X2),bool),bool,hAPP(fun(X6,X2),fun(fun(fun(X6,X2),bool),bool),member(fun(X6,X2)),X7),hAPP(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool)),pi(X6,X2),X9),hAPP(fun(X2,bool),fun(X6,fun(X2,bool)),combk(fun(X2,bool),X6),X10))))
| ~ hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),X8),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X9)))) ),
inference(literals_permutation,[status(thm)],[c_0_5375]) ).
cnf(c_0_5375_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X6,X2),bool),bool,hAPP(fun(X6,X2),fun(fun(fun(X6,X2),bool),bool),member(fun(X6,X2)),X7),hAPP(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool)),pi(X6,X2),X9),hAPP(fun(X2,bool),fun(X6,fun(X2,bool)),combk(fun(X2,bool),X6),X10))))
| ~ hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X5),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X10),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X11))))
| hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),hAPP(fun(X1,X6),fun(X1,X2),hAPP(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2))),compose(X1,X6,X2),X4),X7),X8)) = hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3))),compose(X1,X6,X3),X4),hAPP(fun(X6,X2),fun(X6,X3),hAPP(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3)),hAPP(fun(X6,bool),fun(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3))),compose(X6,X2,X3),X9),X5),X7)),X8)
| ~ hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),X8),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X9)))) ),
inference(literals_permutation,[status(thm)],[c_0_5375]) ).
cnf(c_0_5375_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),X8),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X9))))
| ~ hBOOL(hAPP(fun(fun(X6,X2),bool),bool,hAPP(fun(X6,X2),fun(fun(fun(X6,X2),bool),bool),member(fun(X6,X2)),X7),hAPP(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X2,bool)),fun(fun(X6,X2),bool)),pi(X6,X2),X9),hAPP(fun(X2,bool),fun(X6,fun(X2,bool)),combk(fun(X2,bool),X6),X10))))
| ~ hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X5),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X10),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X11))))
| hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),hAPP(fun(X1,X6),fun(X1,X2),hAPP(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X6,X2),fun(fun(X1,X6),fun(X1,X2))),compose(X1,X6,X2),X4),X7),X8)) = hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3))),compose(X1,X6,X3),X4),hAPP(fun(X6,X2),fun(X6,X3),hAPP(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3)),hAPP(fun(X6,bool),fun(fun(X2,X3),fun(fun(X6,X2),fun(X6,X3))),compose(X6,X2,X3),X9),X5),X7)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_5375]) ).
cnf(c_0_5376_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_esk54_6(X1,X2,X5,X6,X3,X4)),sk1_esk55_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_5376]) ).
cnf(c_0_5376_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk54_6(X1,X2,X5,X6,X3,X4)),sk1_esk55_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_5376]) ).
cnf(c_0_5376_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk54_6(X1,X2,X5,X6,X3,X4)),sk1_esk55_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_5376]) ).
cnf(c_0_5376_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk54_6(X1,X2,X5,X6,X3,X4)),sk1_esk55_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_5376]) ).
cnf(c_0_5376_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_esk54_6(X1,X2,X5,X6,X3,X4)),sk1_esk55_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_5376]) ).
cnf(c_0_5376_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_esk54_6(X1,X2,X5,X6,X3,X4)),sk1_esk55_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_5376]) ).
cnf(c_0_5377_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_esk52_6(X1,X2,X5,X6,X3,X4)),sk1_esk53_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_5377]) ).
cnf(c_0_5377_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk52_6(X1,X2,X5,X6,X3,X4)),sk1_esk53_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_5377]) ).
cnf(c_0_5377_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk52_6(X1,X2,X5,X6,X3,X4)),sk1_esk53_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_5377]) ).
cnf(c_0_5377_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk52_6(X1,X2,X5,X6,X3,X4)),sk1_esk53_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_5377]) ).
cnf(c_0_5377_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_esk52_6(X1,X2,X5,X6,X3,X4)),sk1_esk53_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_5377]) ).
cnf(c_0_5377_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_esk52_6(X1,X2,X5,X6,X3,X4)),sk1_esk53_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_5377]) ).
cnf(c_0_5378_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_esk47_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_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_5378]) ).
cnf(c_0_5378_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk47_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_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_5378]) ).
cnf(c_0_5378_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk47_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_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_5378]) ).
cnf(c_0_5378_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk47_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_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_5378]) ).
cnf(c_0_5378_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_esk47_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_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_5378]) ).
cnf(c_0_5378_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_esk47_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_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_5378]) ).
cnf(c_0_5379_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_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk44_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_5379]) ).
cnf(c_0_5379_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk44_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_5379]) ).
cnf(c_0_5379_2,axiom,
( ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk44_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_5379]) ).
cnf(c_0_5379_3,axiom,
( ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk44_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_5379]) ).
cnf(c_0_5379_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_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk44_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_5379]) ).
cnf(c_0_5379_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_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk44_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_5379]) ).
cnf(c_0_5380_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)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),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),X7))))
| ~ hBOOL(hAPP(fun(fun(X3,X2),bool),bool,hAPP(fun(X3,X2),fun(fun(fun(X3,X2),bool),bool),member(fun(X3,X2)),X5),hAPP(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool)),pi(X3,X2),X8),hAPP(fun(X2,bool),fun(X3,fun(X2,bool)),combk(fun(X2,bool),X3),X7))))
| ~ 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),X4),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X8)))) ),
inference(literals_permutation,[status(thm)],[c_0_5380]) ).
cnf(c_0_5380_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X3,X2),bool),bool,hAPP(fun(X3,X2),fun(fun(fun(X3,X2),bool),bool),member(fun(X3,X2)),X5),hAPP(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool)),pi(X3,X2),X8),hAPP(fun(X2,bool),fun(X3,fun(X2,bool)),combk(fun(X2,bool),X3),X7))))
| hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),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),X7))))
| ~ 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),X4),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X8)))) ),
inference(literals_permutation,[status(thm)],[c_0_5380]) ).
cnf(c_0_5380_2,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),X4),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X8))))
| ~ hBOOL(hAPP(fun(fun(X3,X2),bool),bool,hAPP(fun(X3,X2),fun(fun(fun(X3,X2),bool),bool),member(fun(X3,X2)),X5),hAPP(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X2,bool)),fun(fun(X3,X2),bool)),pi(X3,X2),X8),hAPP(fun(X2,bool),fun(X3,fun(X2,bool)),combk(fun(X2,bool),X3),X7))))
| hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),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),X7)))) ),
inference(literals_permutation,[status(thm)],[c_0_5380]) ).
cnf(c_0_5381_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5381_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5381_2,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5381_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5381_4,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk173_5(X2,X1,X5,X4,X3)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5381]) ).
cnf(c_0_5383_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_esk50_6(X1,X2,X6,X3,X4,X5)),sk1_esk51_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_5383]) ).
cnf(c_0_5383_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk50_6(X1,X2,X6,X3,X4,X5)),sk1_esk51_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_5383]) ).
cnf(c_0_5383_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk50_6(X1,X2,X6,X3,X4,X5)),sk1_esk51_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_5383]) ).
cnf(c_0_5383_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk50_6(X1,X2,X6,X3,X4,X5)),sk1_esk51_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_5383]) ).
cnf(c_0_5383_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_esk50_6(X1,X2,X6,X3,X4,X5)),sk1_esk51_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_5383]) ).
cnf(c_0_5383_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_esk50_6(X1,X2,X6,X3,X4,X5)),sk1_esk51_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_5383]) ).
cnf(c_0_5384_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_esk48_6(X1,X2,X6,X3,X4,X5)),sk1_esk49_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_5384]) ).
cnf(c_0_5384_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk48_6(X1,X2,X6,X3,X4,X5)),sk1_esk49_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_5384]) ).
cnf(c_0_5384_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk48_6(X1,X2,X6,X3,X4,X5)),sk1_esk49_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_5384]) ).
cnf(c_0_5384_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk48_6(X1,X2,X6,X3,X4,X5)),sk1_esk49_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_5384]) ).
cnf(c_0_5384_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_esk48_6(X1,X2,X6,X3,X4,X5)),sk1_esk49_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_5384]) ).
cnf(c_0_5384_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_esk48_6(X1,X2,X6,X3,X4,X5)),sk1_esk49_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_5384]) ).
cnf(c_0_5385_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_esk42_6(X1,X2,X5,X6,X3,X4)),sk1_esk41_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_5385]) ).
cnf(c_0_5385_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk42_6(X1,X2,X5,X6,X3,X4)),sk1_esk41_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_5385]) ).
cnf(c_0_5385_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk42_6(X1,X2,X5,X6,X3,X4)),sk1_esk41_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_5385]) ).
cnf(c_0_5385_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk42_6(X1,X2,X5,X6,X3,X4)),sk1_esk41_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_5385]) ).
cnf(c_0_5385_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_esk42_6(X1,X2,X5,X6,X3,X4)),sk1_esk41_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_5385]) ).
cnf(c_0_5385_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_esk42_6(X1,X2,X5,X6,X3,X4)),sk1_esk41_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_5385]) ).
cnf(c_0_5386_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_esk40_6(X1,X2,X5,X6,X3,X4)),sk1_esk39_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_5386]) ).
cnf(c_0_5386_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk40_6(X1,X2,X5,X6,X3,X4)),sk1_esk39_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_5386]) ).
cnf(c_0_5386_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk40_6(X1,X2,X5,X6,X3,X4)),sk1_esk39_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_5386]) ).
cnf(c_0_5386_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk40_6(X1,X2,X5,X6,X3,X4)),sk1_esk39_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_5386]) ).
cnf(c_0_5386_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_esk40_6(X1,X2,X5,X6,X3,X4)),sk1_esk39_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_5386]) ).
cnf(c_0_5386_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_esk40_6(X1,X2,X5,X6,X3,X4)),sk1_esk39_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_5386]) ).
cnf(c_0_5387_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5387]) ).
cnf(c_0_5387_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5387]) ).
cnf(c_0_5387_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5387]) ).
cnf(c_0_5387_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5387]) ).
cnf(c_0_5387_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5387]) ).
cnf(c_0_5388_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),the_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5388]) ).
cnf(c_0_5388_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),the_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5388]) ).
cnf(c_0_5388_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),the_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5388]) ).
cnf(c_0_5388_3,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),the_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7) ),
inference(literals_permutation,[status(thm)],[c_0_5388]) ).
cnf(c_0_5389_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),hilbert_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = 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),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5389]) ).
cnf(c_0_5389_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),hilbert_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = 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),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5389]) ).
cnf(c_0_5389_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),hilbert_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = 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),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5389]) ).
cnf(c_0_5389_3,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X6),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3))))
| hAPP(X1,X2,hAPP(fun(X1,X4),fun(X1,X2),hAPP(fun(X4,X2),fun(fun(X1,X4),fun(X1,X2)),comp(X4,X2,X1),hAPP(fun(X2,X4),fun(X4,X2),hAPP(fun(X2,bool),fun(fun(X2,X4),fun(X4,X2)),hilbert_inv_into(X2,X4),X3),X6)),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X6),X3)),X5)),X7) = 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),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X5),X6)),X7) ),
inference(literals_permutation,[status(thm)],[c_0_5389]) ).
cnf(c_0_5390_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5390]) ).
cnf(c_0_5390_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5390]) ).
cnf(c_0_5390_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5390]) ).
cnf(c_0_5390_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5390]) ).
cnf(c_0_5390_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5390]) ).
cnf(c_0_5391_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5391]) ).
cnf(c_0_5391_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5391]) ).
cnf(c_0_5391_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5391]) ).
cnf(c_0_5391_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5391]) ).
cnf(c_0_5391_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5391]) ).
cnf(c_0_5392_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X3)),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)),X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5392]) ).
cnf(c_0_5392_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X3)),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)),X4)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5392]) ).
cnf(c_0_5393_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X3)),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)),X4)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5393]) ).
cnf(c_0_5393_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X3)),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)),X4)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5393]) ).
cnf(c_0_5394_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5394_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5394_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5394_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5394_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5394]) ).
cnf(c_0_5395_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5395_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5395_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5395_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5395_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5395_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5395_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5395]) ).
cnf(c_0_5396_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5396_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5396_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5396_3,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5396_4,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5396_5,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5396_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5396]) ).
cnf(c_0_5397_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5397_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5397]) ).
cnf(c_0_5398_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5398_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5398]) ).
cnf(c_0_5399_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_esk59_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,sk1_esk59_5(X2,X1,X4,X5,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5399]) ).
cnf(c_0_5399_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_esk59_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,sk1_esk59_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_5399]) ).
cnf(c_0_5400_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5400_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5400_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5400_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5400_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5401_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5402_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5402]) ).
cnf(c_0_5402_1,axiom,
( ~ linord581940658strict(X1)
| ti(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5402]) ).
cnf(c_0_5402_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5402]) ).
cnf(c_0_5403_0,axiom,
( ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5403]) ).
cnf(c_0_5403_1,axiom,
( ~ linord581940658strict(X1)
| ti(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5403]) ).
cnf(c_0_5403_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ti(X1,X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5403]) ).
cnf(c_0_5404_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),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5404]) ).
cnf(c_0_5404_1,axiom,
( ~ linordered_ring(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),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5404]) ).
cnf(c_0_5405_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_5405]) ).
cnf(c_0_5405_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_5405]) ).
cnf(c_0_5405_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_5405]) ).
cnf(c_0_5406_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_5406]) ).
cnf(c_0_5406_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_5406]) ).
cnf(c_0_5406_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_5406]) ).
cnf(c_0_5407_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5407]) ).
cnf(c_0_5407_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5407]) ).
cnf(c_0_5407_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5407]) ).
cnf(c_0_5407_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5407]) ).
cnf(c_0_5409_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5410_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5)))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk132_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,sk1_esk132_5(X2,X1,X3,X5,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5410]) ).
cnf(c_0_5410_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk132_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,sk1_esk132_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5410]) ).
cnf(c_0_5411_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(X2,X1,X5,sk1_esk173_5(X2,X1,X5,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_1,axiom,
( ~ comm_monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(X2,X1,X5,sk1_esk173_5(X2,X1,X5,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(X2,X1,X5,sk1_esk173_5(X2,X1,X5,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))
| hAPP(X2,X1,X5,sk1_esk173_5(X2,X1,X5,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_4,axiom,
( hAPP(X2,X1,X5,sk1_esk173_5(X2,X1,X5,X4,X3)) != one_one(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5412_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_5412]) ).
cnf(c_0_5412_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_5412]) ).
cnf(c_0_5412_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_5412]) ).
cnf(c_0_5413_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5414_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_4(X1,X2,X4,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_4(X1,X2,X4,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_5414]) ).
cnf(c_0_5416_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5416]) ).
cnf(c_0_5416_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5416]) ).
cnf(c_0_5416_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5416]) ).
cnf(c_0_5416_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5416]) ).
cnf(c_0_5416_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5416]) ).
cnf(c_0_5417_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5417]) ).
cnf(c_0_5417_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5417]) ).
cnf(c_0_5417_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5417]) ).
cnf(c_0_5417_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5417]) ).
cnf(c_0_5417_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5417]) ).
cnf(c_0_5418_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5419_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk137_6(X2,X1,X5,X4,X6,X3)),X3))
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk137_6(X2,X1,X5,X4,X6,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_2,axiom,
( ~ ab_semigroup_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk137_6(X2,X1,X5,X4,X6,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ ab_semigroup_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk137_6(X2,X1,X5,X4,X6,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5420_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_5420]) ).
cnf(c_0_5420_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_5420]) ).
cnf(c_0_5421_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_5421]) ).
cnf(c_0_5421_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_5421]) ).
cnf(c_0_5422_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_esk75_2(X2,X1)),hAPP(nat,nat,X1,sk1_esk75_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk75_2(X2,X1)),hAPP(nat,nat,X1,sk1_esk75_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_5422]) ).
cnf(c_0_5423_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),X4),X5)),X6)),X7) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X4,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X5),X7)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X6),X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X4),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),X4),X5)),X6)),X7) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X4,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X5),X7)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X6),X7))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X4),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X4),X8),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),X4),X5)),X6)),X7) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X4,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X5),X7)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5424_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5425_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_5425]) ).
cnf(c_0_5425_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_5425]) ).
cnf(c_0_5426_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_5426]) ).
cnf(c_0_5426_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_5426]) ).
cnf(c_0_5427_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_5427]) ).
cnf(c_0_5427_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_5427]) ).
cnf(c_0_5427_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_5427]) ).
cnf(c_0_5428_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_5428]) ).
cnf(c_0_5428_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_5428]) ).
cnf(c_0_5428_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_5428]) ).
cnf(c_0_5430_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_5,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5431_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5432_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_5,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5433_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5434_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5435_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5436_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5437_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5438_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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)),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),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X3))))
| hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3) != ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5438_1,axiom,
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3) != ti(fun(X1,bool),X5)
| hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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)),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),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5439_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5439]) ).
cnf(c_0_5440_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5441_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_5441]) ).
cnf(c_0_5441_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_5441]) ).
cnf(c_0_5441_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_5441]) ).
cnf(c_0_5441_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_5441]) ).
cnf(c_0_5442_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_1,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ 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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ 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),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_3,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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ 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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ linord1278240602ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ 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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ linord1278240602ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_6,axiom,
( ~ linord1278240602ring_1(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
| ~ 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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5443_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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_1,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ 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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ 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),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_3,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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ 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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ linord626643107strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ 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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6))
| ~ linord626643107strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_6,axiom,
( ~ linord626643107strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ~ 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)),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != one_one(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5444_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),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_esk133_5(X2,X1,X3,X5,X4))),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk133_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5445_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| ~ ab_semigroup_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) != hAPP(X2,X1,X6,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_1,axiom,
( ~ ab_semigroup_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) != hAPP(X2,X1,X6,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ ab_semigroup_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3)
| hAPP(X2,X1,X4,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) != hAPP(X2,X1,X6,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_3,axiom,
( hAPP(X2,X1,X4,sk1_esk137_6(X2,X1,X5,X4,X6,X3)) != hAPP(X2,X1,X6,sk1_esk137_6(X2,X1,X5,X4,X6,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ ab_semigroup_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X6),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5446_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5447_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5447]) ).
cnf(c_0_5447_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5447]) ).
cnf(c_0_5447_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5447]) ).
cnf(c_0_5447_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5448_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5448_1,axiom,
( ~ lattice(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5449_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5450_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5450]) ).
cnf(c_0_5450_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5450]) ).
cnf(c_0_5450_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5450]) ).
cnf(c_0_5450_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5450]) ).
cnf(c_0_5451_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5451]) ).
cnf(c_0_5451_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5451]) ).
cnf(c_0_5452_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5452]) ).
cnf(c_0_5452_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5452]) ).
cnf(c_0_5453_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5453_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5453_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5453_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5453]) ).
cnf(c_0_5454_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5454]) ).
cnf(c_0_5454_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5454]) ).
cnf(c_0_5455_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5455]) ).
cnf(c_0_5455_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5455]) ).
cnf(c_0_5455_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5455]) ).
cnf(c_0_5455_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5455]) ).
cnf(c_0_5455_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5456_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5456_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5456_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5456_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5456_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5457_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5458_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_1,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5459_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_1,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5460_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_1,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5461_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_1,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5462_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_2,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_4,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5463_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_2,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_4,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5464_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5465_0,axiom,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk147_6(X4,X1,X5,X6,X2,X3)),X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk147_6(X4,X1,X5,X6,X2,X3)),X3))
| hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_2,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk147_6(X4,X1,X5,X6,X2,X3)),X3))
| hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5466_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5466]) ).
cnf(c_0_5466_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5466]) ).
cnf(c_0_5466_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5466]) ).
cnf(c_0_5466_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5466]) ).
cnf(c_0_5466_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5467_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5468_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_3,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5469_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5472_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5473_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5474_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5474_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5474_2,axiom,
( ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5)))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5475_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5475]) ).
cnf(c_0_5475_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5475]) ).
cnf(c_0_5475_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5475]) ).
cnf(c_0_5475_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5475]) ).
cnf(c_0_5475_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5475]) ).
cnf(c_0_5476_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_5476]) ).
cnf(c_0_5476_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_5476]) ).
cnf(c_0_5476_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_5476]) ).
cnf(c_0_5476_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_5476]) ).
cnf(c_0_5477_0,axiom,
( hAPP(fun(X1,bool),X2,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X6,hAPP(fun(X1,bool),X2,X3,X4)),hAPP(fun(X1,bool),X2,X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X6),X7),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X6,hAPP(fun(X1,bool),X2,X3,X4)),hAPP(fun(X1,bool),X2,X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X6),X7),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X6,hAPP(fun(X1,bool),X2,X3,X4)),hAPP(fun(X1,bool),X2,X3,X5))
| ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X6),X7),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X6),X7),X8),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X6,hAPP(fun(X1,bool),X2,X3,X4)),hAPP(fun(X1,bool),X2,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5478_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_5478]) ).
cnf(c_0_5478_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_5478]) ).
cnf(c_0_5479_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_5479]) ).
cnf(c_0_5479_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_5479]) ).
cnf(c_0_5479_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_5479]) ).
cnf(c_0_5479_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_5479]) ).
cnf(c_0_5480_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5481_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_3,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5482_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_5482]) ).
cnf(c_0_5483_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(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,sk1_esk131_5(X1,X2,X3,X5,X4))),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,sk1_esk131_5(X1,X2,X3,X5,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)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5484_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5485_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5485]) ).
cnf(c_0_5486_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5487_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_1,axiom,
( ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_3,axiom,
( ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5488_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5489_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5490_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_5,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5491_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_5,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5492_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_5,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5493_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5494_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5495_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_5,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5496_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5497_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_5,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5498_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_4,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_5,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5499_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_4,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_5,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_6,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5500_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_5,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5501_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_5,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5502_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5503_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5503]) ).
cnf(c_0_5504_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_4(X1,X2,X4,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_4(X1,X2,X4,X3))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_esk22_4(X1,X2,X4,X3)),sk1_esk23_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_5504]) ).
cnf(c_0_5505_0,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5506_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_2,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_3,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5507_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5508_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_1,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_3,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5509_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_1,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_3,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X5)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5510_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5511_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(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),X5),X4)),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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_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(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),X5),X4)),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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_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(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),X5),X4)),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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_3,axiom,
( ~ 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),X5),X4)),X2))
| ~ 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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_4,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,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),X5),X4)),X2))
| ~ 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,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_5,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),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(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),X5),X4)),X2))
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_6,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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X2)),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(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),X5),X4)),X2))
| ~ 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_5511]) ).
cnf(c_0_5512_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5512_1,axiom,
( ~ lattice(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5513_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5514_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_5514]) ).
cnf(c_0_5514_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_5514]) ).
cnf(c_0_5515_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5516_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5517_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5517_1,axiom,
( ~ comm_monoid_add(X2)
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X3)),X4)),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5518_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_4,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5519_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5519]) ).
cnf(c_0_5519_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5519]) ).
cnf(c_0_5519_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5519]) ).
cnf(c_0_5519_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5519]) ).
cnf(c_0_5520_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_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_1,axiom,
( hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_2,axiom,
( hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5520]) ).
cnf(c_0_5520_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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_5520]) ).
cnf(c_0_5521_0,axiom,
( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hAPP(X1,X4,X5,sk1_esk147_6(X4,X1,X5,X6,X2,X3)) != hAPP(X1,X4,X6,sk1_esk147_6(X4,X1,X5,X6,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5521_1,axiom,
( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)
| hAPP(X1,X4,X5,sk1_esk147_6(X4,X1,X5,X6,X2,X3)) != hAPP(X1,X4,X6,sk1_esk147_6(X4,X1,X5,X6,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5521_2,axiom,
( hAPP(X1,X4,X5,sk1_esk147_6(X4,X1,X5,X6,X2,X3)) != hAPP(X1,X4,X6,sk1_esk147_6(X4,X1,X5,X6,X2,X3))
| ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
| hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2) = hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5521]) ).
cnf(c_0_5522_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5522_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5522]) ).
cnf(c_0_5523_0,axiom,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5523_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),X5))
| hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5523_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),X5))
| hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5523]) ).
cnf(c_0_5524_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5524]) ).
cnf(c_0_5524_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5524]) ).
cnf(c_0_5524_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5524]) ).
cnf(c_0_5524_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_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_5524]) ).
cnf(c_0_5524_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5524]) ).
cnf(c_0_5525_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3)),X5)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),X5)
| ~ semiring_0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_1,axiom,
( ~ semiring_0(X1)
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3)),X5)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5526_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_5526]) ).
cnf(c_0_5526_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_5526]) ).
cnf(c_0_5526_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_5526]) ).
cnf(c_0_5526_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_5526]) ).
cnf(c_0_5527_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_5527]) ).
cnf(c_0_5527_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_5527]) ).
cnf(c_0_5528_0,axiom,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X1),X2),X3)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X1),X2),X3)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_2,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X1),X2),X3)),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5529_0,axiom,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X1),X2),X3)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X1),X2),X3)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_2,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X1),X2),X3)),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5530_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5530]) ).
cnf(c_0_5530_1,axiom,
( hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5530]) ).
cnf(c_0_5530_2,axiom,
( hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5530]) ).
cnf(c_0_5530_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),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_5530]) ).
cnf(c_0_5530_4,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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5531_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)),the_inv_into(X1,X2),X3),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X6))
| ~ 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(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X6))
| 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)),the_inv_into(X1,X2),X3),X4),X5)),X6))
| ~ 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(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_2,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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X6))
| 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)),the_inv_into(X1,X2),X3),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),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)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X6))
| 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)),the_inv_into(X1,X2),X3),X4),X5)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5532_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk11_1(X1))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk10_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk11_1(X1))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk10_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk10_1(X1))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk11_1(X1))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5533_0,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_1,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_3,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5534_0,axiom,
( hBOOL(hAPP(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(X1,bool,X4,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),top_top(fun(X1,bool))),X3),sk1_esk108_5(X1,X2,X5,X4,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_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(X1,bool,X4,X5))
| ~ hBOOL(hAPP(X1,bool,X4,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),top_top(fun(X1,bool))),X3),sk1_esk108_5(X1,X2,X5,X4,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X4,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),top_top(fun(X1,bool))),X3),sk1_esk108_5(X1,X2,X5,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))))
| hBOOL(hAPP(X1,bool,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5535_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),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5536_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),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5537_0,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5537_1,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5537_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5537_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5538_0,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5538_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5538_2,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5538]) ).
cnf(c_0_5539_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_5539]) ).
cnf(c_0_5539_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_5539]) ).
cnf(c_0_5540_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X4),X5)),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X4),X5)),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X4),X5)),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X6))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X4),X5)),X6) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5542_0,axiom,
( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X3),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X4)),X5) = ti(fun(X1,X2),X5)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X3)))
| hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X3),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X4)),X5) = ti(fun(X1,X2),X5)
| ~ 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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X3)))
| hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X3),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X4)),X5) = ti(fun(X1,X2),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5543_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_5543]) ).
cnf(c_0_5543_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_5543]) ).
cnf(c_0_5544_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),hAPP(fun(X5,bool),fun(X1,bool),hAPP(fun(X5,X1),fun(fun(X5,bool),fun(X1,bool)),image(X5,X1),X6),X7)) = hAPP(fun(X5,bool),X2,hAPP(X2,fun(fun(X5,bool),X2),hAPP(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2))),finite_fold_image(X2,X5),times_times(X2)),hAPP(fun(X5,X1),fun(X5,X2),hAPP(fun(X1,X2),fun(fun(X5,X1),fun(X5,X2)),comp(X1,X2,X5),X3),X6)),X4),X7)
| ~ hBOOL(hAPP(fun(X5,bool),bool,hAPP(fun(X5,X1),fun(fun(X5,bool),bool),inj_on(X5,X1),X6),X7))
| ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),X7))
| ~ ab_semigroup_mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_1,axiom,
( ~ hBOOL(hAPP(fun(X5,bool),bool,hAPP(fun(X5,X1),fun(fun(X5,bool),bool),inj_on(X5,X1),X6),X7))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),hAPP(fun(X5,bool),fun(X1,bool),hAPP(fun(X5,X1),fun(fun(X5,bool),fun(X1,bool)),image(X5,X1),X6),X7)) = hAPP(fun(X5,bool),X2,hAPP(X2,fun(fun(X5,bool),X2),hAPP(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2))),finite_fold_image(X2,X5),times_times(X2)),hAPP(fun(X5,X1),fun(X5,X2),hAPP(fun(X1,X2),fun(fun(X5,X1),fun(X5,X2)),comp(X1,X2,X5),X3),X6)),X4),X7)
| ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),X7))
| ~ ab_semigroup_mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_2,axiom,
( ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),X7))
| ~ hBOOL(hAPP(fun(X5,bool),bool,hAPP(fun(X5,X1),fun(fun(X5,bool),bool),inj_on(X5,X1),X6),X7))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),hAPP(fun(X5,bool),fun(X1,bool),hAPP(fun(X5,X1),fun(fun(X5,bool),fun(X1,bool)),image(X5,X1),X6),X7)) = hAPP(fun(X5,bool),X2,hAPP(X2,fun(fun(X5,bool),X2),hAPP(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2))),finite_fold_image(X2,X5),times_times(X2)),hAPP(fun(X5,X1),fun(X5,X2),hAPP(fun(X1,X2),fun(fun(X5,X1),fun(X5,X2)),comp(X1,X2,X5),X3),X6)),X4),X7)
| ~ ab_semigroup_mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_3,axiom,
( ~ ab_semigroup_mult(X2)
| ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),X7))
| ~ hBOOL(hAPP(fun(X5,bool),bool,hAPP(fun(X5,X1),fun(fun(X5,bool),bool),inj_on(X5,X1),X6),X7))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),hAPP(fun(X5,bool),fun(X1,bool),hAPP(fun(X5,X1),fun(fun(X5,bool),fun(X1,bool)),image(X5,X1),X6),X7)) = hAPP(fun(X5,bool),X2,hAPP(X2,fun(fun(X5,bool),X2),hAPP(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X5,X2),fun(X2,fun(fun(X5,bool),X2))),finite_fold_image(X2,X5),times_times(X2)),hAPP(fun(X5,X1),fun(X5,X2),hAPP(fun(X1,X2),fun(fun(X5,X1),fun(X5,X2)),comp(X1,X2,X5),X3),X6)),X4),X7) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5545_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_esk59_5(X2,X1,X4,X5,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5545]) ).
cnf(c_0_5545_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk59_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_5545]) ).
cnf(c_0_5546_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5547_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(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5547_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
| 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_5547]) ).
cnf(c_0_5548_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X6),X4),X7),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5548_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X6),X4),X7),X5)
| ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5548_2,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X6),X4),X7),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5549_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),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_esk133_5(X2,X1,X3,X5,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk133_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5550_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5551_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_1,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5552_0,axiom,
( hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X3),X4),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)) = ti(fun(X1,X2),X4)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X3)))
| hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X3),X4),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)) = ti(fun(X1,X2),X4)
| ~ 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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_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),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X3)))
| hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X3),X4),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)) = ti(fun(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5553_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5554_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_5554]) ).
cnf(c_0_5554_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_5554]) ).
cnf(c_0_5555_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_5555]) ).
cnf(c_0_5555_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_5555]) ).
cnf(c_0_5556_0,axiom,
( hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_1,axiom,
( hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_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,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| 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,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| 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,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5557_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5559_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_5559]) ).
cnf(c_0_5559_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_5559]) ).
cnf(c_0_5559_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_5559]) ).
cnf(c_0_5559_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_5559]) ).
cnf(c_0_5560_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_5560]) ).
cnf(c_0_5560_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_5560]) ).
cnf(c_0_5561_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_5,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5562_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_5,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5563_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_4,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_5,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_6,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5564_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_4,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_5,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_6,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5565_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_3,axiom,
( ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_5,axiom,
( ti(arrow_2142409994le_alt,X5) != ti(arrow_2142409994le_alt,X1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5566_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_2,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_3,axiom,
( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_4,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_5,axiom,
( ti(arrow_2142409994le_alt,X4) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5567_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk11_1(X1),X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk10_1(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk11_1(X1),X2)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk10_1(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk10_1(X1),X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk11_1(X1),X2)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5568_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk10_1(X1),X2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk11_1(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk10_1(X1),X2)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk11_1(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_2,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk11_1(X1),X2)))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk10_1(X1),X2)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5569_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_1,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_2,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5570_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_1,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5571_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5572_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_3,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5573_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(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_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(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5))
| 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_5573]) ).
cnf(c_0_5574_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_5574]) ).
cnf(c_0_5574_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_5574]) ).
cnf(c_0_5574_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_5574]) ).
cnf(c_0_5575_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk132_5(X2,X1,X3,X5,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk132_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5576_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_esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk92_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5576_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_esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk92_4(X1,X3,X4,X2)))))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5576_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk92_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_5576]) ).
cnf(c_0_5576_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk92_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_5576]) ).
cnf(c_0_5577_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_5577]) ).
cnf(c_0_5577_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_5577]) ).
cnf(c_0_5577_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_5577]) ).
cnf(c_0_5577_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_5577]) ).
cnf(c_0_5578_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_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_5578]) ).
cnf(c_0_5578_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_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_5578]) ).
cnf(c_0_5578_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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_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_5578]) ).
cnf(c_0_5578_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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_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_5578]) ).
cnf(c_0_5579_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5580_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5580_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5581_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_3,axiom,
( ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X4),X5))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5582_0,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5582_1,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(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5582_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),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(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),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_5582]) ).
cnf(c_0_5583_0,axiom,
( hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5583]) ).
cnf(c_0_5583_1,axiom,
( hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5583]) ).
cnf(c_0_5583_2,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5583]) ).
cnf(c_0_5583_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_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_5583]) ).
cnf(c_0_5583_4,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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk125_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,sk1_esk124_5(X2,X1,X3,X4,X5)))
| hAPP(X1,X2,X3,sk1_esk125_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,sk1_esk124_5(X2,X1,X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5584_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5584]) ).
cnf(c_0_5584_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5584]) ).
cnf(c_0_5584_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5584]) ).
cnf(c_0_5584_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5585_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)),X5)
| ~ semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_1,axiom,
( ~ semiring(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5586_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_5586]) ).
cnf(c_0_5586_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_5586]) ).
cnf(c_0_5587_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X6),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X6),X4),X5))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5588_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X6),X3),X4),X5))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5589_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5590_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5590_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5591_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_5591]) ).
cnf(c_0_5591_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_5591]) ).
cnf(c_0_5591_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_5591]) ).
cnf(c_0_5591_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_5591]) ).
cnf(c_0_5592_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),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_5592]) ).
cnf(c_0_5592_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2)),X4))
| ~ 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_5592]) ).
cnf(c_0_5592_2,axiom,
( ~ 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,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2)),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_5592]) ).
cnf(c_0_5592_3,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,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5594_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_5594]) ).
cnf(c_0_5594_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_5594]) ).
cnf(c_0_5594_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_5594]) ).
cnf(c_0_5594_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_5594]) ).
cnf(c_0_5595_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(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| 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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| 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,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_3,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),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(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_4,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,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),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(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_5595]) ).
cnf(c_0_5596_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_5596]) ).
cnf(c_0_5596_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_5596]) ).
cnf(c_0_5596_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_5596]) ).
cnf(c_0_5597_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_5597]) ).
cnf(c_0_5597_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_5597]) ).
cnf(c_0_5597_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_5597]) ).
cnf(c_0_5598_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk124_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_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_esk124_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_esk124_5(X2,X1,X3,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5599_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk125_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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5599_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_esk125_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5599_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_esk125_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5599_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_esk125_5(X2,X1,X3,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5599]) ).
cnf(c_0_5600_0,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),X4),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5600_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5600_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5600_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| 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),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5600_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5600]) ).
cnf(c_0_5601_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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_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(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_3,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,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2)),X4))
| ~ 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_5601]) ).
cnf(c_0_5602_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_5602]) ).
cnf(c_0_5602_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_5602]) ).
cnf(c_0_5602_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_5602]) ).
cnf(c_0_5603_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)))
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X2),fun(fun(X4,bool),bool),inj_on(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5603_1,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X2),fun(fun(X4,bool),bool),inj_on(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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))) ),
inference(literals_permutation,[status(thm)],[c_0_5603]) ).
cnf(c_0_5604_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_5604]) ).
cnf(c_0_5604_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_5604]) ).
cnf(c_0_5605_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),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(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),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_5605]) ).
cnf(c_0_5605_1,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,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),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_5605]) ).
cnf(c_0_5605_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5606_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_1,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5607_0,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_3,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5608_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5609_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_5609]) ).
cnf(c_0_5609_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_5609]) ).
cnf(c_0_5610_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk11_1(X1))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk10_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5610_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk11_1(X1))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk10_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5610_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk10_1(X1))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk11_1(X1))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5610]) ).
cnf(c_0_5611_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X4),X5))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5611_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X4),X5))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5611_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X4),X5))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5611_3,axiom,
( ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X5))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X4),X5))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5611]) ).
cnf(c_0_5612_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_5612]) ).
cnf(c_0_5612_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_5612]) ).
cnf(c_0_5613_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5613_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),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5613]) ).
cnf(c_0_5614_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5614_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),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5614]) ).
cnf(c_0_5615_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5615_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5615_2,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_atLeastAtMost(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5615_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(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_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5615]) ).
cnf(c_0_5616_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5616]) ).
cnf(c_0_5616_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ 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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5616]) ).
cnf(c_0_5616_2,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_atLeastAtMost(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5616]) ).
cnf(c_0_5616_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(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_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5616]) ).
cnf(c_0_5617_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_atLeastAtMost(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_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5617]) ).
cnf(c_0_5617_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_atLeastAtMost(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_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5617]) ).
cnf(c_0_5617_2,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5617]) ).
cnf(c_0_5617_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5617]) ).
cnf(c_0_5618_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_atLeastAtMost(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_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ 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_atLeastAtMost(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_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_2,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| 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),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5618_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5618]) ).
cnf(c_0_5619_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5619]) ).
cnf(c_0_5619_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5619]) ).
cnf(c_0_5619_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5619]) ).
cnf(c_0_5619_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5619]) ).
cnf(c_0_5620_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5621_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_2,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5622_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5622_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ 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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5622_2,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5622_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5622]) ).
cnf(c_0_5623_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5623_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5623_2,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5623_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5624_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5624_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ 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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5624_2,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5624_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5624]) ).
cnf(c_0_5625_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_2,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5626_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ 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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_2,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5627_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr676655987ssThan(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_gr676655987ssThan(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_2,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5628_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ 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_gr676655987ssThan(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_2,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5629_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ dense_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_gr1471790799AtMost(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),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_gr1471790799AtMost(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_2,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5630_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ 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_gr1471790799AtMost(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_2,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| 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),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5631_0,axiom,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk145_5(X1,X2,X5,X3,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk145_5(X1,X2,X5,X3,X4)),X4))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk145_5(X1,X2,X5,X3,X4)),X4))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_3,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk145_5(X1,X2,X5,X3,X4)),X4))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5632_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5632]) ).
cnf(c_0_5632_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5632]) ).
cnf(c_0_5632_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5632]) ).
cnf(c_0_5632_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_5632]) ).
cnf(c_0_5632_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5633_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk124_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5633]) ).
cnf(c_0_5633_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk124_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5633]) ).
cnf(c_0_5633_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk124_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_5633]) ).
cnf(c_0_5633_3,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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk124_5(X2,X1,X3,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5634_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk125_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5634]) ).
cnf(c_0_5634_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk125_5(X2,X1,X3,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),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_5634]) ).
cnf(c_0_5634_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk125_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_5634]) ).
cnf(c_0_5634_3,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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk125_5(X2,X1,X3,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5635_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5636_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_1,axiom,
( ti(X1,X2) = zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_2,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X2) = zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5637_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5637_1,axiom,
( ti(X1,X3) = zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5637_2,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X3) = zero_zero(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5637]) ).
cnf(c_0_5638_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5638_1,axiom,
( ~ linordered_ring(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5639_0,axiom,
( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5639_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
| ~ 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_5639]) ).
cnf(c_0_5639_2,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,finite_finite_1(X1),X3))
| hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5640_0,axiom,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5640_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3)))
| hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5641_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_5641]) ).
cnf(c_0_5641_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_5641]) ).
cnf(c_0_5642_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_5642]) ).
cnf(c_0_5642_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_5642]) ).
cnf(c_0_5642_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_5642]) ).
cnf(c_0_5642_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_5642]) ).
cnf(c_0_5643_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_5643]) ).
cnf(c_0_5643_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_5643]) ).
cnf(c_0_5643_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_5643]) ).
cnf(c_0_5643_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_5643]) ).
cnf(c_0_5644_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_5644]) ).
cnf(c_0_5644_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_5644]) ).
cnf(c_0_5645_0,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5645_1,axiom,
( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5645_2,axiom,
( ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5646_0,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_1,axiom,
( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_2,axiom,
( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5647_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_3,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),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_4,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),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ 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),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5648_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ 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),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_3,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),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(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),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_4,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),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_5,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_eq(X1),X3),X5))
| ~ 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),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5649_0,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_1,axiom,
( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5650_0,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_1,axiom,
( ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4)
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5651_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4)))
| ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5651]) ).
cnf(c_0_5651_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5651]) ).
cnf(c_0_5652_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk111_5(X3,X1,X4,X5,X2)),X5))
| ~ 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),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_5652]) ).
cnf(c_0_5652_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk111_5(X3,X1,X4,X5,X2)),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_5652]) ).
cnf(c_0_5652_2,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(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk111_5(X3,X1,X4,X5,X2)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5652]) ).
cnf(c_0_5653_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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| ~ 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_5653]) ).
cnf(c_0_5653_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)))
| ~ 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_5653]) ).
cnf(c_0_5653_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)),X3),X5))
| 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5654_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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| ~ 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_5654]) ).
cnf(c_0_5654_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X5))
| 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ 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_5654]) ).
cnf(c_0_5654_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)),X3),X5))
| 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5654]) ).
cnf(c_0_5655_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_5655]) ).
cnf(c_0_5655_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_5655]) ).
cnf(c_0_5655_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_5655]) ).
cnf(c_0_5655_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_5655]) ).
cnf(c_0_5656_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(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk131_5(X1,X2,X3,X5,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5656]) ).
cnf(c_0_5656_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk131_5(X1,X2,X3,X5,X4)),X4))
| 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_5656]) ).
cnf(c_0_5657_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5657_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5657]) ).
cnf(c_0_5658_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5658_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5658]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5660_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5661_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_5661]) ).
cnf(c_0_5661_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_5661]) ).
cnf(c_0_5661_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_5661]) ).
cnf(c_0_5662_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_5662]) ).
cnf(c_0_5662_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_5662]) ).
cnf(c_0_5662_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_5662]) ).
cnf(c_0_5663_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_5663]) ).
cnf(c_0_5663_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_5663]) ).
cnf(c_0_5664_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_5664]) ).
cnf(c_0_5664_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_5664]) ).
cnf(c_0_5664_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_5664]) ).
cnf(c_0_5665_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_5665]) ).
cnf(c_0_5665_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_5665]) ).
cnf(c_0_5665_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_5665]) ).
cnf(c_0_5666_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)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5666_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5666_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5666_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5667_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)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5668_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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_1,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(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5669_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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_1,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(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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(X1),X2),X3))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_3,axiom,
( ~ linordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5670_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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_1,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(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ 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(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ 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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5671_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),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_1,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(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ 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(X1),X2),X3))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_3,axiom,
( ~ linordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ 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(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5672_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_1,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5673_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_1,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5674_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_1,axiom,
( ~ linord581940658strict(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),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5675_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_1,axiom,
( ~ linord581940658strict(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),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5676_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,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),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_5676]) ).
cnf(c_0_5677_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5677_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5678_0,axiom,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hAPP(X1,X2,X3,sk1_esk145_5(X1,X2,X5,X3,X4)) != hAPP(X1,X2,X5,sk1_esk145_5(X1,X2,X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_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)),X3),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hAPP(X1,X2,X3,sk1_esk145_5(X1,X2,X5,X3,X4)) != hAPP(X1,X2,X5,sk1_esk145_5(X1,X2,X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5)
| hAPP(X1,X2,X3,sk1_esk145_5(X1,X2,X5,X3,X4)) != hAPP(X1,X2,X5,sk1_esk145_5(X1,X2,X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_3,axiom,
( hAPP(X1,X2,X3,sk1_esk145_5(X1,X2,X5,X3,X4)) != hAPP(X1,X2,X5,sk1_esk145_5(X1,X2,X5,X3,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5679_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk109_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_5679]) ).
cnf(c_0_5679_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_esk109_5(X1,X3,X2,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5680_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk103_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_5680]) ).
cnf(c_0_5680_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_esk103_5(X1,X3,X2,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5681_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_3,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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_4,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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_5,axiom,
( ~ linord20386208strict(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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5682_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_3,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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_4,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_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_5,axiom,
( ~ linord20386208strict(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_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5683_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_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(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_3,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_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(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_4,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_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(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_5,axiom,
( ~ linord20386208strict(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_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(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5684_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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)),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),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),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),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_3,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),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_4,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),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_5,axiom,
( ~ linord20386208strict(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),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5685_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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)),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),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_3,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),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_4,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),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_5,axiom,
( ~ ordered_semiring(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),zero_zero(X1)),X4))
| ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5686_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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))
| ~ 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))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ 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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_3,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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_4,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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_5,axiom,
( ~ ordered_semiring(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),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5687_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_5687]) ).
cnf(c_0_5687_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_5687]) ).
cnf(c_0_5688_0,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),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_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),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5689_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(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_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_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5690_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),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| 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),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5691_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),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| 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),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5692_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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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_5692]) ).
cnf(c_0_5692_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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),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_5692]) ).
cnf(c_0_5692_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_3,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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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_5692]) ).
cnf(c_0_5693_0,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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_1,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),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_2,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5694_0,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),X3),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_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),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_2,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5695_0,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),X4),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_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),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_2,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5696_0,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),X4),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_2,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5697_0,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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_1,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),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_2,axiom,
( ~ linord581940658strict(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),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5698_0,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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_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),X2),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_2,axiom,
( ~ linord581940658strict(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),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(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),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5699_0,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),X4),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_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),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_2,axiom,
( ~ linord581940658strict(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),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5700_0,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),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_2,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| 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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5701_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_5701]) ).
cnf(c_0_5701_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_5701]) ).
cnf(c_0_5702_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)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),X4) = ti(fun(X2,bool),X7)
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X5),X8) != ti(fun(X2,bool),X7)
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X4) != ti(fun(X3,bool),X8) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_1,axiom,
( hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X5),X8) != ti(fun(X2,bool),X7)
| 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)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),X4) = ti(fun(X2,bool),X7)
| hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X4) != ti(fun(X3,bool),X8) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_2,axiom,
( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X6),X4) != ti(fun(X3,bool),X8)
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X5),X8) != ti(fun(X2,bool),X7)
| 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)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),X4) = ti(fun(X2,bool),X7) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5703_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_5703]) ).
cnf(c_0_5704_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_5704]) ).
cnf(c_0_5705_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_5705]) ).
cnf(c_0_5705_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_5705]) ).
cnf(c_0_5706_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_5706]) ).
cnf(c_0_5706_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_5706]) ).
cnf(c_0_5707_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_5707]) ).
cnf(c_0_5707_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_5707]) ).
cnf(c_0_5708_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_3,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5709_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4)))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_2,axiom,
( ~ comm_monoid_add(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5710_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5711_0,axiom,
( hBOOL(hAPP(X1,bool,X4,X5))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk108_5(X1,X2,X5,X4,X3)),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)))))
| ~ 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_5711]) ).
cnf(c_0_5711_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk108_5(X1,X2,X5,X4,X3)),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)))))
| hBOOL(hAPP(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)))) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_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))))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk108_5(X1,X2,X5,X4,X3)),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)))))
| hBOOL(hAPP(X1,bool,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5712_0,axiom,
( hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X4),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))),X5))),X5) = ti(fun(X1,X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),top_top(fun(X1,bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),top_top(fun(X1,bool))))
| hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X4),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))),X5))),X5) = ti(fun(X1,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5713_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk15_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_1,axiom,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk15_1(X1))))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5714_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5714_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5714]) ).
cnf(c_0_5715_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5715]) ).
cnf(c_0_5715_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5715]) ).
cnf(c_0_5716_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5717_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5718_0,axiom,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X1),X2)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5718_1,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X1),X2)),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5719_0,axiom,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X1),X2)),arrow_1568854078le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_1,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X1),X2)),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5720_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,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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_5720]) ).
cnf(c_0_5721_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_4,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5722_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X4),top_top(fun(X3,bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),top_top(fun(X1,bool))))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X4),top_top(fun(X3,bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X4),top_top(fun(X3,bool))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),top_top(fun(X1,bool))))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5723_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_5723]) ).
cnf(c_0_5723_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_5723]) ).
cnf(c_0_5723_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_5723]) ).
cnf(c_0_5724_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_5724]) ).
cnf(c_0_5724_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_5724]) ).
cnf(c_0_5724_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_5724]) ).
cnf(c_0_5725_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_5725]) ).
cnf(c_0_5725_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_5725]) ).
cnf(c_0_5725_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_5725]) ).
cnf(c_0_5726_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_5726]) ).
cnf(c_0_5726_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_5726]) ).
cnf(c_0_5726_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_5726]) ).
cnf(c_0_5727_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_5727]) ).
cnf(c_0_5727_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_5727]) ).
cnf(c_0_5727_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_5727]) ).
cnf(c_0_5728_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_5728]) ).
cnf(c_0_5728_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_5728]) ).
cnf(c_0_5728_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_5728]) ).
cnf(c_0_5729_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_5729]) ).
cnf(c_0_5729_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_5729]) ).
cnf(c_0_5729_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_5729]) ).
cnf(c_0_5730_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_5730]) ).
cnf(c_0_5730_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_5730]) ).
cnf(c_0_5730_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_5730]) ).
cnf(c_0_5733_0,axiom,
( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5733_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3)))
| hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5733]) ).
cnf(c_0_5734_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_5734]) ).
cnf(c_0_5734_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_5734]) ).
cnf(c_0_5735_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),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_5735]) ).
cnf(c_0_5735_1,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(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5735]) ).
cnf(c_0_5736_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5736]) ).
cnf(c_0_5736_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5736]) ).
cnf(c_0_5737_0,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5737_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5737]) ).
cnf(c_0_5738_0,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5738]) ).
cnf(c_0_5738_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5738]) ).
cnf(c_0_5739_0,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5739_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5739]) ).
cnf(c_0_5740_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_5740]) ).
cnf(c_0_5740_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_5740]) ).
cnf(c_0_5741_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_5741]) ).
cnf(c_0_5741_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_5741]) ).
cnf(c_0_5742_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_esk43_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk43_4(X1,X2,X3,X4))))
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5742]) ).
cnf(c_0_5742_1,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk43_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_5742]) ).
cnf(c_0_5742_2,axiom,
( ~ ord(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk43_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_5742]) ).
cnf(c_0_5743_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_esk30_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk30_4(X2,X1,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5743_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_esk30_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk30_4(X2,X1,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5743]) ).
cnf(c_0_5743_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk30_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk30_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_5743]) ).
cnf(c_0_5744_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5745_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)),the_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)))
| ~ 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_5745]) ).
cnf(c_0_5745_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)),the_inv_into(X1,X2),X4),X3),X5)) = ti(X2,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_5745]) ).
cnf(c_0_5745_2,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(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)),the_inv_into(X1,X2),X4),X3),X5)) = ti(X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5746_0,axiom,
( hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X3),X4),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X5),X4)),X3)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3)
| hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_1,axiom,
( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5) != ti(fun(X1,bool),X3)
| hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X3),X4),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X5),X4)),X3)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5747_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_2,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5748_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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_5748]) ).
cnf(c_0_5748_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(X1,fun(fun(X1,bool),bool),member(X1),X4),X5))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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_5748]) ).
cnf(c_0_5748_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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(X1,fun(fun(X1,bool),bool),member(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5749_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_5749]) ).
cnf(c_0_5749_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_5749]) ).
cnf(c_0_5750_0,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_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_1,axiom,
( ~ dense_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_atLeastAtMost(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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_3,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),X5))
| ~ dense_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_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5751_0,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| ~ 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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_1,axiom,
( ~ dense_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_atLeastAtMost(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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_atLeastAtMost(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_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_3,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(X1),X3),X5))
| ~ dense_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_atLeastAtMost(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_5751]) ).
cnf(c_0_5752_0,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_1,axiom,
( ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_3,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),X5))
| ~ order(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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5753_0,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5753_1,axiom,
( ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5753_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5753_3,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),X5))
| ~ dense_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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5753]) ).
cnf(c_0_5754_0,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_1,axiom,
( ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_3,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),X5))
| ~ dense_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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5755_0,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_1,axiom,
( ~ dense_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_gr676655987ssThan(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_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ dense_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_gr676655987ssThan(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_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_3,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),X5))
| ~ dense_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_gr676655987ssThan(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_5755]) ).
cnf(c_0_5756_0,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1)
| ~ 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),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_1,axiom,
( ~ dense_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_gr1471790799AtMost(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),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(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_eq(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_3,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(X1),X3),X5))
| ~ dense_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_gr1471790799AtMost(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_5756]) ).
cnf(c_0_5757_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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| ~ 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_5757]) ).
cnf(c_0_5757_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
| 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4))
| ~ 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_5757]) ).
cnf(c_0_5757_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)),X3),X4))
| 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5758_0,axiom,
( ti(X1,X3) = ti(X1,X5)
| ti(X1,X2) = ti(X1,X4)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_1,axiom,
( ti(X1,X2) = ti(X1,X4)
| ti(X1,X3) = ti(X1,X5)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_2,axiom,
( ~ semiri456707255roduct(X1)
| ti(X1,X2) = ti(X1,X4)
| ti(X1,X3) = ti(X1,X5)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_3,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) = ti(X1,X4)
| ti(X1,X3) = ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5759_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ti(X1,X4) = ti(X1,X5)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_1,axiom,
( ti(X1,X4) = ti(X1,X5)
| ti(X1,X2) = ti(X1,X3)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_2,axiom,
( ~ semiri456707255roduct(X1)
| ti(X1,X4) = ti(X1,X5)
| ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_3,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
| ~ semiri456707255roduct(X1)
| ti(X1,X4) = ti(X1,X5)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5760_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),X4),X3)),X5)) = ti(fun(X2,bool),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X6))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X6))
| 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),X4),X3)),X5)) = ti(fun(X2,bool),X5)
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_2,axiom,
( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X6)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X6))
| 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),X4),X3)),X5)) = ti(fun(X2,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5761_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5761_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5761_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5762_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5762_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5762_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5763_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(nat,X1,X2,X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(nat,X1,X2,X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4)))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_2,axiom,
( ~ comm_monoid_add(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))),hAPP(nat,X1,X2,X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5764_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X1)),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_1,axiom,
( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X1)),arrow_301600364e_Prof)) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5765_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_1,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_2,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_3,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_4,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n)) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5766_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| 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),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5766]) ).
cnf(c_0_5766_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5766]) ).
cnf(c_0_5766_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5766]) ).
cnf(c_0_5766_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5766]) ).
cnf(c_0_5767_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk135_3(X1,X2,X3)),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_1,axiom,
( ~ linord1117847801e_zero(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),times_times(X1),sk1_esk135_3(X1,X2,X3)),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5767_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),sk1_esk135_3(X1,X2,X3)),X2)),X3))
| ~ linord1117847801e_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5767]) ).
cnf(c_0_5768_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5768_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5768_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5768_3,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk170_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5768]) ).
cnf(c_0_5769_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_3,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk171_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5770_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_1,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),X2) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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_5770]) ).
cnf(c_0_5771_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk79_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_5771]) ).
cnf(c_0_5771_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_esk79_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_5771]) ).
cnf(c_0_5771_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_esk79_5(X2,X1,X3,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5772_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk79_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_5772]) ).
cnf(c_0_5772_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_esk79_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_5772]) ).
cnf(c_0_5772_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_esk79_5(X2,X1,X3,X4,X5)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5773_0,axiom,
( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),sk1_esk111_5(X3,X1,X4,X5,X2)))
| ~ 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),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_5773]) ).
cnf(c_0_5773_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),sk1_esk111_5(X3,X1,X4,X5,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_5773]) ).
cnf(c_0_5773_2,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(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),sk1_esk111_5(X3,X1,X4,X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5774_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_2,axiom,
( ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5775_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_2,axiom,
( ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5776_0,axiom,
( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,X3)
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_1,axiom,
( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,X3)
| ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_2,axiom,
( ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X3))
| ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
| hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5777_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_5777]) ).
cnf(c_0_5777_3,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),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5778_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ linord893533164strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord893533164strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_2,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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord893533164strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_3,axiom,
( ~ linord893533164strict(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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5779_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_2,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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_3,axiom,
( ~ linord20386208strict(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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5780_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_3,axiom,
( ~ linord20386208strict(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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5781_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_3,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),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5782_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_3,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),X3),X4))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5783_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_3,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))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5784_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ ordere1490568538miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere1490568538miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_2,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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ ordere1490568538miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_3,axiom,
( ~ ordere1490568538miring(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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5785_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X3),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_2,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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_3,axiom,
( ~ ordered_semiring(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),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5786_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ ordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_3,axiom,
( ~ ordered_semiring(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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5787_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_3,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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5788_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_3,axiom,
( ~ linord581940658strict(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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5789_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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),X4),X2))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ 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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_3,axiom,
( ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ 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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5790_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_3,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),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5791_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(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),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_3,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),X4),X3))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5792_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_3,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),X4),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5793_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ 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),X4),X3))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_3,axiom,
( ~ ordered_ring(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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5794_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ 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),X4),X2))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_2,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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_3,axiom,
( ~ ordered_ring(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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5795_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4))
| hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_1,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk166_4(X1,X2,X4,X5)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5796_0,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk167_4(X1,X2,X4,X5)),X5))
| hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5797_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_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),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_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),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X4),X5)))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_3,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5798_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(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))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_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),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_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),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X5)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5798_3,axiom,
( ~ semilattice_sup(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),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5798]) ).
cnf(c_0_5799_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_5799]) ).
cnf(c_0_5799_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_5799]) ).
cnf(c_0_5799_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_5799]) ).
cnf(c_0_5799_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_5799]) ).
cnf(c_0_5800_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_5800]) ).
cnf(c_0_5800_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_5800]) ).
cnf(c_0_5800_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_5800]) ).
cnf(c_0_5800_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_5800]) ).
cnf(c_0_5801_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_5801]) ).
cnf(c_0_5801_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_5801]) ).
cnf(c_0_5801_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_5801]) ).
cnf(c_0_5801_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_5801]) ).
cnf(c_0_5802_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_5802]) ).
cnf(c_0_5802_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_5802]) ).
cnf(c_0_5802_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_5802]) ).
cnf(c_0_5802_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_5802]) ).
cnf(c_0_5803_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_5803]) ).
cnf(c_0_5803_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_5803]) ).
cnf(c_0_5803_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_5803]) ).
cnf(c_0_5804_0,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))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_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)),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_2,axiom,
( ~ linord581940658strict(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))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5805_0,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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_1,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),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_2,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5806_0,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),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_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),X3),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_2,axiom,
( ~ linord581940658strict(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),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),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),X3),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5807_0,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),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_1,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)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_2,axiom,
( ~ linord581940658strict(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),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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))) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5808_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_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),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5809_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5809]) ).
cnf(c_0_5809_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),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5810_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_2,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),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5811_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ 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),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5811_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5811_2,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),X1),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5812_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ 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),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_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),zero_zero(nat)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5813_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ 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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5813_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),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5813]) ).
cnf(c_0_5814_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5814]) ).
cnf(c_0_5814_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5814]) ).
cnf(c_0_5814_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5814]) ).
cnf(c_0_5815_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_5815]) ).
cnf(c_0_5815_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_5815]) ).
cnf(c_0_5815_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_5815]) ).
cnf(c_0_5816_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_5816]) ).
cnf(c_0_5816_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_5816]) ).
cnf(c_0_5816_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_5816]) ).
cnf(c_0_5817_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),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_5817]) ).
cnf(c_0_5818_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5819_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5820_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(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))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),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)),X2))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_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),X3),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_3,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),X3),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_4,axiom,
( ~ linordered_idom(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),X3),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5821_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(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))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3))
| ~ 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))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_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),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_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))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_4,axiom,
( ~ linordered_idom(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))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5822_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_5822]) ).
cnf(c_0_5822_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_5822]) ).
cnf(c_0_5822_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_5822]) ).
cnf(c_0_5823_0,axiom,
( hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk154_1(X1)),X2)) = hAPP(nat,nat,X1,sk1_esk154_1(X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,hAPP(nat,nat,suc,sk1_esk153_1(X1)))),hAPP(nat,nat,X1,sk1_esk153_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,hAPP(nat,nat,suc,sk1_esk153_1(X1)))),hAPP(nat,nat,X1,sk1_esk153_1(X1))))
| hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk154_1(X1)),X2)) = hAPP(nat,nat,X1,sk1_esk154_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5824_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_3,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,sk1_esk171_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk170_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5827_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_5827]) ).
cnf(c_0_5827_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_5827]) ).
cnf(c_0_5828_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_5828]) ).
cnf(c_0_5828_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_5828]) ).
cnf(c_0_5829_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_2,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
| hAPP(arrow_1998540521e_indi,nat,h,X1) != n ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_3,axiom,
( hAPP(arrow_1998540521e_indi,nat,h,X1) != n
| hAPP(arrow_1998540521e_indi,nat,h,X1) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5830_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_esk111_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2)
| ~ 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),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_5830]) ).
cnf(c_0_5830_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk111_5(X3,X1,X4,X5,X2)) = 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_5830]) ).
cnf(c_0_5830_2,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(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk111_5(X3,X1,X4,X5,X2)) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5831_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_1,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_2,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_3,axiom,
( ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5832_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_1,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
| ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_3,axiom,
( ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5833_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_3,axiom,
( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5834_0,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_1,axiom,
( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_2,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
| ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_3,axiom,
( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4)
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5835_0,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_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(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_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(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_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5836_0,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_atLeastAtMost(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_eq(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(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_5836]) ).
cnf(c_0_5837_0,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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5838_0,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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5839_0,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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5840_0,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_gr676655987ssThan(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))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(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_5840]) ).
cnf(c_0_5841_0,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_gr1471790799AtMost(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))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(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(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(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_5841]) ).
cnf(c_0_5842_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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)))) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_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(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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_5842]) ).
cnf(c_0_5843_0,axiom,
( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)) = hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)
| ~ hBOOL(hAPP(fun(fun(X3,bool),fun(X2,X2)),bool,hAPP(fun(X3,fun(X2,X2)),fun(fun(fun(X3,bool),fun(X2,X2)),bool),finite_folding_idem(X3,X2),X4),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5843_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X3,bool),fun(X2,X2)),bool,hAPP(fun(X3,fun(X2,X2)),fun(fun(fun(X3,bool),fun(X2,X2)),bool),finite_folding_idem(X3,X2),X4),X7))
| hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6)) = hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),comp(X2,X2,X1),hAPP(X3,fun(X2,X2),X4,X5)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5844_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
| hAPP(X2,X1,X5,hAPP(X1,X2,X3,sk1_esk69_5(X2,X1,X5,X3,X4))) != ti(X1,sk1_esk69_5(X2,X1,X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5844_1,axiom,
( hAPP(X2,X1,X5,hAPP(X1,X2,X3,sk1_esk69_5(X2,X1,X5,X3,X4))) != ti(X1,sk1_esk69_5(X2,X1,X5,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_5844]) ).
cnf(c_0_5845_0,axiom,
( ti(X1,X5) = ti(X1,sk1_esk104_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))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_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,X5) = ti(X1,sk1_esk104_4(X1,X2,X4,X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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,X5) = ti(X1,sk1_esk104_4(X1,X2,X4,X3))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_3,axiom,
( ti(X2,X4) != hAPP(X1,X2,X3,X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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,X5) = ti(X1,sk1_esk104_4(X1,X2,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5846_0,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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(X1,fun(fun(X1,bool),bool),member(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_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(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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(X1,fun(fun(X1,bool),bool),member(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),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(X2,fun(fun(X2,bool),bool),member(X2),hAPP(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_5846]) ).
cnf(c_0_5847_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X5))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5848_0,axiom,
( hBOOL(hAPP(X1,bool,X4,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4))))
| hBOOL(hAPP(X1,bool,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5849_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(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(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),X4),X5)) = ti(fun(X2,bool),X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),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_5849]) ).
cnf(c_0_5849_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X3))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5)) = ti(fun(X2,bool),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_5849]) ).
cnf(c_0_5849_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(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X3))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X5)) = ti(fun(X2,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5850_0,axiom,
( hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)),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),X3))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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_5850]) ).
cnf(c_0_5850_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)),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),X3))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5851_0,axiom,
( hAPP(X1,X2,X3,sk1_esk104_4(X1,X2,X4,X3)) = ti(X2,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))))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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))))) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_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,sk1_esk104_4(X1,X2,X4,X3)) = ti(X2,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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))))) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5851_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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_esk104_4(X1,X2,X4,X3)) = ti(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5851]) ).
cnf(c_0_5852_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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_5852]) ).
cnf(c_0_5852_1,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,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5853_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_5853]) ).
cnf(c_0_5853_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_5853]) ).
cnf(c_0_5853_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_5853]) ).
cnf(c_0_5854_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_5854]) ).
cnf(c_0_5854_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_5854]) ).
cnf(c_0_5854_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_5854]) ).
cnf(c_0_5855_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_5855]) ).
cnf(c_0_5855_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_5855]) ).
cnf(c_0_5855_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_5855]) ).
cnf(c_0_5856_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5856_1,axiom,
( ~ semilattice_sup(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),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5856_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5856]) ).
cnf(c_0_5857_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_1,axiom,
( ~ semilattice_sup(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),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5858_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_1,axiom,
( ~ semilattice_sup(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),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5859_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_1,axiom,
( ~ semilattice_sup(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),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5860_0,axiom,
( ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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(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_5860]) ).
cnf(c_0_5860_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ti(fun(X1,bool),X4) = ti(fun(X1,bool),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(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_5860]) ).
cnf(c_0_5860_2,axiom,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5861_0,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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(X2,X4) != hAPP(X1,X2,X3,X5)
| ti(X1,sk1_esk105_5(X1,X2,X4,X3,X5)) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_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(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5)
| ti(X1,sk1_esk105_5(X1,X2,X4,X3,X5)) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_2,axiom,
( ti(X2,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))))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X1,sk1_esk105_5(X1,X2,X4,X3,X5)) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5861_3,axiom,
( ti(X1,sk1_esk105_5(X1,X2,X4,X3,X5)) != ti(X1,X5)
| ti(X2,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))))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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))))) ),
inference(literals_permutation,[status(thm)],[c_0_5861]) ).
cnf(c_0_5862_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),times_times(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_5862]) ).
cnf(c_0_5862_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),times_times(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_5862]) ).
cnf(c_0_5862_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),times_times(X1),X2),X3)),ring_1_Ints(X1)))
| ~ ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5862_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),times_times(X1),X2),X3)),ring_1_Ints(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5862]) ).
cnf(c_0_5863_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_5863]) ).
cnf(c_0_5863_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_5863]) ).
cnf(c_0_5863_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_5863]) ).
cnf(c_0_5863_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_5863]) ).
cnf(c_0_5866_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)),top_top(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),top_top(fun(X2,bool))) != top_top(fun(X1,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5866_1,axiom,
( 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))) != top_top(fun(X1,bool))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)),top_top(fun(X1,bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5867_0,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),sk1_esk121_2(X1,X2)),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)),sk1_esk120_2(X1,X2)))))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5867_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),sk1_esk121_2(X1,X2)),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)),sk1_esk120_2(X1,X2))))) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5868_0,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5)))
| hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_1,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk167_4(X1,X2,X4,X5)))
| hBOOL(hAPP(X1,bool,X2,sk1_esk166_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5869_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5869_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5870_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5871_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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5872_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_5872]) ).
cnf(c_0_5872_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_5872]) ).
cnf(c_0_5873_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_5873]) ).
cnf(c_0_5873_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_5873]) ).
cnf(c_0_5873_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_5873]) ).
cnf(c_0_5873_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_5873]) ).
cnf(c_0_5874_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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_5874]) ).
cnf(c_0_5875_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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_5875]) ).
cnf(c_0_5876_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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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_5876]) ).
cnf(c_0_5877_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_5877]) ).
cnf(c_0_5877_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_5877]) ).
cnf(c_0_5878_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_5878]) ).
cnf(c_0_5878_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_5878]) ).
cnf(c_0_5879_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_5879]) ).
cnf(c_0_5879_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_5879]) ).
cnf(c_0_5880_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_5880]) ).
cnf(c_0_5880_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_5880]) ).
cnf(c_0_5881_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_5881]) ).
cnf(c_0_5881_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_5881]) ).
cnf(c_0_5882_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_5882]) ).
cnf(c_0_5882_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_5882]) ).
cnf(c_0_5882_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_5882]) ).
cnf(c_0_5883_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_5883]) ).
cnf(c_0_5883_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_5883]) ).
cnf(c_0_5883_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_5883]) ).
cnf(c_0_5884_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_5884]) ).
cnf(c_0_5884_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_5884]) ).
cnf(c_0_5884_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_5884]) ).
cnf(c_0_5885_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_5885]) ).
cnf(c_0_5885_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_5885]) ).
cnf(c_0_5885_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_5885]) ).
cnf(c_0_5886_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_5886]) ).
cnf(c_0_5886_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_5886]) ).
cnf(c_0_5886_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_5886]) ).
cnf(c_0_5887_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_5887]) ).
cnf(c_0_5887_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_5887]) ).
cnf(c_0_5887_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_5887]) ).
cnf(c_0_5888_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_5888]) ).
cnf(c_0_5888_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_5888]) ).
cnf(c_0_5888_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_5888]) ).
cnf(c_0_5889_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_5889]) ).
cnf(c_0_5889_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_5889]) ).
cnf(c_0_5889_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_5889]) ).
cnf(c_0_5890_0,axiom,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk134_5(X2,X1,X3,X5,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5890_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk134_5(X2,X1,X3,X5,X4)),X4))
| hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5891_0,axiom,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk172_3(X1,X3,X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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_5891]) ).
cnf(c_0_5891_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk172_3(X1,X3,X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5891]) ).
cnf(c_0_5891_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_esk172_3(X1,X3,X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_5891]) ).
cnf(c_0_5891_3,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(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk172_3(X1,X3,X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_5891]) ).
cnf(c_0_5892_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X3),X4)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X3),X4)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X3),X4)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_3,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X3),X4)),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5893_0,axiom,
( hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X3,X1),fun(X3,X1),hAPP(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),combb(X1,X1,X3),hAPP(X1,fun(X1,X1),times_times(X1),X2)),X4)),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X4),X5))
| ~ semiring_0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5893]) ).
cnf(c_0_5893_1,axiom,
( ~ semiring_0(X1)
| hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X3,X1),fun(X3,X1),hAPP(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),combb(X1,X1,X3),hAPP(X1,fun(X1,X1),times_times(X1),X2)),X4)),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5893]) ).
cnf(c_0_5894_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk136_4(X2,X1,X4,X3)),X3))
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5894_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk136_4(X2,X1,X4,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5894_2,axiom,
( ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk136_4(X2,X1,X4,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5894_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),sk1_esk136_4(X2,X1,X4,X3)),X3))
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5895_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_esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk79_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_5895]) ).
cnf(c_0_5895_1,axiom,
( hAPP(X1,X2,X3,sk1_esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk79_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_5895]) ).
cnf(c_0_5895_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_esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk79_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_5895]) ).
cnf(c_0_5896_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_esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk79_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_5896]) ).
cnf(c_0_5896_1,axiom,
( hAPP(X1,X2,X3,sk1_esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk79_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_5896]) ).
cnf(c_0_5896_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_esk79_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk79_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_5896]) ).
cnf(c_0_5897_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_5(X2,X1,X5,X3,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5897_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk69_5(X2,X1,X5,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_5897]) ).
cnf(c_0_5898_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4)))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5898_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5899_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4)))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5900_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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_1,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)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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_5900]) ).
cnf(c_0_5900_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)),X2),X4))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5901_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5901]) ).
cnf(c_0_5901_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5902_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5902]) ).
cnf(c_0_5902_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5903_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5903]) ).
cnf(c_0_5903_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5903]) ).
cnf(c_0_5904_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_5904]) ).
cnf(c_0_5904_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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5904]) ).
cnf(c_0_5905_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_5905]) ).
cnf(c_0_5905_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_5905]) ).
cnf(c_0_5906_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_5906]) ).
cnf(c_0_5906_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_5906]) ).
cnf(c_0_5907_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_5907]) ).
cnf(c_0_5907_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_5907]) ).
cnf(c_0_5908_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_5908]) ).
cnf(c_0_5908_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_5908]) ).
cnf(c_0_5909_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),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_5909]) ).
cnf(c_0_5909_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),sk1_esk107_4(X3,X1,X4,X2)),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_5909]) ).
cnf(c_0_5909_2,axiom,
( ~ 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(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2))
| ~ 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_5909]) ).
cnf(c_0_5909_3,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,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),sk1_esk107_4(X3,X1,X4,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5909]) ).
cnf(c_0_5911_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_5911]) ).
cnf(c_0_5911_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_5911]) ).
cnf(c_0_5911_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_5911]) ).
cnf(c_0_5914_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5914_3,axiom,
( ~ linord20386208strict(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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5914]) ).
cnf(c_0_5915_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_3,axiom,
( ~ linord20386208strict(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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5916_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_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),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_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),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_3,axiom,
( ~ linord20386208strict(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),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5917_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5917_1,axiom,
( ~ ordere453448008miring(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5917_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ ordere453448008miring(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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_5917]) ).
cnf(c_0_5917_3,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),X3),zero_zero(X1)))
| ~ ordere453448008miring(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5917]) ).
cnf(c_0_5918_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(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),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_1,axiom,
( ~ ordere453448008miring(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5918_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),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_5918]) ).
cnf(c_0_5918_3,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),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5918]) ).
cnf(c_0_5919_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),X2),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_3,axiom,
( ~ ordere453448008miring(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),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5920_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_1,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5920_3,axiom,
( ~ ordere453448008miring(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),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5920]) ).
cnf(c_0_5921_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_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),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_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),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),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5921_3,axiom,
( ~ ordere453448008miring(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),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),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5921]) ).
cnf(c_0_5922_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5922_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5922_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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_5922]) ).
cnf(c_0_5922_3,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),X3),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5922]) ).
cnf(c_0_5923_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord581940658strict(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),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),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_5923]) ).
cnf(c_0_5923_3,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),zero_zero(X1)),X3))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5924_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_5924]) ).
cnf(c_0_5924_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_5924]) ).
cnf(c_0_5924_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_5924]) ).
cnf(c_0_5924_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_5924]) ).
cnf(c_0_5925_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_5925]) ).
cnf(c_0_5925_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_5925]) ).
cnf(c_0_5925_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_5925]) ).
cnf(c_0_5925_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_5925]) ).
cnf(c_0_5926_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_5926]) ).
cnf(c_0_5926_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_5926]) ).
cnf(c_0_5926_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_5926]) ).
cnf(c_0_5926_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_5926]) ).
cnf(c_0_5927_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_5927]) ).
cnf(c_0_5927_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_5927]) ).
cnf(c_0_5927_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_5927]) ).
cnf(c_0_5927_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_5927]) ).
cnf(c_0_5928_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5928_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),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5928_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),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5928_3,axiom,
( ~ semilattice_sup(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),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5929_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_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),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_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),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_3,axiom,
( ~ semilattice_sup(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),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5930_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ semilattice_sup(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),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5930_1,axiom,
( ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ 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),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5930_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5930_3,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),X4))
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5931_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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))
| ~ 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_5931]) ).
cnf(c_0_5931_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(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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_5931]) ).
cnf(c_0_5931_2,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,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),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5931]) ).
cnf(c_0_5932_0,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| hAPP(X1,X2,X3,sk1_esk105_5(X1,X2,X4,X3,X5)) = ti(X2,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))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5932_1,axiom,
( hAPP(X1,X2,X3,sk1_esk105_5(X1,X2,X4,X3,X5)) = ti(X2,X4)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ~ 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(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5932_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,sk1_esk105_5(X1,X2,X4,X3,X5)) = ti(X2,X4)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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)))))
| ti(X2,X4) != hAPP(X1,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5932_3,axiom,
( ti(X2,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))))
| hAPP(X1,X2,X3,sk1_esk105_5(X1,X2,X4,X3,X5)) = ti(X2,X4)
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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))))) ),
inference(literals_permutation,[status(thm)],[c_0_5932]) ).
cnf(c_0_5933_0,axiom,
( 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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5933]) ).
cnf(c_0_5933_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_5933]) ).
cnf(c_0_5933_2,axiom,
( ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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(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_5933]) ).
cnf(c_0_5934_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(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),X2,hAPP(fun(X4,X2),fun(fun(X4,bool),X2),big_co1399186613setsum(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5934_1,axiom,
( ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(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),X2,hAPP(fun(X4,X2),fun(fun(X4,bool),X2),big_co1399186613setsum(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5934_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(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),X2,hAPP(fun(X4,X2),fun(fun(X4,bool),X2),big_co1399186613setsum(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_5934]) ).
cnf(c_0_5935_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))
| ~ 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_5935]) ).
cnf(c_0_5935_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5935]) ).
cnf(c_0_5936_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),zero_zero(X1)))
| ~ linordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5936]) ).
cnf(c_0_5936_1,axiom,
( ~ linordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_5936]) ).
cnf(c_0_5937_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ 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_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5937]) ).
cnf(c_0_5937_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5937]) ).
cnf(c_0_5937_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),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5937]) ).
cnf(c_0_5937_3,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),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5937]) ).
cnf(c_0_5938_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ 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))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_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),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5938_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_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5938]) ).
cnf(c_0_5939_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5939_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5939_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),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5939_3,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_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5939]) ).
cnf(c_0_5940_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_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),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5940_3,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_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5940]) ).
cnf(c_0_5941_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5941_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5941_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),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5941_3,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_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5941]) ).
cnf(c_0_5942_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ 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),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5942_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5942_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),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5942_3,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_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5942]) ).
cnf(c_0_5943_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ 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_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5943_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5943_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),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5943_3,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),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5943]) ).
cnf(c_0_5944_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ 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))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_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),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5944_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_eq(X1),X3),X4))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5944]) ).
cnf(c_0_5945_0,axiom,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(fun(X2,bool),fun(X1,X1),X3,X5)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5945_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X4))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(fun(X2,bool),fun(X1,X1),X3,X5)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5945_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X4))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(fun(X2,bool),fun(X1,X1),X3,X5)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5945_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X6),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X5),X4))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(fun(X2,bool),fun(X1,X1),X3,X5)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5946_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk15_1(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5946_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk15_1(X1),X2)))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5946]) ).
cnf(c_0_5947_0,axiom,
( hAPP(X3,X1,X4,sk1_esk109_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_5947]) ).
cnf(c_0_5947_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_esk109_5(X1,X3,X2,X4,X5)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5947]) ).
cnf(c_0_5948_0,axiom,
( hAPP(X3,X1,X4,sk1_esk103_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_5948]) ).
cnf(c_0_5948_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_esk103_5(X1,X3,X2,X4,X5)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5949_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4))))
| ~ hBOOL(hAPP(X1,bool,X4,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_5949]) ).
cnf(c_0_5949_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X4,X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),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_5949]) ).
cnf(c_0_5949_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,X4,X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_5949]) ).
cnf(c_0_5950_0,axiom,
( hAPP(fun(X1,bool),fun(X2,X2),X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X3,X4)),hAPP(fun(X1,bool),fun(X2,X2),X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5950_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),fun(X2,X2),X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X3,X4)),hAPP(fun(X1,bool),fun(X2,X2),X3,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5950_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),fun(X2,X2),X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X3,X4)),hAPP(fun(X1,bool),fun(X2,X2),X3,X5))
| ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X6),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5950_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X6),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
| hAPP(fun(X1,bool),fun(X2,X2),X3,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X3,X4)),hAPP(fun(X1,bool),fun(X2,X2),X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5950]) ).
cnf(c_0_5951_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X3),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5951]) ).
cnf(c_0_5951_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X3),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5951]) ).
cnf(c_0_5951_2,axiom,
( ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X2,X3)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X3),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5951]) ).
cnf(c_0_5952_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_5952]) ).
cnf(c_0_5952_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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5952]) ).
cnf(c_0_5953_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5953]) ).
cnf(c_0_5953_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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5953]) ).
cnf(c_0_5955_0,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_esk117_4(X3,X1,X4,X2)),X2))
| ~ 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),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5955_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk117_4(X3,X1,X4,X2)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ 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),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5955_2,axiom,
( ~ 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),X4),X2)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk117_4(X3,X1,X4,X2)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5955]) ).
cnf(c_0_5958_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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_5958]) ).
cnf(c_0_5958_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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_5958]) ).
cnf(c_0_5958_2,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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5959_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| ~ 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_5959]) ).
cnf(c_0_5959_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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_5959]) ).
cnf(c_0_5959_2,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(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5960_0,axiom,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X5,X6)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X4))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X5,X6)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X4))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X5,X6)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_3,axiom,
( ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X5),X3))
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X4))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(fun(X2,bool),fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X5,X6)) = hAPP(fun(X2,bool),fun(X1,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5961_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk168_4(X1,X2,X4,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk168_4(X1,X2,X4,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk168_4(X1,X2,X4,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5962_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk168_4(X1,X2,X5,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk168_4(X1,X2,X5,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk168_4(X1,X2,X5,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5963_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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_5963]) ).
cnf(c_0_5963_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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5963]) ).
cnf(c_0_5964_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5964_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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_5964]) ).
cnf(c_0_5965_0,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5966_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5966]) ).
cnf(c_0_5966_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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_5966]) ).
cnf(c_0_5967_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_5967]) ).
cnf(c_0_5967_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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_5967]) ).
cnf(c_0_5968_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5968_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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_5968]) ).
cnf(c_0_5969_0,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5969_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5970_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_5970]) ).
cnf(c_0_5970_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_5970]) ).
cnf(c_0_5971_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_5971]) ).
cnf(c_0_5971_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_5971]) ).
cnf(c_0_5972_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_5972]) ).
cnf(c_0_5972_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_5972]) ).
cnf(c_0_5972_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_5972]) ).
cnf(c_0_5972_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_5972]) ).
cnf(c_0_5973_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5973]) ).
cnf(c_0_5973_1,axiom,
( hBOOL(hAPP(X1,bool,X2,X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5973]) ).
cnf(c_0_5973_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3))
| hBOOL(hAPP(X1,bool,X2,X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5973]) ).
cnf(c_0_5974_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_1,axiom,
( hBOOL(hAPP(X1,bool,X2,X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
| hBOOL(hAPP(X1,bool,X2,X5))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk169_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5975_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),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,finite_finite_1(X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_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(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_2,axiom,
( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),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)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5976_0,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),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_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)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_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),times_times(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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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)) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5977_0,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),times_times(X1),X3),X2)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_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)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_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),times_times(X1),X3),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)),X2))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),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)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5978_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6),X7) = hAPP(X3,X2,X5,hAPP(X1,X3,X6,X7))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X4))
| hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6),X7) = hAPP(X3,X2,X5,hAPP(X1,X3,X6,X7)) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5979_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(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),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_5979]) ).
cnf(c_0_5979_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(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5979]) ).
cnf(c_0_5980_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(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),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_5980]) ).
cnf(c_0_5980_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(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) = ti(fun(X2,bool),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5981_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_5981]) ).
cnf(c_0_5981_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_5981]) ).
cnf(c_0_5981_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_5981]) ).
cnf(c_0_5984_0,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))
| ~ 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),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_1,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))
| ~ 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),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_2,axiom,
( ~ 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),X4),X2)))
| ~ 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)) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5991_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_1,axiom,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_2,axiom,
( ti(X1,X2) != ti(X1,X4)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5992_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_1,axiom,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ti(X1,X3) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_2,axiom,
( ti(X1,X3) != ti(X1,X5)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5993_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_1,axiom,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_2,axiom,
( ti(X1,X2) != ti(X1,X4)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5994_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_1,axiom,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
| ti(X1,X3) != ti(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_2,axiom,
( ti(X1,X3) != ti(X1,X5)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5995_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5996_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5997_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_5997]) ).
cnf(c_0_5997_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_5997]) ).
cnf(c_0_5998_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_5998]) ).
cnf(c_0_5998_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_5998]) ).
cnf(c_0_5999_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(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),X3)) = ti(fun(X2,bool),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_5999]) ).
cnf(c_0_5999_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3))
| hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(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),X4),X3)) = ti(fun(X2,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5999]) ).
cnf(c_0_6000_0,axiom,
( hAPP(X3,X1,X4,sk1_esk116_4(X1,X3,X2,X4)) = 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),top_top(fun(X3,bool))))) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6000_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),top_top(fun(X3,bool)))))
| hAPP(X3,X1,X4,sk1_esk116_4(X1,X3,X2,X4)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6000]) ).
cnf(c_0_6001_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| ~ comm_monoid_mult(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,sk1_esk136_4(X2,X1,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_1,axiom,
( ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| hAPP(X2,X1,X4,sk1_esk136_4(X2,X1,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1)
| hAPP(X2,X1,X4,sk1_esk136_4(X2,X1,X4,X3)) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_3,axiom,
( hAPP(X2,X1,X4,sk1_esk136_4(X2,X1,X4,X3)) != one_one(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
| ~ comm_monoid_mult(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6003_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_1,axiom,
( ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6004_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6004_1,axiom,
( ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6005_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk163_2(X1,X3)),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk163_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk163_2(X1,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6006_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk115_2(X1,X3)),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk115_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk115_2(X1,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6007_0,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),X2),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_1,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),zero_zero(X1)),X2))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_2,axiom,
( ~ linord581940658strict(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),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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_3,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6008_0,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),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_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),zero_zero(X1)),X2))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_2,axiom,
( ~ linord581940658strict(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),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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_3,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6009_0,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),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_1,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),zero_zero(X1)),X3))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_2,axiom,
( ~ linord581940658strict(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),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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_3,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6010_0,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),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_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),zero_zero(X1)),X3))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_2,axiom,
( ~ linord581940658strict(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),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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_3,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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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),zero_zero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6011_0,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(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),top_top(fun(X1,bool))),X3),sk1_esk106_3(X1,X2,X3))) != ti(X2,sk1_esk106_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_1,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),top_top(fun(X1,bool))),X3),sk1_esk106_3(X1,X2,X3))) != ti(X2,sk1_esk106_3(X1,X2,X3))
| 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_6011]) ).
cnf(c_0_6012_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X3),zero_zero(X2)),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6012_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X3),zero_zero(X2)),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6012_2,axiom,
( ~ comm_monoid_add(X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X3),zero_zero(X2)),X4) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6013_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),plus_plus(X1)),X3),zero_zero(X1)),X4) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6013_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),plus_plus(X1)),X3),zero_zero(X1)),X4) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6013_2,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1)
| hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),plus_plus(X1)),X3),zero_zero(X1)),X4) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6014_0,axiom,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4)
| hAPP(X1,X2,X3,sk1_esk134_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X5,sk1_esk134_5(X2,X1,X3,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_1,axiom,
( hAPP(X1,X2,X3,sk1_esk134_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X5,sk1_esk134_5(X2,X1,X3,X5,X4))
| hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6015_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_6015]) ).
cnf(c_0_6015_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_6015]) ).
cnf(c_0_6015_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_6015]) ).
cnf(c_0_6016_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_6016]) ).
cnf(c_0_6016_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_6016]) ).
cnf(c_0_6016_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_6016]) ).
cnf(c_0_6017_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_6017]) ).
cnf(c_0_6017_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_6017]) ).
cnf(c_0_6017_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_6017]) ).
cnf(c_0_6018_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk164_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk164_2(X1,X3)),X3))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk164_2(X1,X3)),X3))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6019_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk112_2(X1,X3)),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk112_2(X1,X3)),X3))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk112_2(X1,X3)),X3))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6020_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_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),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_2,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6021_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_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),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_2,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6022_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6022_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),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6022_2,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6022]) ).
cnf(c_0_6023_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6023_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),semilattice_inf_inf(X1),X2),X3)),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6023_2,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6023]) ).
cnf(c_0_6025_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_6025]) ).
cnf(c_0_6025_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_6025]) ).
cnf(c_0_6025_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_6025]) ).
cnf(c_0_6026_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_6026]) ).
cnf(c_0_6026_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_6026]) ).
cnf(c_0_6027_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_6027]) ).
cnf(c_0_6027_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_6027]) ).
cnf(c_0_6028_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_6028]) ).
cnf(c_0_6028_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_6028]) ).
cnf(c_0_6029_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_6029]) ).
cnf(c_0_6029_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_6029]) ).
cnf(c_0_6031_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_esk57_4(X2,X1,X4,X3)),sk1_esk58_4(X2,X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6031_1,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X4,sk1_esk57_4(X2,X1,X4,X3)),sk1_esk58_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_6031]) ).
cnf(c_0_6032_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)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),top_top(fun(X3,bool))) != top_top(fun(X2,bool))
| 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))) != top_top(fun(X3,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_1,axiom,
( hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),top_top(fun(X3,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),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| 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))) != top_top(fun(X3,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_2,axiom,
( 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))) != top_top(fun(X3,bool))
| hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),top_top(fun(X3,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),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = top_top(fun(X2,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6033_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(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),ord_atLeast(X1),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),ord_atLeast(X1),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_2,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),ord_atLeast(X1),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6034_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ 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),ord_greaterThan(X1),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6034_1,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),ord_greaterThan(X1),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6034_2,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),ord_greaterThan(X1),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)))
| ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6035_0,axiom,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk18_2(X1,X2)),arrow_301600364e_Prof)) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_1,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk18_2(X1,X2)),arrow_301600364e_Prof))
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6036_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6036_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6036_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6036_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6037_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),times_times(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))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_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),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_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),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_3,axiom,
( ~ linord20386208strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6038_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),times_times(X1),X2),X3)))
| ~ ordered_ring(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)) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_1,axiom,
( ~ ordered_ring(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),times_times(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)) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordered_ring(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),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_3,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))
| ~ ordered_ring(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6039_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),times_times(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))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6039_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),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6039_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),times_times(X1),X2),X3)))
| ~ ordere453448008miring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6039_3,axiom,
( ~ ordere453448008miring(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6040_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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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)) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_1,axiom,
( ~ linord581940658strict(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),times_times(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)) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ linord581940658strict(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),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6040_3,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))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6041_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_6041]) ).
cnf(c_0_6041_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_6041]) ).
cnf(c_0_6041_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_6041]) ).
cnf(c_0_6041_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_6041]) ).
cnf(c_0_6042_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_6042]) ).
cnf(c_0_6042_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_6042]) ).
cnf(c_0_6042_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_6042]) ).
cnf(c_0_6042_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_6042]) ).
cnf(c_0_6043_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_6043]) ).
cnf(c_0_6043_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_6043]) ).
cnf(c_0_6043_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_6043]) ).
cnf(c_0_6043_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_6043]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6046_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),times_times(X1),X2),X3)))
| ~ 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)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6046_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),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6046_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),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6046_3,axiom,
( ~ linord581940658strict(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),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6046]) ).
cnf(c_0_6047_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),times_times(X1),X2),X3)))
| ~ ordered_ring(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))) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6047_1,axiom,
( ~ ordered_ring(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),times_times(X1),X2),X3)))
| ~ 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))) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6047_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ ordered_ring(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),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6047_3,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)))
| ~ ordered_ring(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6047]) ).
cnf(c_0_6048_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),times_times(X1),X2),X3)))
| ~ 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)))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_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),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_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),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ ordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_3,axiom,
( ~ ordered_ring(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),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6049_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),times_times(X1),X2),X3)))
| ~ linord581940658strict(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))) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_1,axiom,
( ~ linord581940658strict(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),times_times(X1),X2),X3)))
| ~ 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))) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ linord581940658strict(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),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_3,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)))
| ~ linord581940658strict(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),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6050_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),sk1_esk27_2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6050_1,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),sk1_esk27_2(X1,X2)))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6050]) ).
cnf(c_0_6051_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_6051]) ).
cnf(c_0_6051_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_6051]) ).
cnf(c_0_6051_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_6051]) ).
cnf(c_0_6051_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_6051]) ).
cnf(c_0_6052_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_6052]) ).
cnf(c_0_6052_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_6052]) ).
cnf(c_0_6052_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_6052]) ).
cnf(c_0_6052_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_6052]) ).
cnf(c_0_6053_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_6053]) ).
cnf(c_0_6053_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_6053]) ).
cnf(c_0_6053_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_6053]) ).
cnf(c_0_6053_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_6053]) ).
cnf(c_0_6054_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_6054]) ).
cnf(c_0_6054_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_6054]) ).
cnf(c_0_6054_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_6054]) ).
cnf(c_0_6054_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_6054]) ).
cnf(c_0_6055_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_6055]) ).
cnf(c_0_6055_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_6055]) ).
cnf(c_0_6055_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_6055]) ).
cnf(c_0_6055_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_6055]) ).
cnf(c_0_6056_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6056]) ).
cnf(c_0_6056_1,axiom,
( ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6056]) ).
cnf(c_0_6056_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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_6056]) ).
cnf(c_0_6056_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),X2),X4))
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6056]) ).
cnf(c_0_6057_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6057_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),semilattice_inf_inf(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6057_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),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6057_3,axiom,
( ~ semilattice_inf(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),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6057]) ).
cnf(c_0_6058_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(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),X2),X3))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6058_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),semilattice_inf_inf(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6058_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),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6058_3,axiom,
( ~ semilattice_inf(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),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6058]) ).
cnf(c_0_6059_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_esk100_3(X1,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_6059]) ).
cnf(c_0_6059_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_esk100_3(X1,X2,X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_6059]) ).
cnf(c_0_6059_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_esk100_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_6059]) ).
cnf(c_0_6066_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk164_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6066_1,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk164_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6066_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk164_2(X1,X3)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6067_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk112_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6067_1,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk112_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6067_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk112_2(X1,X3)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6068_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_6068]) ).
cnf(c_0_6068_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_6068]) ).
cnf(c_0_6068_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_6068]) ).
cnf(c_0_6068_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_6068]) ).
cnf(c_0_6069_0,axiom,
( hBOOL(hAPP(nat,bool,X1,sk1_esk163_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6069_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk163_2(X1,X3)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6069_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk163_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6070_0,axiom,
( hBOOL(hAPP(nat,bool,X1,sk1_esk115_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6070_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk115_2(X1,X3)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6070_2,axiom,
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk115_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6071_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_6071]) ).
cnf(c_0_6071_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_6071]) ).
cnf(c_0_6071_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_6071]) ).
cnf(c_0_6071_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_6071]) ).
cnf(c_0_6071_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_6071]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6073_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_6073]) ).
cnf(c_0_6073_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_6073]) ).
cnf(c_0_6073_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_6073]) ).
cnf(c_0_6073_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_6073]) ).
cnf(c_0_6073_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_6073]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6075_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4)
| ~ distrib_lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_1,axiom,
( ~ distrib_lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6076_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4)
| ~ distrib_lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6076_1,axiom,
( ~ distrib_lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6077_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
| ~ comm_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6077_1,axiom,
( ~ comm_semiring(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6078_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6079_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_6079]) ).
cnf(c_0_6079_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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6080_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),times_times(nat),X1),X2)))
| ~ 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_6080]) ).
cnf(c_0_6080_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),times_times(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_6080]) ).
cnf(c_0_6080_2,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),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6081_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_6081]) ).
cnf(c_0_6081_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_6081]) ).
cnf(c_0_6081_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_6081]) ).
cnf(c_0_6082_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_6082]) ).
cnf(c_0_6082_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_6082]) ).
cnf(c_0_6082_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_6082]) ).
cnf(c_0_6083_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_6083]) ).
cnf(c_0_6083_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_6083]) ).
cnf(c_0_6083_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_6083]) ).
cnf(c_0_6084_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk176_4(X1,X3,X2,X4)),X2))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk176_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_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_esk176_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ 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_esk176_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6084_4,axiom,
( hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ 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_esk176_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6084]) ).
cnf(c_0_6085_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_6085]) ).
cnf(c_0_6085_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_6085]) ).
cnf(c_0_6086_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(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)),top_top(fun(X1,bool))) = top_top(fun(X2,bool))
| ~ 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_6086]) ).
cnf(c_0_6086_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(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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)),top_top(fun(X1,bool))) = top_top(fun(X2,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6087_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_6087]) ).
cnf(c_0_6087_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_6087]) ).
cnf(c_0_6087_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_6087]) ).
cnf(c_0_6087_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_6087]) ).
cnf(c_0_6087_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_6087]) ).
cnf(c_0_6088_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6088_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6089_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),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_6089]) ).
cnf(c_0_6089_1,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6090_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),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_6090]) ).
cnf(c_0_6090_1,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6091_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6092_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6093_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),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_6093]) ).
cnf(c_0_6093_1,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6097_0,axiom,
( 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)))
| ~ ring_char_0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6097]) ).
cnf(c_0_6097_1,axiom,
( ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2) != zero_zero(X1)
| ~ ring_char_0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6097]) ).
cnf(c_0_6097_2,axiom,
( ~ 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),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_6097]) ).
cnf(c_0_6098_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6098_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6098_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X4)),X3))
| ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6098]) ).
cnf(c_0_6099_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_6099]) ).
cnf(c_0_6099_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_6099]) ).
cnf(c_0_6099_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_6099]) ).
cnf(c_0_6100_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_6100]) ).
cnf(c_0_6100_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_6100]) ).
cnf(c_0_6100_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_6100]) ).
cnf(c_0_6101_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6101]) ).
cnf(c_0_6101_1,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6101]) ).
cnf(c_0_6101_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6101]) ).
cnf(c_0_6102_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6102]) ).
cnf(c_0_6102_1,axiom,
( ~ semilattice_inf(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),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6102]) ).
cnf(c_0_6102_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6102]) ).
cnf(c_0_6103_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_1,axiom,
( ~ semilattice_inf(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),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6104_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6104_1,axiom,
( ~ semilattice_inf(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),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6104_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6104]) ).
cnf(c_0_6105_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_6105]) ).
cnf(c_0_6105_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_6105]) ).
cnf(c_0_6105_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_6105]) ).
cnf(c_0_6106_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X4,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_1,axiom,
( hBOOL(hAPP(X1,bool,X4,X3))
| hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3))
| hBOOL(hAPP(X1,bool,X4,X3))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6107_0,axiom,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_6107]) ).
cnf(c_0_6107_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)),the_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_6107]) ).
cnf(c_0_6107_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)),the_inv_into(X2,X1),X3),X4),hAPP(X2,X1,X4,X5)) = ti(X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6108_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_6108]) ).
cnf(c_0_6108_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_6108]) ).
cnf(c_0_6108_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_6108]) ).
cnf(c_0_6109_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_6109]) ).
cnf(c_0_6109_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_6109]) ).
cnf(c_0_6109_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_6109]) ).
cnf(c_0_6110_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_6110]) ).
cnf(c_0_6110_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_6110]) ).
cnf(c_0_6110_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_6110]) ).
cnf(c_0_6111_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_6111]) ).
cnf(c_0_6111_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_6111]) ).
cnf(c_0_6111_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_6111]) ).
cnf(c_0_6112_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_6112]) ).
cnf(c_0_6112_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_6112]) ).
cnf(c_0_6112_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_6112]) ).
cnf(c_0_6113_0,axiom,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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))
| hAPP(X2,X1,X4,X6) != ti(X1,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_6113]) ).
cnf(c_0_6113_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
| hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_2,axiom,
( 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))
| hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_6113]) ).
cnf(c_0_6113_3,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3))
| 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))
| hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6114_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_6114]) ).
cnf(c_0_6114_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_6114]) ).
cnf(c_0_6114_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_6114]) ).
cnf(c_0_6114_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_6114]) ).
cnf(c_0_6115_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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6115]) ).
cnf(c_0_6115_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_6115]) ).
cnf(c_0_6116_0,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),times_times(nat),X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6116_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_6116]) ).
cnf(c_0_6117_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk178_4(X1,X3,X2,X4)),X2))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk178_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_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_esk178_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_3,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ 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_esk178_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hAPP(X1,nat,X3,X4) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_4,axiom,
( hAPP(X1,nat,X3,X4) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ 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_esk178_4(X1,X3,X2,X4)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6118_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6118_1,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6118_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6119_0,axiom,
( ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6119_1,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6119_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6120_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_6120]) ).
cnf(c_0_6120_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_6120]) ).
cnf(c_0_6120_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_6120]) ).
cnf(c_0_6120_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_6120]) ).
cnf(c_0_6121_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6121]) ).
cnf(c_0_6121_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6121]) ).
cnf(c_0_6122_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6122_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6125_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_6125]) ).
cnf(c_0_6125_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_6125]) ).
cnf(c_0_6125_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_6125]) ).
cnf(c_0_6126_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_6126]) ).
cnf(c_0_6126_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_6126]) ).
cnf(c_0_6126_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_6126]) ).
cnf(c_0_6127_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_6127]) ).
cnf(c_0_6127_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_6127]) ).
cnf(c_0_6127_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_6127]) ).
cnf(c_0_6128_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_6128]) ).
cnf(c_0_6128_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_6128]) ).
cnf(c_0_6128_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_6128]) ).
cnf(c_0_6129_0,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk162_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk162_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk162_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6130_0,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk114_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk114_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk114_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6131_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6131_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4),X3))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6132_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6132_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2),X3))
| hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6133_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6133_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4))
| hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6134_0,axiom,
( hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4))
| hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6135_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_6135]) ).
cnf(c_0_6135_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_6135]) ).
cnf(c_0_6136_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_6136]) ).
cnf(c_0_6136_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_6136]) ).
cnf(c_0_6137_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_6137]) ).
cnf(c_0_6137_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_6137]) ).
cnf(c_0_6139_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_6139]) ).
cnf(c_0_6139_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_6139]) ).
cnf(c_0_6139_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_6139]) ).
cnf(c_0_6140_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_6140]) ).
cnf(c_0_6140_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_6140]) ).
cnf(c_0_6140_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_6140]) ).
cnf(c_0_6141_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk165_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6141_1,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk165_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6141_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk165_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6141]) ).
cnf(c_0_6142_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk113_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6142_1,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk113_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6142_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk113_2(X1,X3)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6142]) ).
cnf(c_0_6143_0,axiom,
( hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(X2,fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X3,X4)) = hAPP(X2,fun(X1,X1),X3,X4)
| ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6143_1,axiom,
( ~ hBOOL(hAPP(fun(fun(X2,bool),fun(X1,X1)),bool,hAPP(fun(X2,fun(X1,X1)),fun(fun(fun(X2,bool),fun(X1,X1)),bool),finite_folding_idem(X2,X1),X3),X5))
| hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,X1),fun(X1,X1)),comp(X1,X1,X1),hAPP(X2,fun(X1,X1),X3,X4)),hAPP(X2,fun(X1,X1),X3,X4)) = hAPP(X2,fun(X1,X1),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6143]) ).
cnf(c_0_6144_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),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_6144]) ).
cnf(c_0_6144_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6144_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6145_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),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_6145]) ).
cnf(c_0_6145_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6145_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6146_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(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_6146]) ).
cnf(c_0_6146_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6147_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),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_6147]) ).
cnf(c_0_6147_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6147_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6148_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_6148]) ).
cnf(c_0_6148_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_6148]) ).
cnf(c_0_6148_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_6148]) ).
cnf(c_0_6149_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X7,X2,hAPP(fun(X7,X8),fun(X7,X2),hAPP(fun(X8,X2),fun(fun(X7,X8),fun(X7,X2)),comp(X8,X2,X7),X9),X10),X11)
| hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)) != hAPP(X8,X2,X9,hAPP(X7,X8,X10,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_1,axiom,
( hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)) != hAPP(X8,X2,X9,hAPP(X7,X8,X10,X11))
| hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X7,X2,hAPP(fun(X7,X8),fun(X7,X2),hAPP(fun(X8,X2),fun(fun(X7,X8),fun(X7,X2)),comp(X8,X2,X7),X9),X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6150_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))),X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_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),times_times(X1),X2),X3)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6151_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ distrib_lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6151_1,axiom,
( ~ distrib_lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6152_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ distrib_lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6152_1,axiom,
( ~ distrib_lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6153_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6153_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6154_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_6154]) ).
cnf(c_0_6154_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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6155_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_6155]) ).
cnf(c_0_6155_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_6155]) ).
cnf(c_0_6156_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6156_1,axiom,
( ~ lattice(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6157_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6157_1,axiom,
( ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6158_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_1,axiom,
( ~ lattice(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6159_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6159_1,axiom,
( ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6160_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_6160]) ).
cnf(c_0_6160_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_6160]) ).
cnf(c_0_6160_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_6160]) ).
cnf(c_0_6161_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_6161]) ).
cnf(c_0_6161_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_6161]) ).
cnf(c_0_6161_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_6161]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6163_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_6163]) ).
cnf(c_0_6163_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_6163]) ).
cnf(c_0_6163_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_6163]) ).
cnf(c_0_6164_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_6164]) ).
cnf(c_0_6164_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_6164]) ).
cnf(c_0_6164_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_6164]) ).
cnf(c_0_6165_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_6165]) ).
cnf(c_0_6165_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_6165]) ).
cnf(c_0_6165_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_6165]) ).
cnf(c_0_6166_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_6166]) ).
cnf(c_0_6166_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_6166]) ).
cnf(c_0_6166_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_6166]) ).
cnf(c_0_6167_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_6167]) ).
cnf(c_0_6167_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_6167]) ).
cnf(c_0_6167_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_6167]) ).
cnf(c_0_6167_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_6167]) ).
cnf(c_0_6168_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_6168]) ).
cnf(c_0_6168_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_6168]) ).
cnf(c_0_6168_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_6168]) ).
cnf(c_0_6168_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_6168]) ).
cnf(c_0_6169_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk15_1(X1)),arrow_301600364e_Prof)) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_1,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk15_1(X1)),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6170_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk10_1(X1)),arrow_301600364e_Prof)) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6170_1,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk10_1(X1)),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6171_0,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk11_1(X1)),arrow_301600364e_Prof)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_1,axiom,
( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sk1_esk11_1(X1)),arrow_301600364e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6172_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_6172]) ).
cnf(c_0_6172_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_6172]) ).
cnf(c_0_6172_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_6172]) ).
cnf(c_0_6173_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_6173]) ).
cnf(c_0_6173_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_6173]) ).
cnf(c_0_6173_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_6173]) ).
cnf(c_0_6174_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_6174]) ).
cnf(c_0_6174_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_6174]) ).
cnf(c_0_6174_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_6174]) ).
cnf(c_0_6175_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_6175]) ).
cnf(c_0_6175_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_6175]) ).
cnf(c_0_6176_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_6176]) ).
cnf(c_0_6176_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_6176]) ).
cnf(c_0_6176_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_6176]) ).
cnf(c_0_6176_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_6176]) ).
cnf(c_0_6176_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_6176]) ).
cnf(c_0_6177_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_6177]) ).
cnf(c_0_6177_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_6177]) ).
cnf(c_0_6177_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_6177]) ).
cnf(c_0_6177_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_6177]) ).
cnf(c_0_6177_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_6177]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6179_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_6179]) ).
cnf(c_0_6179_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_6179]) ).
cnf(c_0_6179_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_6179]) ).
cnf(c_0_6179_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_6179]) ).
cnf(c_0_6179_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_6179]) ).
cnf(c_0_6180_0,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),ord_atLeast(X1),X2)),hAPP(X1,fun(X1,bool),ord_atLeast(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_6180]) ).
cnf(c_0_6180_1,axiom,
( ~ order(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),ord_atLeast(X1),X2)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(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),ord_atLeast(X1),X2)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6181_0,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),ord_greaterThan(X1),X2)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),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_6181]) ).
cnf(c_0_6181_1,axiom,
( ~ 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),ord_greaterThan(X1),X2)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6181_2,axiom,
( ~ 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),ord_greaterThan(X1),X2)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6181]) ).
cnf(c_0_6182_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X3)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))
| hAPP(nat,X1,X2,zero_zero(nat)) != zero_zero(X1)
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6182_1,axiom,
( hAPP(nat,X1,X2,zero_zero(nat)) != zero_zero(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X3)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6182_2,axiom,
( ~ comm_monoid_add(X1)
| hAPP(nat,X1,X2,zero_zero(nat)) != zero_zero(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X3)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6182]) ).
cnf(c_0_6183_0,axiom,
( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2))
| hAPP(nat,nat,X1,zero_zero(nat)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6183]) ).
cnf(c_0_6183_1,axiom,
( hAPP(nat,nat,X1,zero_zero(nat)) != zero_zero(nat)
| hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6183]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6186_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_esk57_4(X2,X1,X4,X3)),sk1_esk58_4(X2,X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X3,sk1_esk57_4(X2,X1,X4,X3)),sk1_esk58_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_6186]) ).
cnf(c_0_6187_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_6187]) ).
cnf(c_0_6187_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_6187]) ).
cnf(c_0_6187_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_6187]) ).
cnf(c_0_6187_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_6187]) ).
cnf(c_0_6188_0,axiom,
( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = ti(fun(X1,X2),X3)
| ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_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)),X3),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
| hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = ti(fun(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6189_0,axiom,
( ti(X1,X4) = ti(X1,X6)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X2) != ti(X1,X5)
| ~ semiri456707255roduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_1,axiom,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X4) = ti(X1,X6)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X2) != ti(X1,X5)
| ~ semiri456707255roduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X4) = ti(X1,X6)
| ti(X1,X2) != ti(X1,X5)
| ~ semiri456707255roduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_3,axiom,
( ti(X1,X2) != ti(X1,X5)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X4) = ti(X1,X6)
| ~ semiri456707255roduct(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_4,axiom,
( ~ semiri456707255roduct(X1)
| ti(X1,X2) != ti(X1,X5)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X6))
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X4) = ti(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6190_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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,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_6190]) ).
cnf(c_0_6190_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(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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6191_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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,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_6191]) ).
cnf(c_0_6191_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(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),top_top(fun(X1,bool))),X3),X4)) = ti(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6192_0,axiom,
( hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),sk1_esk121_2(X1,X2)),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)),sk1_esk120_2(X1,X2)))) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),sk1_esk121_2(X1,X2)),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)),sk1_esk120_2(X1,X2)))) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6193_0,axiom,
( hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),sk1_esk119_2(X1,X2)),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)),sk1_esk118_2(X1,X2)))) = ti(fun(X1,bool),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),sk1_esk119_2(X1,X2)),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)),sk1_esk118_2(X1,X2)))) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6194_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_6194]) ).
cnf(c_0_6194_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_6194]) ).
cnf(c_0_6194_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_6194]) ).
cnf(c_0_6195_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_6195]) ).
cnf(c_0_6195_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_6195]) ).
cnf(c_0_6195_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_6195]) ).
cnf(c_0_6196_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_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(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_2,axiom,
( ~ semilattice_sup(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),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6197_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_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),semilattice_sup_sup(X1),X3),X4)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_2,axiom,
( ~ semilattice_sup(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),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6198_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_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),semilattice_sup_sup(X1),X3),X4)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_2,axiom,
( ~ semilattice_sup(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),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6199_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6199_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),semilattice_sup_sup(X1),X3),X4)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6199_2,axiom,
( ~ semilattice_sup(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),semilattice_sup_sup(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6200_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_6200]) ).
cnf(c_0_6200_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_6200]) ).
cnf(c_0_6200_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_6200]) ).
cnf(c_0_6201_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_6201]) ).
cnf(c_0_6201_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_6201]) ).
cnf(c_0_6201_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_6201]) ).
cnf(c_0_6202_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_6202]) ).
cnf(c_0_6202_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_6202]) ).
cnf(c_0_6202_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_6202]) ).
cnf(c_0_6203_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_6203]) ).
cnf(c_0_6203_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_6203]) ).
cnf(c_0_6203_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_6203]) ).
cnf(c_0_6204_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_6204]) ).
cnf(c_0_6204_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_6204]) ).
cnf(c_0_6205_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_6205]) ).
cnf(c_0_6205_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_6205]) ).
cnf(c_0_6206_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_6206]) ).
cnf(c_0_6206_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_6206]) ).
cnf(c_0_6207_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_6207]) ).
cnf(c_0_6207_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_6207]) ).
cnf(c_0_6208_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_6208]) ).
cnf(c_0_6208_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_6208]) ).
cnf(c_0_6209_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_6209]) ).
cnf(c_0_6209_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_6209]) ).
cnf(c_0_6210_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_6210]) ).
cnf(c_0_6210_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_6210]) ).
cnf(c_0_6211_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_6211]) ).
cnf(c_0_6211_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_6211]) ).
cnf(c_0_6212_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_6212]) ).
cnf(c_0_6212_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_6212]) ).
cnf(c_0_6213_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_6213]) ).
cnf(c_0_6213_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_6213]) ).
cnf(c_0_6214_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_6214]) ).
cnf(c_0_6214_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_6214]) ).
cnf(c_0_6214_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_6214]) ).
cnf(c_0_6214_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_6214]) ).
cnf(c_0_6215_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk95_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_6215]) ).
cnf(c_0_6215_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_esk95_2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6216_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_6216]) ).
cnf(c_0_6216_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_6216]) ).
cnf(c_0_6217_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_6217]) ).
cnf(c_0_6217_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_6217]) ).
cnf(c_0_6218_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_6218]) ).
cnf(c_0_6218_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_6218]) ).
cnf(c_0_6219_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_6219]) ).
cnf(c_0_6219_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_6219]) ).
cnf(c_0_6220_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_6220]) ).
cnf(c_0_6220_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_6220]) ).
cnf(c_0_6223_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_6223]) ).
cnf(c_0_6223_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_2,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,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6224_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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_6224]) ).
cnf(c_0_6224_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_2,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,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6226_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_6226]) ).
cnf(c_0_6226_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_6226]) ).
cnf(c_0_6227_0,axiom,
( ti(fun(X1,bool),X4) = ti(fun(X1,bool),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(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_6227]) ).
cnf(c_0_6227_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(fun(X1,bool),X4) = ti(fun(X1,bool),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(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_6227]) ).
cnf(c_0_6227_2,axiom,
( 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))))
| ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_6227]) ).
cnf(c_0_6228_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_6228]) ).
cnf(c_0_6228_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_6228]) ).
cnf(c_0_6229_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_6229]) ).
cnf(c_0_6229_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_6229]) ).
cnf(c_0_6230_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_6230]) ).
cnf(c_0_6230_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_6230]) ).
cnf(c_0_6231_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,sk1_esk176_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,sk1_esk176_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,sk1_esk176_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_3,axiom,
( hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,sk1_esk176_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_4,axiom,
( hAPP(X1,nat,X3,sk1_esk176_4(X1,X3,X2,X4)) != zero_zero(nat)
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6232_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,sk1_esk146_3(X1,X4,X2))),hAPP(X1,nat,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6232_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,sk1_esk146_3(X1,X4,X2))),hAPP(X1,nat,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6232_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,sk1_esk146_3(X1,X4,X2))),hAPP(X1,nat,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_6232]) ).
cnf(c_0_6233_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_6233]) ).
cnf(c_0_6233_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_6233]) ).
cnf(c_0_6233_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_6233]) ).
cnf(c_0_6234_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_6234]) ).
cnf(c_0_6234_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_6234]) ).
cnf(c_0_6234_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_6234]) ).
cnf(c_0_6236_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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,X3,sk1_esk150_3(X1,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,sk1_esk150_3(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(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6237_0,axiom,
( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| zero_zero(nat) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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))
| zero_zero(nat) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))
| zero_zero(nat) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_3,axiom,
( zero_zero(nat) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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_6237]) ).
cnf(c_0_6240_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6240_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6240_2,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6241_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(X2,X1,X4,hAPP(X1,X2,X3,sk1_esk110_4(X1,X2,X4,X3))) != ti(X1,sk1_esk110_4(X1,X2,X4,X3))
| 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_6241]) ).
cnf(c_0_6241_1,axiom,
( hAPP(X2,X1,X4,hAPP(X1,X2,X3,sk1_esk110_4(X1,X2,X4,X3))) != ti(X1,sk1_esk110_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)
| 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_6241]) ).
cnf(c_0_6241_2,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(X2,X1,X4,hAPP(X1,X2,X3,sk1_esk110_4(X1,X2,X4,X3))) != ti(X1,sk1_esk110_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_6241]) ).
cnf(c_0_6242_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_6242]) ).
cnf(c_0_6242_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_6242]) ).
cnf(c_0_6242_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_6242]) ).
cnf(c_0_6242_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_6242]) ).
cnf(c_0_6243_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_6243]) ).
cnf(c_0_6243_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_6243]) ).
cnf(c_0_6243_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_6243]) ).
cnf(c_0_6244_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_6244]) ).
cnf(c_0_6244_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_6244]) ).
cnf(c_0_6244_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_6244]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6245_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_6245]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6246_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_6246]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6247_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_6247]) ).
cnf(c_0_6248_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_6248]) ).
cnf(c_0_6248_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_6248]) ).
cnf(c_0_6248_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_6248]) ).
cnf(c_0_6248_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_6248]) ).
cnf(c_0_6249_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_6249]) ).
cnf(c_0_6249_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_6249]) ).
cnf(c_0_6249_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_6249]) ).
cnf(c_0_6249_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_6249]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6251_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_6251]) ).
cnf(c_0_6251_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_6251]) ).
cnf(c_0_6251_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_6251]) ).
cnf(c_0_6251_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_6251]) ).
cnf(c_0_6252_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_6252]) ).
cnf(c_0_6252_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_6252]) ).
cnf(c_0_6252_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_6252]) ).
cnf(c_0_6252_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_6252]) ).
cnf(c_0_6253_0,axiom,
( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),the_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_6253]) ).
cnf(c_0_6253_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)),the_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_6253]) ).
cnf(c_0_6254_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_6254]) ).
cnf(c_0_6254_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_6254]) ).
cnf(c_0_6255_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ti(X1,sk1_esk176_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6255_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ti(X1,sk1_esk176_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6255_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ti(X1,sk1_esk176_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6255_3,axiom,
( hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat))
| ti(X1,sk1_esk176_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6255_4,axiom,
( ti(X1,sk1_esk176_4(X1,X3,X2,X4)) != ti(X1,X4)
| hAPP(X1,nat,X3,X4) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6257_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_6257]) ).
cnf(c_0_6257_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_6257]) ).
cnf(c_0_6257_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_6257]) ).
cnf(c_0_6258_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_6258]) ).
cnf(c_0_6258_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_6258]) ).
cnf(c_0_6258_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_6258]) ).
cnf(c_0_6260_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_6260]) ).
cnf(c_0_6260_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_6260]) ).
cnf(c_0_6260_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_6260]) ).
cnf(c_0_6261_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6261_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),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),one_one(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6262_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6262_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6263_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6263_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6264_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6264_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6265_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6265]) ).
cnf(c_0_6265_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6265]) ).
cnf(c_0_6266_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6266_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6266]) ).
cnf(c_0_6267_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6267_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6267]) ).
cnf(c_0_6268_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ ab_semigroup_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6268_1,axiom,
( ~ ab_semigroup_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6268]) ).
cnf(c_0_6269_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6269_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6270_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6270_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6271_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_6271]) ).
cnf(c_0_6271_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_6271]) ).
cnf(c_0_6272_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_6272]) ).
cnf(c_0_6272_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_6272]) ).
cnf(c_0_6273_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_6273]) ).
cnf(c_0_6273_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_6273]) ).
cnf(c_0_6274_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_6274]) ).
cnf(c_0_6274_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_6274]) ).
cnf(c_0_6274_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_6274]) ).
cnf(c_0_6275_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_6275]) ).
cnf(c_0_6275_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_6275]) ).
cnf(c_0_6276_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_6276]) ).
cnf(c_0_6276_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_6276]) ).
cnf(c_0_6276_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_6276]) ).
cnf(c_0_6276_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_6276]) ).
cnf(c_0_6277_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_6277]) ).
cnf(c_0_6277_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_6277]) ).
cnf(c_0_6277_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_6277]) ).
cnf(c_0_6277_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_6277]) ).
cnf(c_0_6277_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_6277]) ).
cnf(c_0_6278_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_6278]) ).
cnf(c_0_6278_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_6278]) ).
cnf(c_0_6278_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_6278]) ).
cnf(c_0_6278_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_6278]) ).
cnf(c_0_6278_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_6278]) ).
cnf(c_0_6279_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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
| hBOOL(hAPP(X1,bool,X2,sk1_esk150_3(X1,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6279_1,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk150_3(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(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6280_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| hAPP(X1,nat,X3,sk1_esk178_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6280_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| hAPP(X1,nat,X3,sk1_esk178_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6280_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hAPP(X1,nat,X3,X4) != one_one(nat)
| hAPP(X1,nat,X3,sk1_esk178_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6280_3,axiom,
( hAPP(X1,nat,X3,X4) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hAPP(X1,nat,X3,sk1_esk178_4(X1,X3,X2,X4)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6280_4,axiom,
( hAPP(X1,nat,X3,sk1_esk178_4(X1,X3,X2,X4)) != zero_zero(nat)
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6283_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)))
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6284_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6284_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6284_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)))
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6285_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_6285]) ).
cnf(c_0_6285_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_6285]) ).
cnf(c_0_6285_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_6285]) ).
cnf(c_0_6286_0,axiom,
( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ comm_monoid_add(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6286_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6286_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ comm_monoid_add(X1)
| hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),hAPP(nat,nat,suc,X4))) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6287_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6287_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6288_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6288_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6289_0,axiom,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ti(X1,sk1_esk175_3(X1,X3,X2)) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_1,axiom,
( ti(X1,sk1_esk175_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(X1,sk1_esk175_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_3,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(X1,sk1_esk175_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(X1,sk1_esk175_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6290_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_6290]) ).
cnf(c_0_6290_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_6290]) ).
cnf(c_0_6290_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_6290]) ).
cnf(c_0_6290_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_6290]) ).
cnf(c_0_6290_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_6290]) ).
cnf(c_0_6290_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_6290]) ).
cnf(c_0_6291_0,axiom,
( 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,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6291]) ).
cnf(c_0_6291_1,axiom,
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X4))
| 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_6291]) ).
cnf(c_0_6292_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_6292]) ).
cnf(c_0_6292_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_6292]) ).
cnf(c_0_6293_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_6293]) ).
cnf(c_0_6293_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_6293]) ).
cnf(c_0_6294_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_6294]) ).
cnf(c_0_6294_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_6294]) ).
cnf(c_0_6295_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6295_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6296_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6296_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6297_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6298_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6298_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X4))
| hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6299_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ 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),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ti(X1,sk1_esk178_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ti(X1,sk1_esk178_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ti(X1,sk1_esk178_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_3,axiom,
( hAPP(X1,nat,X3,X4) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat)
| ti(X1,sk1_esk178_4(X1,X3,X2,X4)) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_4,axiom,
( ti(X1,sk1_esk178_4(X1,X3,X2,X4)) != ti(X1,X4)
| hAPP(X1,nat,X3,X4) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6301_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_6301]) ).
cnf(c_0_6301_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_6301]) ).
cnf(c_0_6302_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_esk77_4(X2,X1,X3,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6302_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk77_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_6302]) ).
cnf(c_0_6303_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_esk78_4(X2,X1,X3,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6303_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk78_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_6303]) ).
cnf(c_0_6304_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_6304]) ).
cnf(c_0_6304_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_6304]) ).
cnf(c_0_6305_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_esk32_4(X1,X2,X3,X4)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6305_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk32_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_6305]) ).
cnf(c_0_6306_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_6306]) ).
cnf(c_0_6306_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_6306]) ).
cnf(c_0_6306_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_6306]) ).
cnf(c_0_6307_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_6307]) ).
cnf(c_0_6307_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_6307]) ).
cnf(c_0_6307_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_6307]) ).
cnf(c_0_6308_0,axiom,
( hAPP(nat,nat,suc,sk1_esk95_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_6308]) ).
cnf(c_0_6308_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_esk95_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6309_0,axiom,
( hAPP(nat,nat,suc,sk1_esk93_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_6309]) ).
cnf(c_0_6309_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_esk93_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6310_0,axiom,
( hBOOL(hAPP(nat,bool,X3,X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk87_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_6310]) ).
cnf(c_0_6310_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk87_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_6310]) ).
cnf(c_0_6310_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_esk87_3(X3,X1,X2)),X2))
| hBOOL(hAPP(nat,bool,X3,X1))
| ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6310_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_esk87_3(X3,X1,X2)),X2))
| hBOOL(hAPP(nat,bool,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6311_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_6311]) ).
cnf(c_0_6311_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_6311]) ).
cnf(c_0_6311_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_6311]) ).
cnf(c_0_6311_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_6311]) ).
cnf(c_0_6312_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6312_1,axiom,
( ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6312_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6312_3,axiom,
( ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linord581940658strict(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6313_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk169_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6313_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,sk1_esk169_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6313_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk169_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,bool,X2,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6314_0,axiom,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk169_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,sk1_esk169_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
| ~ hBOOL(hAPP(X1,bool,X2,sk1_esk169_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,bool,X2,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6316_0,axiom,
( 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))))
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_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(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)
| ti(fun(X1,bool),X4) != ti(fun(X1,bool),X5) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_2,axiom,
( ti(fun(X1,bool),X4) != ti(fun(X1,bool),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(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_6316]) ).
cnf(c_0_6317_0,axiom,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ti(X1,sk1_esk177_3(X1,X3,X2)) = ti(X1,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_1,axiom,
( ti(X1,sk1_esk177_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(X1,sk1_esk177_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_3,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(X1,sk1_esk177_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_4,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ti(X1,sk1_esk177_3(X1,X3,X2)) = ti(X1,X4)
| hAPP(X1,nat,X3,X4) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6318_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_6318]) ).
cnf(c_0_6318_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_6318]) ).
cnf(c_0_6318_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_6318]) ).
cnf(c_0_6319_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_esk60_3(X1,X3,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6319]) ).
cnf(c_0_6319_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk60_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_6319]) ).
cnf(c_0_6320_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_6320]) ).
cnf(c_0_6320_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_6320]) ).
cnf(c_0_6321_0,axiom,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6))
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6321_1,axiom,
( hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9)
| hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_6321]) ).
cnf(c_0_6322_0,axiom,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6))
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_1,axiom,
( hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != hAPP(fun(X4,X7),fun(X4,X2),hAPP(fun(X7,X2),fun(fun(X4,X7),fun(X4,X2)),comp(X7,X2,X4),X8),X9)
| hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X7,X2,X8,hAPP(X4,X7,X9,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6323_0,axiom,
( hBOOL(hAPP(nat,bool,X3,X1))
| hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,sk1_esk87_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_6323]) ).
cnf(c_0_6323_1,axiom,
( hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,sk1_esk87_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_6323]) ).
cnf(c_0_6323_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_esk87_3(X3,X1,X2))))
| hBOOL(hAPP(nat,bool,X3,X1))
| ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_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_esk87_3(X3,X1,X2))))
| hBOOL(hAPP(nat,bool,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6324_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_6324]) ).
cnf(c_0_6324_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_6324]) ).
cnf(c_0_6324_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_6324]) ).
cnf(c_0_6325_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_6325]) ).
cnf(c_0_6325_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_6325]) ).
cnf(c_0_6325_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_6325]) ).
cnf(c_0_6326_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_6326]) ).
cnf(c_0_6326_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_6326]) ).
cnf(c_0_6326_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_6326]) ).
cnf(c_0_6326_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_6326]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6328_0,axiom,
( hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ 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),X4),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6328_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6328_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,X4) = zero_zero(nat)
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6328_3,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,X4) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6328]) ).
cnf(c_0_6329_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_6329]) ).
cnf(c_0_6329_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_6329]) ).
cnf(c_0_6329_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_6329]) ).
cnf(c_0_6330_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_6330]) ).
cnf(c_0_6330_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_6330]) ).
cnf(c_0_6330_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_6330]) ).
cnf(c_0_6331_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_6331]) ).
cnf(c_0_6331_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_6331]) ).
cnf(c_0_6331_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_6331]) ).
cnf(c_0_6332_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_6332]) ).
cnf(c_0_6332_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_6332]) ).
cnf(c_0_6332_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_6332]) ).
cnf(c_0_6333_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_6333]) ).
cnf(c_0_6333_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_6333]) ).
cnf(c_0_6335_0,axiom,
( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6336_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_6336]) ).
cnf(c_0_6336_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_6336]) ).
cnf(c_0_6336_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_6336]) ).
cnf(c_0_6337_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_6337]) ).
cnf(c_0_6337_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_6337]) ).
cnf(c_0_6337_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_6337]) ).
cnf(c_0_6338_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6338_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6338_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ ord(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6339_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6339_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6339_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ ord(X1)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6340_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_6340]) ).
cnf(c_0_6340_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_6340]) ).
cnf(c_0_6341_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_6341]) ).
cnf(c_0_6341_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_6341]) ).
cnf(c_0_6342_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_6342]) ).
cnf(c_0_6342_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_6342]) ).
cnf(c_0_6343_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_6343]) ).
cnf(c_0_6343_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_6343]) ).
cnf(c_0_6343_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_6343]) ).
cnf(c_0_6345_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_6345]) ).
cnf(c_0_6345_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_esk73_1(X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6345]) ).
cnf(c_0_6345_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_esk73_1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6345]) ).
cnf(c_0_6346_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk71_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_6346]) ).
cnf(c_0_6346_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_esk71_1(X2)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6346]) ).
cnf(c_0_6346_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_esk71_1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6346]) ).
cnf(c_0_6349_0,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk168_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6349_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk168_4(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6349_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk168_4(X1,X2,X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_6349]) ).
cnf(c_0_6350_0,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk168_4(X1,X2,X5,X4)))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6350_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk168_4(X1,X2,X5,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6350_2,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk168_4(X1,X2,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_6350]) ).
cnf(c_0_6351_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_esk80_2(X2,X1)),one_one(nat))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_1,axiom,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk80_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_6351]) ).
cnf(c_0_6351_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_esk80_2(X2,X1)),one_one(nat))))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6352_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_6352]) ).
cnf(c_0_6352_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_6352]) ).
cnf(c_0_6352_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_6352]) ).
cnf(c_0_6352_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_6352]) ).
cnf(c_0_6353_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk175_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6353_1,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_esk175_3(X1,X3,X2)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6353_2,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ 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_esk175_3(X1,X3,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6353]) ).
cnf(c_0_6354_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_6354]) ).
cnf(c_0_6354_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_6354]) ).
cnf(c_0_6355_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_6355]) ).
cnf(c_0_6355_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_6355]) ).
cnf(c_0_6355_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_6355]) ).
cnf(c_0_6355_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_6355]) ).
cnf(c_0_6356_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_6356]) ).
cnf(c_0_6356_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_6356]) ).
cnf(c_0_6356_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_6356]) ).
cnf(c_0_6356_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_6356]) ).
cnf(c_0_6357_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_6357]) ).
cnf(c_0_6357_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_6357]) ).
cnf(c_0_6357_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_6357]) ).
cnf(c_0_6357_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_6357]) ).
cnf(c_0_6358_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_6358]) ).
cnf(c_0_6358_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_6358]) ).
cnf(c_0_6358_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_6358]) ).
cnf(c_0_6358_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_6358]) ).
cnf(c_0_6359_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_6359]) ).
cnf(c_0_6359_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_6359]) ).
cnf(c_0_6359_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_6359]) ).
cnf(c_0_6360_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_6360]) ).
cnf(c_0_6360_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_6360]) ).
cnf(c_0_6360_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_6360]) ).
cnf(c_0_6360_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_6360]) ).
cnf(c_0_6361_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_6361]) ).
cnf(c_0_6361_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_6361]) ).
cnf(c_0_6361_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_6361]) ).
cnf(c_0_6362_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_6362]) ).
cnf(c_0_6362_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_6362]) ).
cnf(c_0_6362_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_6362]) ).
cnf(c_0_6363_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_6363]) ).
cnf(c_0_6363_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_6363]) ).
cnf(c_0_6363_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_6363]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6367_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_6367]) ).
cnf(c_0_6367_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_6367]) ).
cnf(c_0_6367_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_6367]) ).
cnf(c_0_6368_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_6368]) ).
cnf(c_0_6368_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_6368]) ).
cnf(c_0_6368_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_6368]) ).
cnf(c_0_6369_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_6369]) ).
cnf(c_0_6369_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_6369]) ).
cnf(c_0_6369_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_6369]) ).
cnf(c_0_6370_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_6370]) ).
cnf(c_0_6370_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_6370]) ).
cnf(c_0_6370_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_6370]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6372_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_6372]) ).
cnf(c_0_6372_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_6372]) ).
cnf(c_0_6373_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_6373]) ).
cnf(c_0_6373_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_6373]) ).
cnf(c_0_6374_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_6374]) ).
cnf(c_0_6374_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_6374]) ).
cnf(c_0_6375_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_6375]) ).
cnf(c_0_6375_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_6375]) ).
cnf(c_0_6376_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_6376]) ).
cnf(c_0_6376_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_6376]) ).
cnf(c_0_6377_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_6377]) ).
cnf(c_0_6377_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_6377]) ).
cnf(c_0_6378_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6378_1,axiom,
( ~ lattice(X2)
| hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6379_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6379]) ).
cnf(c_0_6379_1,axiom,
( ~ lattice(X2)
| hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6379]) ).
cnf(c_0_6380_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6380_1,axiom,
( ~ lattice(X2)
| hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6381_0,axiom,
( hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6381_1,axiom,
( ~ lattice(X2)
| hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X3),X4),X5) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_6381]) ).
cnf(c_0_6382_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6382_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6382_2,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6382]) ).
cnf(c_0_6383_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_6383]) ).
cnf(c_0_6383_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_6383]) ).
cnf(c_0_6384_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_6384]) ).
cnf(c_0_6384_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_6384]) ).
cnf(c_0_6384_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_6384]) ).
cnf(c_0_6385_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6385_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6386_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),times_times(X1),X2),X2)))
| ~ linordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6386_1,axiom,
( ~ linordered_ring(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),times_times(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6387_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_6387]) ).
cnf(c_0_6387_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_6387]) ).
cnf(c_0_6388_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6388_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6389_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6389_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6390_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6390_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6391_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6391_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6392_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6392]) ).
cnf(c_0_6392_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6392]) ).
cnf(c_0_6393_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6393]) ).
cnf(c_0_6393_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6393]) ).
cnf(c_0_6394_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6394]) ).
cnf(c_0_6394_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6394]) ).
cnf(c_0_6395_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_6395]) ).
cnf(c_0_6395_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_6395]) ).
cnf(c_0_6396_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_esk87_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_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_esk87_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_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_esk87_3(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_3,axiom,
( ~ hBOOL(hAPP(nat,bool,X3,sk1_esk87_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_6396]) ).
cnf(c_0_6397_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6397_1,axiom,
( ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6398_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6398]) ).
cnf(c_0_6398_1,axiom,
( ~ lattice(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6398]) ).
cnf(c_0_6399_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6399_1,axiom,
( ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6400_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6400_1,axiom,
( ~ lattice(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6401_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_6401]) ).
cnf(c_0_6401_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_6401]) ).
cnf(c_0_6401_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_6401]) ).
cnf(c_0_6402_0,axiom,
( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),sk1_esk122_2(X1,X2)),X2) = 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)),sk1_esk123_2(X1,X2)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),sk1_esk122_2(X1,X2)),X2) = 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)),sk1_esk123_2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6403_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_6403]) ).
cnf(c_0_6403_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_6403]) ).
cnf(c_0_6404_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_6404]) ).
cnf(c_0_6404_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_6404]) ).
cnf(c_0_6404_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_6404]) ).
cnf(c_0_6405_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_6405]) ).
cnf(c_0_6405_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_6405]) ).
cnf(c_0_6405_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_6405]) ).
cnf(c_0_6406_0,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(X1,X2,X3,hAPP(X2,X1,X4,sk1_esk128_4(X1,X2,X3,X4))) != ti(X2,sk1_esk128_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6406_1,axiom,
( hAPP(X1,X2,X3,hAPP(X2,X1,X4,sk1_esk128_4(X1,X2,X3,X4))) != ti(X2,sk1_esk128_4(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),top_top(fun(X1,bool))) = top_top(fun(X2,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6406]) ).
cnf(c_0_6407_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk177_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6407_1,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_esk177_3(X1,X3,X2)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6407_2,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ 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_esk177_3(X1,X3,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6407]) ).
cnf(c_0_6413_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_6413]) ).
cnf(c_0_6413_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_6413]) ).
cnf(c_0_6413_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_6413]) ).
cnf(c_0_6413_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_6413]) ).
cnf(c_0_6415_0,axiom,
( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
| hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk18_2(X1,X2)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk18_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_1,axiom,
( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,sk1_esk18_2(X1,X2)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sk1_esk18_2(X1,X2),X2)
| hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6416_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_esk82_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_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_esk82_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_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_esk82_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk82_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_6416]) ).
cnf(c_0_6417_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_esk80_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_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_esk80_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_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_esk80_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk80_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_6417]) ).
cnf(c_0_6418_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_6418]) ).
cnf(c_0_6418_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_6418]) ).
cnf(c_0_6418_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_6418]) ).
cnf(c_0_6419_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_6419]) ).
cnf(c_0_6419_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_6419]) ).
cnf(c_0_6419_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_6419]) ).
cnf(c_0_6420_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_esk70_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk70_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_6420]) ).
cnf(c_0_6420_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_esk70_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_6420]) ).
cnf(c_0_6421_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),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_6421]) ).
cnf(c_0_6421_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6422_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),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)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6423_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),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)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6423_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = ti(fun(X1,bool),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6424_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6424_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6424]) ).
cnf(c_0_6425_0,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6425]) ).
cnf(c_0_6425_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6425]) ).
cnf(c_0_6426_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_6426]) ).
cnf(c_0_6426_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_6426]) ).
cnf(c_0_6428_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_esk60_3(X1,X3,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6428]) ).
cnf(c_0_6428_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk60_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_6428]) ).
cnf(c_0_6429_0,axiom,
( X2 = hAPP(nat,nat,suc,X1)
| 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),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk94_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_6429]) ).
cnf(c_0_6429_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_esk94_2(X1,X2)))
| X2 = hAPP(nat,nat,suc,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6430_0,axiom,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk88_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_6430]) ).
cnf(c_0_6430_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_esk88_2(X2,X1))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6431_0,axiom,
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk86_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_6431]) ).
cnf(c_0_6431_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_esk86_2(X2,X1))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6432_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_6432]) ).
cnf(c_0_6432_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_6432]) ).
cnf(c_0_6432_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_6432]) ).
cnf(c_0_6433_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_6433]) ).
cnf(c_0_6433_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_6433]) ).
cnf(c_0_6433_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_6433]) ).
cnf(c_0_6433_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_6433]) ).
cnf(c_0_6434_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_6434]) ).
cnf(c_0_6434_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_6434]) ).
cnf(c_0_6434_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_6434]) ).
cnf(c_0_6434_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_6434]) ).
cnf(c_0_6435_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_6435]) ).
cnf(c_0_6435_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_6435]) ).
cnf(c_0_6435_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_6435]) ).
cnf(c_0_6435_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_6435]) ).
cnf(c_0_6436_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_6436]) ).
cnf(c_0_6436_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_6436]) ).
cnf(c_0_6436_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_6436]) ).
cnf(c_0_6436_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_6436]) ).
cnf(c_0_6437_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_6437]) ).
cnf(c_0_6437_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_6437]) ).
cnf(c_0_6437_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_6437]) ).
cnf(c_0_6437_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_6437]) ).
cnf(c_0_6438_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_6438]) ).
cnf(c_0_6438_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_6438]) ).
cnf(c_0_6438_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_6438]) ).
cnf(c_0_6438_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_6438]) ).
cnf(c_0_6439_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_6439]) ).
cnf(c_0_6439_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_6439]) ).
cnf(c_0_6439_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_6439]) ).
cnf(c_0_6439_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_6439]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6441_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_6441]) ).
cnf(c_0_6441_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_6441]) ).
cnf(c_0_6441_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_6441]) ).
cnf(c_0_6441_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_6441]) ).
cnf(c_0_6442_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_6442]) ).
cnf(c_0_6442_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_6442]) ).
cnf(c_0_6442_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_6442]) ).
cnf(c_0_6442_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_6442]) ).
cnf(c_0_6443_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_6443]) ).
cnf(c_0_6443_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_6443]) ).
cnf(c_0_6443_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_6443]) ).
cnf(c_0_6443_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_6443]) ).
cnf(c_0_6444_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_6444]) ).
cnf(c_0_6444_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_6444]) ).
cnf(c_0_6444_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_6444]) ).
cnf(c_0_6444_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_6444]) ).
cnf(c_0_6445_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_6445]) ).
cnf(c_0_6445_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_6445]) ).
cnf(c_0_6445_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_6445]) ).
cnf(c_0_6445_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_6445]) ).
cnf(c_0_6446_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_6446]) ).
cnf(c_0_6446_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_6446]) ).
cnf(c_0_6446_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_6446]) ).
cnf(c_0_6446_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_6446]) ).
cnf(c_0_6447_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_6447]) ).
cnf(c_0_6447_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_6447]) ).
cnf(c_0_6447_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_6447]) ).
cnf(c_0_6447_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_6447]) ).
cnf(c_0_6448_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_6448]) ).
cnf(c_0_6448_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_6448]) ).
cnf(c_0_6448_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_6448]) ).
cnf(c_0_6448_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_6448]) ).
cnf(c_0_6449_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_6449]) ).
cnf(c_0_6449_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_6449]) ).
cnf(c_0_6449_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_6449]) ).
cnf(c_0_6450_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_6450]) ).
cnf(c_0_6450_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_6450]) ).
cnf(c_0_6450_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_6450]) ).
cnf(c_0_6451_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_6451]) ).
cnf(c_0_6451_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_6451]) ).
cnf(c_0_6451_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_6451]) ).
cnf(c_0_6451_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_6451]) ).
cnf(c_0_6452_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_6452]) ).
cnf(c_0_6452_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_6452]) ).
cnf(c_0_6452_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_6452]) ).
cnf(c_0_6452_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_6452]) ).
cnf(c_0_6453_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_6453]) ).
cnf(c_0_6453_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_6453]) ).
cnf(c_0_6453_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_6453]) ).
cnf(c_0_6453_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_6453]) ).
cnf(c_0_6454_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_6454]) ).
cnf(c_0_6454_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_6454]) ).
cnf(c_0_6454_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_6454]) ).
cnf(c_0_6454_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_6454]) ).
cnf(c_0_6455_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk174_3(X1,X3,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6455]) ).
cnf(c_0_6455_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk174_3(X1,X3,X2)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6455]) ).
cnf(c_0_6455_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_esk174_3(X1,X3,X2)),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6455]) ).
cnf(c_0_6456_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_6456]) ).
cnf(c_0_6456_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_6456]) ).
cnf(c_0_6456_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_6456]) ).
cnf(c_0_6457_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_6457]) ).
cnf(c_0_6457_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_6457]) ).
cnf(c_0_6457_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_6457]) ).
cnf(c_0_6458_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_6458]) ).
cnf(c_0_6458_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_6458]) ).
cnf(c_0_6458_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_6458]) ).
cnf(c_0_6459_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_6459]) ).
cnf(c_0_6459_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_6459]) ).
cnf(c_0_6459_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_6459]) ).
cnf(c_0_6460_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_6460]) ).
cnf(c_0_6460_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_6460]) ).
cnf(c_0_6460_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_6460]) ).
cnf(c_0_6461_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_6461]) ).
cnf(c_0_6461_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_6461]) ).
cnf(c_0_6467_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk83_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6467_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_esk83_2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6467]) ).
cnf(c_0_6468_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6468_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6468_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6468]) ).
cnf(c_0_6470_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_6470]) ).
cnf(c_0_6470_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_6470]) ).
cnf(c_0_6470_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_6470]) ).
cnf(c_0_6471_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_6471]) ).
cnf(c_0_6471_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_6471]) ).
cnf(c_0_6471_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_6471]) ).
cnf(c_0_6472_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_6472]) ).
cnf(c_0_6472_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_6472]) ).
cnf(c_0_6472_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_6472]) ).
cnf(c_0_6473_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_6473]) ).
cnf(c_0_6473_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_6473]) ).
cnf(c_0_6474_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_6474]) ).
cnf(c_0_6474_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_6474]) ).
cnf(c_0_6475_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_6475]) ).
cnf(c_0_6475_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_6475]) ).
cnf(c_0_6476_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_6476]) ).
cnf(c_0_6476_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_6476]) ).
cnf(c_0_6477_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_6477]) ).
cnf(c_0_6477_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_6477]) ).
cnf(c_0_6478_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_6478]) ).
cnf(c_0_6478_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_6478]) ).
cnf(c_0_6479_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))
| hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) != ti(fun(X1,bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6479_1,axiom,
( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6479]) ).
cnf(c_0_6480_0,axiom,
( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
| hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sk1_esk27_2(X1,X2)),arrow_1568854078le_Lin)) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6480_1,axiom,
( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sk1_esk27_2(X1,X2)),arrow_1568854078le_Lin))
| ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6481_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_6481]) ).
cnf(c_0_6481_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_6481]) ).
cnf(c_0_6482_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_6482]) ).
cnf(c_0_6482_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_6482]) ).
cnf(c_0_6482_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_6482]) ).
cnf(c_0_6488_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk165_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6488_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk165_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6488_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk165_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6489_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk113_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6489]) ).
cnf(c_0_6489_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk113_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6489]) ).
cnf(c_0_6489_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk113_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6489]) ).
cnf(c_0_6490_0,axiom,
( hBOOL(hAPP(nat,bool,X1,sk1_esk162_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6490_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk162_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6490_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk162_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6491_0,axiom,
( hBOOL(hAPP(nat,bool,X1,sk1_esk114_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6491]) ).
cnf(c_0_6491_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk114_2(X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6491]) ).
cnf(c_0_6491_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk114_2(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_6491]) ).
cnf(c_0_6492_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_6492]) ).
cnf(c_0_6492_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_6492]) ).
cnf(c_0_6492_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_6492]) ).
cnf(c_0_6492_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_6492]) ).
cnf(c_0_6493_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_esk99_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6493_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_esk99_2(X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6493_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk99_2(X2,X1))))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6493]) ).
cnf(c_0_6494_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_6494]) ).
cnf(c_0_6494_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_6494]) ).
cnf(c_0_6495_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_6495]) ).
cnf(c_0_6495_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_6495]) ).
cnf(c_0_6496_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_esk135_3(X1,X2,X3)),one_one(X1)))
| ~ linord1117847801e_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6496_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk135_3(X1,X2,X3)),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6496_2,axiom,
( ~ linord1117847801e_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk135_3(X1,X2,X3)),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6497_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_6497]) ).
cnf(c_0_6497_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_6497]) ).
cnf(c_0_6497_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_6497]) ).
cnf(c_0_6503_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_esk78_4(X2,X1,X3,X4)) != ti(X1,sk1_esk77_4(X2,X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6503_1,axiom,
( ti(X1,sk1_esk78_4(X2,X1,X3,X4)) != ti(X1,sk1_esk77_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_6503]) ).
cnf(c_0_6504_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_esk32_4(X1,X2,X3,X4)) != ti(X1,sk1_esk31_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_1,axiom,
( ti(X1,sk1_esk32_4(X1,X2,X3,X4)) != ti(X1,sk1_esk31_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_6504]) ).
cnf(c_0_6506_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6506_1,axiom,
( X2 != X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6507_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_esk78_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,sk1_esk77_4(X2,X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6507_1,axiom,
( hAPP(X1,X2,X3,sk1_esk78_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,sk1_esk77_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_6507]) ).
cnf(c_0_6508_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_esk32_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,sk1_esk31_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6508_1,axiom,
( hAPP(X1,X2,X3,sk1_esk32_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,sk1_esk31_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_6508]) ).
cnf(c_0_6509_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_esk135_3(X1,X2,X3)))
| ~ linord1117847801e_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6509_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk135_3(X1,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord1117847801e_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6509_2,axiom,
( ~ linord1117847801e_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk135_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_6509]) ).
cnf(c_0_6510_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_esk100_3(X1,X2,X3)))
| ~ linordered_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6510_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk100_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_6510]) ).
cnf(c_0_6510_2,axiom,
( ~ linordered_field(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk100_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_6510]) ).
cnf(c_0_6511_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_6511]) ).
cnf(c_0_6511_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_6511]) ).
cnf(c_0_6512_0,axiom,
( hAPP(X1,nat,X3,sk1_esk175_3(X1,X3,X2)) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6512_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,sk1_esk175_3(X1,X3,X2)) = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6512_2,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,sk1_esk175_3(X1,X3,X2)) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6513_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_6513]) ).
cnf(c_0_6513_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_6513]) ).
cnf(c_0_6514_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6514_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = 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_6514]) ).
cnf(c_0_6514_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6515_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6515_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6515_2,axiom,
( ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6516_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6516_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X3)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6516_2,axiom,
( ~ semilattice_inf(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6516]) ).
cnf(c_0_6517_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_2,axiom,
( ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6518_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6518_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6518_2,axiom,
( ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6518]) ).
cnf(c_0_6519_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
| ~ semilattice_sup(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6519_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = 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_6519]) ).
cnf(c_0_6519_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6519]) ).
cnf(c_0_6520_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),sk1_esk83_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_6520]) ).
cnf(c_0_6520_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_esk83_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6521_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk56_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_6521]) ).
cnf(c_0_6521_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_esk56_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6522_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_6522]) ).
cnf(c_0_6522_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_6522]) ).
cnf(c_0_6522_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_6522]) ).
cnf(c_0_6522_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_6522]) ).
cnf(c_0_6523_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_6523]) ).
cnf(c_0_6523_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_6523]) ).
cnf(c_0_6523_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_6523]) ).
cnf(c_0_6523_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_6523]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6524_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_6524]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6526_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_6526]) ).
cnf(c_0_6526_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_6526]) ).
cnf(c_0_6526_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_6526]) ).
cnf(c_0_6526_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_6526]) ).
cnf(c_0_6527_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_6527]) ).
cnf(c_0_6527_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_6527]) ).
cnf(c_0_6527_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_6527]) ).
cnf(c_0_6527_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_6527]) ).
cnf(c_0_6528_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_6528]) ).
cnf(c_0_6528_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_6528]) ).
cnf(c_0_6528_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_6528]) ).
cnf(c_0_6528_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_6528]) ).
cnf(c_0_6529_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_6529]) ).
cnf(c_0_6529_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_6529]) ).
cnf(c_0_6529_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_6529]) ).
cnf(c_0_6529_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_6529]) ).
cnf(c_0_6530_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6530_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6531_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6531_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6532_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6532_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6533_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6533]) ).
cnf(c_0_6533_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6533]) ).
cnf(c_0_6534_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6534]) ).
cnf(c_0_6534_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6534]) ).
cnf(c_0_6535_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6535_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6536_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)
| ~ ab_sem1668676832m_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6536_1,axiom,
( ~ ab_sem1668676832m_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6537_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(X1,bool,X3,sk1_esk151_3(X1,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6537]) ).
cnf(c_0_6537_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X3,sk1_esk151_3(X1,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_6537]) ).
cnf(c_0_6538_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_6538]) ).
cnf(c_0_6538_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_6538]) ).
cnf(c_0_6538_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_6538]) ).
cnf(c_0_6539_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_6539]) ).
cnf(c_0_6539_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_6539]) ).
cnf(c_0_6539_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_6539]) ).
cnf(c_0_6540_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_6540]) ).
cnf(c_0_6540_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_6540]) ).
cnf(c_0_6540_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_6540]) ).
cnf(c_0_6541_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_6541]) ).
cnf(c_0_6541_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_6541]) ).
cnf(c_0_6541_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_6541]) ).
cnf(c_0_6542_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_6542]) ).
cnf(c_0_6542_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_6542]) ).
cnf(c_0_6542_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_6542]) ).
cnf(c_0_6543_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_6543]) ).
cnf(c_0_6543_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_6543]) ).
cnf(c_0_6543_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_6543]) ).
cnf(c_0_6544_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_6544]) ).
cnf(c_0_6544_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_6544]) ).
cnf(c_0_6544_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_6544]) ).
cnf(c_0_6545_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(X2,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6545]) ).
cnf(c_0_6545_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk76_2(X2,X1)),X2))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6545]) ).
cnf(c_0_6546_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_esk74_2(X1,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6546_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_6546]) ).
cnf(c_0_6547_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_esk72_2(X1,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6547_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk72_2(X1,X2)),X2))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6548_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_6548]) ).
cnf(c_0_6548_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_6548]) ).
cnf(c_0_6548_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_6548]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6550_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_6550]) ).
cnf(c_0_6550_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_6550]) ).
cnf(c_0_6550_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_6550]) ).
cnf(c_0_6551_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_6551]) ).
cnf(c_0_6551_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_6551]) ).
cnf(c_0_6551_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_6551]) ).
cnf(c_0_6552_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_6552]) ).
cnf(c_0_6552_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_6552]) ).
cnf(c_0_6553_0,axiom,
( hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X4,X2,X7,X6)
| hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != ti(fun(X4,X2),X7) ),
inference(literals_permutation,[status(thm)],[c_0_6553]) ).
cnf(c_0_6553_1,axiom,
( hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5) != ti(fun(X4,X2),X7)
| hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X4,X2,X7,X6) ),
inference(literals_permutation,[status(thm)],[c_0_6553]) ).
cnf(c_0_6554_0,axiom,
( ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk149_2(X1,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6554_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk149_2(X1,X2)),X2))
| ti(fun(X1,bool),X2) = top_top(fun(X1,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6555_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_6555]) ).
cnf(c_0_6555_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_6555]) ).
cnf(c_0_6556_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_6556]) ).
cnf(c_0_6556_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_6556]) ).
cnf(c_0_6557_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_6557]) ).
cnf(c_0_6557_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_6557]) ).
cnf(c_0_6558_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_6558]) ).
cnf(c_0_6558_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_6558]) ).
cnf(c_0_6559_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_esk81_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6559_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk81_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_6559]) ).
cnf(c_0_6559_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_esk81_2(X1,X2)),X2))
| hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6559]) ).
cnf(c_0_6564_0,axiom,
( X2 = hAPP(nat,nat,suc,X1)
| hAPP(nat,nat,suc,sk1_esk94_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_6564]) ).
cnf(c_0_6564_1,axiom,
( hAPP(nat,nat,suc,sk1_esk94_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_6564]) ).
cnf(c_0_6564_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hAPP(nat,nat,suc,sk1_esk94_2(X1,X2)) = X2
| X2 = hAPP(nat,nat,suc,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6564]) ).
cnf(c_0_6566_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),sk1_esk122_2(X1,X2)),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6566]) ).
cnf(c_0_6566_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),sk1_esk122_2(X1,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6566]) ).
cnf(c_0_6567_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk82_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6567_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk82_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_6567]) ).
cnf(c_0_6567_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk82_2(X2,X1)),X2))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6568_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk80_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6568_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk80_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_6568]) ).
cnf(c_0_6568_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk80_2(X2,X1)),X2))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6569_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_6569]) ).
cnf(c_0_6569_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_6569]) ).
cnf(c_0_6570_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_6570]) ).
cnf(c_0_6570_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_6570]) ).
cnf(c_0_6570_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_6570]) ).
cnf(c_0_6571_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6571_1,axiom,
( ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6571_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != ti(X1,X2)
| ~ semilattice_inf(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6571]) ).
cnf(c_0_6572_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6572]) ).
cnf(c_0_6572_1,axiom,
( ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6572]) ).
cnf(c_0_6572_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != ti(X1,X3)
| ~ semilattice_sup(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6572]) ).
cnf(c_0_6573_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_6573]) ).
cnf(c_0_6573_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_6573]) ).
cnf(c_0_6577_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(X1,bool,X2,sk1_esk151_3(X1,X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6577]) ).
cnf(c_0_6577_1,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk151_3(X1,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_6577]) ).
cnf(c_0_6578_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_6578]) ).
cnf(c_0_6578_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_6578]) ).
cnf(c_0_6579_0,axiom,
( hAPP(X1,nat,X3,sk1_esk177_3(X1,X3,X2)) = one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6579_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,sk1_esk177_3(X1,X3,X2)) = one_one(nat)
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6579_2,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) != one_one(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,sk1_esk177_3(X1,X3,X2)) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6579]) ).
cnf(c_0_6580_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk98_1(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6580_1,axiom,
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk98_1(X1))))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6580_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk98_1(X1))))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6580]) ).
cnf(c_0_6583_0,axiom,
( hAPP(nat,nat,suc,sk1_esk89_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_6583]) ).
cnf(c_0_6583_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hAPP(nat,nat,suc,sk1_esk89_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6584_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_6584]) ).
cnf(c_0_6584_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_6584]) ).
cnf(c_0_6585_0,axiom,
( hAPP(X3,X1,X4,sk1_esk129_4(X3,X1,X4,X2)) = ti(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))) != top_top(fun(X1,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6585_1,axiom,
( 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))) != top_top(fun(X1,bool))
| hAPP(X3,X1,X4,sk1_esk129_4(X3,X1,X4,X2)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6585]) ).
cnf(c_0_6586_0,axiom,
( hAPP(X3,X1,X4,sk1_esk127_4(X3,X1,X2,X4)) = ti(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))) != top_top(fun(X1,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6586_1,axiom,
( 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))) != top_top(fun(X1,bool))
| hAPP(X3,X1,X4,sk1_esk127_4(X3,X1,X2,X4)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6586]) ).
cnf(c_0_6587_0,axiom,
( hAPP(X3,X1,X4,sk1_esk126_4(X3,X1,X2,X4)) = ti(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))) != top_top(fun(X1,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6587_1,axiom,
( 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))) != top_top(fun(X1,bool))
| hAPP(X3,X1,X4,sk1_esk126_4(X3,X1,X2,X4)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6591_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_6591]) ).
cnf(c_0_6591_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_6591]) ).
cnf(c_0_6592_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_6592]) ).
cnf(c_0_6592_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_6592]) ).
cnf(c_0_6593_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_6593]) ).
cnf(c_0_6593_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_6593]) ).
cnf(c_0_6594_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_6594]) ).
cnf(c_0_6594_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_6594]) ).
cnf(c_0_6594_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_6594]) ).
cnf(c_0_6595_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_6595]) ).
cnf(c_0_6595_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_6595]) ).
cnf(c_0_6595_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_6595]) ).
cnf(c_0_6596_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_6596]) ).
cnf(c_0_6596_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_6596]) ).
cnf(c_0_6596_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_6596]) ).
cnf(c_0_6597_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_6597]) ).
cnf(c_0_6597_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_6597]) ).
cnf(c_0_6597_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_6597]) ).
cnf(c_0_6598_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_6598]) ).
cnf(c_0_6598_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_6598]) ).
cnf(c_0_6598_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_6598]) ).
cnf(c_0_6599_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_6599]) ).
cnf(c_0_6599_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_6599]) ).
cnf(c_0_6599_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_6599]) ).
cnf(c_0_6600_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_6600]) ).
cnf(c_0_6600_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_6600]) ).
cnf(c_0_6600_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_6600]) ).
cnf(c_0_6601_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_6601]) ).
cnf(c_0_6601_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_6601]) ).
cnf(c_0_6601_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_6601]) ).
cnf(c_0_6602_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_6602]) ).
cnf(c_0_6602_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_6602]) ).
cnf(c_0_6602_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_6602]) ).
cnf(c_0_6603_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_6603]) ).
cnf(c_0_6603_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_6603]) ).
cnf(c_0_6603_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_6603]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6604_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_6604]) ).
cnf(c_0_6605_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_6605]) ).
cnf(c_0_6605_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_6605]) ).
cnf(c_0_6605_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_6605]) ).
cnf(c_0_6606_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_6606]) ).
cnf(c_0_6606_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_6606]) ).
cnf(c_0_6606_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_6606]) ).
cnf(c_0_6607_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_6607]) ).
cnf(c_0_6607_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_6607]) ).
cnf(c_0_6607_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_6607]) ).
cnf(c_0_6608_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_6608]) ).
cnf(c_0_6608_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_6608]) ).
cnf(c_0_6608_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_6608]) ).
cnf(c_0_6609_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_6609]) ).
cnf(c_0_6609_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_6609]) ).
cnf(c_0_6610_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_6610]) ).
cnf(c_0_6610_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_6610]) ).
cnf(c_0_6612_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_6612]) ).
cnf(c_0_6612_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_6612]) ).
cnf(c_0_6613_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_6613]) ).
cnf(c_0_6613_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_6613]) ).
cnf(c_0_6614_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_6614]) ).
cnf(c_0_6614_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_6614]) ).
cnf(c_0_6616_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_6616]) ).
cnf(c_0_6616_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_6616]) ).
cnf(c_0_6617_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_6617]) ).
cnf(c_0_6617_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_6617]) ).
cnf(c_0_6618_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_6618]) ).
cnf(c_0_6618_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_6618]) ).
cnf(c_0_6619_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_6619]) ).
cnf(c_0_6619_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_6619]) ).
cnf(c_0_6623_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_6623]) ).
cnf(c_0_6623_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_6623]) ).
cnf(c_0_6624_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_6624]) ).
cnf(c_0_6624_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_6624]) ).
cnf(c_0_6625_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_6625]) ).
cnf(c_0_6625_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_6625]) ).
cnf(c_0_6626_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_6626]) ).
cnf(c_0_6626_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_6626]) ).
cnf(c_0_6627_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_6627]) ).
cnf(c_0_6627_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_6627]) ).
cnf(c_0_6628_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_6628]) ).
cnf(c_0_6628_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_6628]) ).
cnf(c_0_6629_0,axiom,
( X1 = X2
| X3 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6629_1,axiom,
( X3 = zero_zero(nat)
| X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6629_2,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X3 = zero_zero(nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6630_0,axiom,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6630_1,axiom,
( X2 = X3
| X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6630_2,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 = X3
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6631_0,axiom,
( X1 = zero_zero(nat)
| X2 = X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6631]) ).
cnf(c_0_6631_1,axiom,
( X2 = X3
| X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6631]) ).
cnf(c_0_6631_2,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)
| X2 = X3
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6631]) ).
cnf(c_0_6634_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_6634]) ).
cnf(c_0_6634_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_6634]) ).
cnf(c_0_6635_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_6635]) ).
cnf(c_0_6635_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_6635]) ).
cnf(c_0_6637_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_6637]) ).
cnf(c_0_6637_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_6637]) ).
cnf(c_0_6637_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_6637]) ).
cnf(c_0_6638_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = ti(X1,X2)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6638_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6639_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = ti(X1,X2)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6639_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6640_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6640]) ).
cnf(c_0_6640_1,axiom,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6640]) ).
cnf(c_0_6641_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6641]) ).
cnf(c_0_6641_1,axiom,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6641]) ).
cnf(c_0_6642_0,axiom,
( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(X1,nat,X3,sk1_esk174_3(X1,X3,X2)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6642]) ).
cnf(c_0_6642_1,axiom,
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat)
| hAPP(X1,nat,X3,sk1_esk174_3(X1,X3,X2)) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6642]) ).
cnf(c_0_6642_2,axiom,
( hAPP(X1,nat,X3,sk1_esk174_3(X1,X3,X2)) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X2) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6642]) ).
cnf(c_0_6643_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(X2,X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6643_1,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk76_2(X2,X1)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6644_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_6644]) ).
cnf(c_0_6644_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_6644]) ).
cnf(c_0_6645_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_esk72_2(X1,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6645]) ).
cnf(c_0_6645_1,axiom,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk72_2(X1,X2)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6645]) ).
cnf(c_0_6646_0,axiom,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,sk1_esk21_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,sk1_esk21_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_6646]) ).
cnf(c_0_6646_1,axiom,
( hAPP(X1,X2,X3,sk1_esk21_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,sk1_esk21_4(X1,X2,X3,X4))
| ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_6646]) ).
cnf(c_0_6649_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_6649]) ).
cnf(c_0_6649_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_6649]) ).
cnf(c_0_6650_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_6650]) ).
cnf(c_0_6650_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_6650]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6651_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_6651]) ).
cnf(c_0_6654_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),zero_zero(X2))),X3) = zero_zero(X2)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6654_1,axiom,
( ~ comm_monoid_add(X2)
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),combk(X2,X1),zero_zero(X2))),X3) = zero_zero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6655_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_6655]) ).
cnf(c_0_6655_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_6655]) ).
cnf(c_0_6656_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_6656]) ).
cnf(c_0_6656_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_6656]) ).
cnf(c_0_6657_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_6657]) ).
cnf(c_0_6657_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_6657]) ).
cnf(c_0_6658_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_6658]) ).
cnf(c_0_6658_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_6658]) ).
cnf(c_0_6659_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_6659]) ).
cnf(c_0_6659_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_6659]) ).
cnf(c_0_6660_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_6660]) ).
cnf(c_0_6660_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_6660]) ).
cnf(c_0_6661_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_6661]) ).
cnf(c_0_6661_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_6661]) ).
cnf(c_0_6666_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_6666]) ).
cnf(c_0_6666_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_6666]) ).
cnf(c_0_6666_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_6666]) ).
cnf(c_0_6667_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_6667]) ).
cnf(c_0_6667_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_6667]) ).
cnf(c_0_6667_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_6667]) ).
cnf(c_0_6669_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk98_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6669_1,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,sk1_esk98_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6669_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk98_1(X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6670_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_6670]) ).
cnf(c_0_6670_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_6670]) ).
cnf(c_0_6670_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_6670]) ).
cnf(c_0_6671_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_6671]) ).
cnf(c_0_6671_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_6671]) ).
cnf(c_0_6671_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_6671]) ).
cnf(c_0_6675_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_6675]) ).
cnf(c_0_6675_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_6675]) ).
cnf(c_0_6681_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_6681]) ).
cnf(c_0_6681_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_6681]) ).
cnf(c_0_6682_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_6682]) ).
cnf(c_0_6682_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_6682]) ).
cnf(c_0_6683_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_6683]) ).
cnf(c_0_6683_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_6683]) ).
cnf(c_0_6683_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_6683]) ).
cnf(c_0_6684_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_6684]) ).
cnf(c_0_6684_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_6684]) ).
cnf(c_0_6684_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_6684]) ).
cnf(c_0_6685_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_6685]) ).
cnf(c_0_6685_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_6685]) ).
cnf(c_0_6685_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_6685]) ).
cnf(c_0_6686_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_6686]) ).
cnf(c_0_6686_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_6686]) ).
cnf(c_0_6686_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_6686]) ).
cnf(c_0_6687_0,axiom,
( X1 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6687]) ).
cnf(c_0_6687_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_6687]) ).
cnf(c_0_6688_0,axiom,
( X2 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6688]) ).
cnf(c_0_6688_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
| X2 = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6688]) ).
cnf(c_0_6689_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_6689]) ).
cnf(c_0_6689_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_6689]) ).
cnf(c_0_6690_0,axiom,
( hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk99_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6690]) ).
cnf(c_0_6690_1,axiom,
( hBOOL(hAPP(nat,bool,X1,sk1_esk99_2(X2,X1)))
| hBOOL(hAPP(nat,bool,X1,X2))
| ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6690]) ).
cnf(c_0_6690_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,sk1_esk99_2(X2,X1)))
| hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6690]) ).
cnf(c_0_6691_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,X1,sk1_esk82_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6691]) ).
cnf(c_0_6691_1,axiom,
( hBOOL(hAPP(nat,bool,X1,sk1_esk82_2(X2,X1)))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6691]) ).
cnf(c_0_6691_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,X1,sk1_esk82_2(X2,X1)))
| hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_6691]) ).
cnf(c_0_6692_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_6692]) ).
cnf(c_0_6692_1,axiom,
( X2 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_6692]) ).
cnf(c_0_6692_2,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),times_times(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6692]) ).
cnf(c_0_6693_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_6693]) ).
cnf(c_0_6693_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_6693]) ).
cnf(c_0_6694_0,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))
| ti(X2,sk1_esk130_3(X1,X2,X3)) != hAPP(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_6694]) ).
cnf(c_0_6694_1,axiom,
( ti(X2,sk1_esk130_3(X1,X2,X3)) != hAPP(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),top_top(fun(X1,bool))) = top_top(fun(X2,bool)) ),
inference(literals_permutation,[status(thm)],[c_0_6694]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6695_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_6695]) ).
cnf(c_0_6696_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_6696]) ).
cnf(c_0_6696_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_6696]) ).
cnf(c_0_6696_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_6696]) ).
cnf(c_0_6697_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_6697]) ).
cnf(c_0_6697_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_6697]) ).
cnf(c_0_6697_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_6697]) ).
cnf(c_0_6698_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_6698]) ).
cnf(c_0_6698_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_6698]) ).
cnf(c_0_6698_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_6698]) ).
cnf(c_0_6699_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_6699]) ).
cnf(c_0_6699_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_6699]) ).
cnf(c_0_6699_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_6699]) ).
cnf(c_0_6700_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_6700]) ).
cnf(c_0_6700_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_6700]) ).
cnf(c_0_6700_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_6700]) ).
cnf(c_0_6701_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_6701]) ).
cnf(c_0_6701_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_6701]) ).
cnf(c_0_6702_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_6702]) ).
cnf(c_0_6702_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_6702]) ).
cnf(c_0_6703_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_6703]) ).
cnf(c_0_6703_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_6703]) ).
cnf(c_0_6704_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_6704]) ).
cnf(c_0_6704_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_6704]) ).
cnf(c_0_6704_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_6704]) ).
cnf(c_0_6705_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_6705]) ).
cnf(c_0_6705_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_6705]) ).
cnf(c_0_6705_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_6705]) ).
cnf(c_0_6706_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_6706]) ).
cnf(c_0_6706_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_6706]) ).
cnf(c_0_6706_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_6706]) ).
cnf(c_0_6707_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6707]) ).
cnf(c_0_6707_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6707]) ).
cnf(c_0_6708_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6708]) ).
cnf(c_0_6708_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6708]) ).
cnf(c_0_6709_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6709]) ).
cnf(c_0_6709_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6709]) ).
cnf(c_0_6710_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6710]) ).
cnf(c_0_6710_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6710]) ).
cnf(c_0_6711_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6711_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6712_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6712]) ).
cnf(c_0_6712_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6712]) ).
cnf(c_0_6713_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6713_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6714_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_6714]) ).
cnf(c_0_6714_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_6714]) ).
cnf(c_0_6715_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_6715]) ).
cnf(c_0_6715_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_6715]) ).
cnf(c_0_6717_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_6717]) ).
cnf(c_0_6717_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_6717]) ).
cnf(c_0_6717_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_6717]) ).
cnf(c_0_6718_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_6718]) ).
cnf(c_0_6718_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_6718]) ).
cnf(c_0_6719_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_6719]) ).
cnf(c_0_6719_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_6719]) ).
cnf(c_0_6720_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_6720]) ).
cnf(c_0_6720_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_6720]) ).
cnf(c_0_6723_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_6723]) ).
cnf(c_0_6723_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_6723]) ).
cnf(c_0_6724_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6724_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6724_2,axiom,
( ~ comm_monoid_add(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6725_0,axiom,
( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6725_1,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6725_2,axiom,
( ~ comm_monoid_add(X2)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
| hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X3),X4) = zero_zero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6726_0,axiom,
( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) = zero_zero(X1)
| hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6726]) ).
cnf(c_0_6726_1,axiom,
( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) = zero_zero(X1)
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6726]) ).
cnf(c_0_6726_2,axiom,
( ~ comm_monoid_add(X1)
| hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
| hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6726]) ).
cnf(c_0_6727_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6727]) ).
cnf(c_0_6727_1,axiom,
( X1 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6727]) ).
cnf(c_0_6728_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6728]) ).
cnf(c_0_6728_1,axiom,
( X1 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6728]) ).
cnf(c_0_6729_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6729]) ).
cnf(c_0_6729_1,axiom,
( X2 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6729]) ).
cnf(c_0_6730_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_6730]) ).
cnf(c_0_6730_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_6730]) ).
cnf(c_0_6731_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_6731]) ).
cnf(c_0_6731_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_6731]) ).
cnf(c_0_6732_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_6732]) ).
cnf(c_0_6732_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_6732]) ).
cnf(c_0_6733_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6733]) ).
cnf(c_0_6733_1,axiom,
( X2 != X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6733]) ).
cnf(c_0_6734_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6734_1,axiom,
( X2 != X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6735_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6735_1,axiom,
( X1 != X3
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6736_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_6736]) ).
cnf(c_0_6736_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_6736]) ).
cnf(c_0_6737_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_6737]) ).
cnf(c_0_6737_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_6737]) ).
cnf(c_0_6741_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_6741]) ).
cnf(c_0_6741_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_6741]) ).
cnf(c_0_6741_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_6741]) ).
cnf(c_0_6742_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6742_1,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6743_0,axiom,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6743]) ).
cnf(c_0_6743_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6743]) ).
cnf(c_0_6744_0,axiom,
( hBOOL(hAPP(X1,bool,X2,sk1_esk146_3(X1,X4,X2)))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6744]) ).
cnf(c_0_6744_1,axiom,
( ~ hBOOL(hAPP(X1,bool,X2,X3))
| hBOOL(hAPP(X1,bool,X2,sk1_esk146_3(X1,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_6744]) ).
cnf(c_0_6745_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_6745]) ).
cnf(c_0_6745_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_6745]) ).
cnf(c_0_6745_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_6745]) ).
cnf(c_0_6746_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_6746]) ).
cnf(c_0_6746_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_6746]) ).
cnf(c_0_6746_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_6746]) ).
cnf(c_0_6747_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_6747]) ).
cnf(c_0_6747_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_6747]) ).
cnf(c_0_6747_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_6747]) ).
cnf(c_0_6748_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_6748]) ).
cnf(c_0_6748_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_6748]) ).
cnf(c_0_6748_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_6748]) ).
cnf(c_0_6752_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6752_1,axiom,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6752_2,axiom,
( ~ ring_n68954251visors(X1)
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6752_3,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6752]) ).
cnf(c_0_6753_0,axiom,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6753_1,axiom,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6753_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6753_3,axiom,
( ~ no_zero_divisors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6753]) ).
cnf(c_0_6754_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6754_1,axiom,
( ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6754_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6754_3,axiom,
( ~ no_zero_divisors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) != zero_zero(X1)
| ti(X1,X3) = zero_zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6754]) ).
cnf(c_0_6755_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_6755]) ).
cnf(c_0_6755_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_6755]) ).
cnf(c_0_6755_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_6755]) ).
cnf(c_0_6758_0,axiom,
( ti(X1,X2) = top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6758_1,axiom,
( ~ bounded_lattice_top(X1)
| ti(X1,X2) = top_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6758_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1)
| ~ bounded_lattice_top(X1)
| ti(X1,X2) = top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6758]) ).
cnf(c_0_6759_0,axiom,
( ti(X1,X3) = top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6759_1,axiom,
( ~ bounded_lattice_top(X1)
| ti(X1,X3) = top_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6759_2,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1)
| ~ bounded_lattice_top(X1)
| ti(X1,X3) = top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6759]) ).
cnf(c_0_6760_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_6760]) ).
cnf(c_0_6760_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_6760]) ).
cnf(c_0_6760_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_6760]) ).
cnf(c_0_6761_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_6761]) ).
cnf(c_0_6761_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_6761]) ).
cnf(c_0_6761_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_6761]) ).
cnf(c_0_6764_0,axiom,
( X1 = zero_zero(nat)
| X2 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6764]) ).
cnf(c_0_6764_1,axiom,
( X2 = zero_zero(nat)
| X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6764]) ).
cnf(c_0_6764_2,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != zero_zero(nat)
| X2 = zero_zero(nat)
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6764]) ).
cnf(c_0_6765_0,axiom,
( X1 = zero_zero(nat)
| X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6765]) ).
cnf(c_0_6765_1,axiom,
( X2 = one_one(nat)
| X1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_6765]) ).
cnf(c_0_6765_2,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != X1
| X2 = one_one(nat)
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6765]) ).
cnf(c_0_6766_0,axiom,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6766]) ).
cnf(c_0_6766_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat)
| X1 = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6766]) ).
cnf(c_0_6767_0,axiom,
( X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6767]) ).
cnf(c_0_6767_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat)
| X2 = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6767]) ).
cnf(c_0_6768_0,axiom,
( X1 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6768]) ).
cnf(c_0_6768_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat)
| X1 = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6768]) ).
cnf(c_0_6769_0,axiom,
( X2 = one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6769]) ).
cnf(c_0_6769_1,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat)
| X2 = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6769]) ).
cnf(c_0_6770_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_6770]) ).
cnf(c_0_6770_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_6770]) ).
cnf(c_0_6771_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_6771]) ).
cnf(c_0_6771_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_6771]) ).
cnf(c_0_6772_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_6772]) ).
cnf(c_0_6772_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_6772]) ).
cnf(c_0_6776_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_6776]) ).
cnf(c_0_6776_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_6776]) ).
cnf(c_0_6776_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_6776]) ).
cnf(c_0_6788_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6788]) ).
cnf(c_0_6788_1,axiom,
( ~ linorder(X1)
| ti(X1,X2) = ti(X1,X3)
| hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6788]) ).
cnf(c_0_6788_2,axiom,
( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6788]) ).
cnf(c_0_6789_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6789]) ).
cnf(c_0_6789_1,axiom,
( ~ linorder(X1)
| ti(X1,X2) = ti(X1,X3)
| hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6789]) ).
cnf(c_0_6789_2,axiom,
( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6789]) ).
cnf(c_0_6790_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
| ~ bounded_lattice_top(X1)
| ti(X1,X3) != top_top(X1)
| ti(X1,X2) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6790]) ).
cnf(c_0_6790_1,axiom,
( ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
| ti(X1,X3) != top_top(X1)
| ti(X1,X2) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6790]) ).
cnf(c_0_6790_2,axiom,
( ti(X1,X3) != top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
| ti(X1,X2) != top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6790]) ).
cnf(c_0_6790_3,axiom,
( ti(X1,X2) != top_top(X1)
| ti(X1,X3) != top_top(X1)
| ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6790]) ).
cnf(c_0_6792_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_6792]) ).
cnf(c_0_6792_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_6792]) ).
cnf(c_0_6792_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_6792]) ).
cnf(c_0_6793_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6793]) ).
cnf(c_0_6793_1,axiom,
( ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6793]) ).
cnf(c_0_6793_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6793]) ).
cnf(c_0_6794_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ~ ring_n68954251visors(X1)
| ti(X1,X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6794]) ).
cnf(c_0_6794_1,axiom,
( ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
| ti(X1,X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6794]) ).
cnf(c_0_6794_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ ring_n68954251visors(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6794]) ).
cnf(c_0_6795_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_6795]) ).
cnf(c_0_6795_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_6795]) ).
cnf(c_0_6795_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_6795]) ).
cnf(c_0_6796_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_6796]) ).
cnf(c_0_6796_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_6796]) ).
cnf(c_0_6796_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_6796]) ).
cnf(c_0_6797_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X2) = ti(X1,X2)
| ~ bounded_lattice_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6797]) ).
cnf(c_0_6797_1,axiom,
( ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6797]) ).
cnf(c_0_6798_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6798]) ).
cnf(c_0_6798_1,axiom,
( ~ comm_monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6798]) ).
cnf(c_0_6799_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6799]) ).
cnf(c_0_6799_1,axiom,
( ~ monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6799]) ).
cnf(c_0_6800_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6800]) ).
cnf(c_0_6800_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6800]) ).
cnf(c_0_6801_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_6801]) ).
cnf(c_0_6801_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_6801]) ).
cnf(c_0_6802_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_6802]) ).
cnf(c_0_6802_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_6802]) ).
cnf(c_0_6803_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_6803]) ).
cnf(c_0_6803_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_6803]) ).
cnf(c_0_6804_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),top_top(X1)) = ti(X1,X2)
| ~ bounded_lattice_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6804]) ).
cnf(c_0_6804_1,axiom,
( ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),top_top(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6804]) ).
cnf(c_0_6805_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6805]) ).
cnf(c_0_6805_1,axiom,
( ~ comm_monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6805]) ).
cnf(c_0_6806_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6806]) ).
cnf(c_0_6806_1,axiom,
( ~ monoid_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6806]) ).
cnf(c_0_6807_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6807]) ).
cnf(c_0_6807_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6807]) ).
cnf(c_0_6808_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_6808]) ).
cnf(c_0_6808_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_6808]) ).
cnf(c_0_6809_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_6809]) ).
cnf(c_0_6809_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_6809]) ).
cnf(c_0_6810_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_6810]) ).
cnf(c_0_6810_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_6810]) ).
cnf(c_0_6811_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_6811]) ).
cnf(c_0_6811_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_6811]) ).
cnf(c_0_6812_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_6812]) ).
cnf(c_0_6812_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_6812]) ).
cnf(c_0_6813_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X2) = top_top(X1)
| ~ bounded_lattice_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6813]) ).
cnf(c_0_6813_1,axiom,
( ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X2) = top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6813]) ).
cnf(c_0_6814_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ mult_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6814]) ).
cnf(c_0_6814_1,axiom,
( ~ mult_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6814]) ).
cnf(c_0_6815_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6815]) ).
cnf(c_0_6815_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6815]) ).
cnf(c_0_6816_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6816]) ).
cnf(c_0_6816_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6816]) ).
cnf(c_0_6817_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6817]) ).
cnf(c_0_6817_1,axiom,
( ~ lattice(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6817]) ).
cnf(c_0_6818_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6818]) ).
cnf(c_0_6818_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6818]) ).
cnf(c_0_6819_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6819_1,axiom,
( ~ semilattice_inf(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6819]) ).
cnf(c_0_6820_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6820_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6820]) ).
cnf(c_0_6821_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6821]) ).
cnf(c_0_6821_1,axiom,
( ~ semilattice_sup(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6821]) ).
cnf(c_0_6822_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6822]) ).
cnf(c_0_6822_1,axiom,
( ~ ab_sem1668676832m_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6822]) ).
cnf(c_0_6823_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
| ~ ab_sem1668676832m_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6823_1,axiom,
( ~ ab_sem1668676832m_mult(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6823]) ).
cnf(c_0_6824_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),top_top(X1)) = top_top(X1)
| ~ bounded_lattice_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6824_1,axiom,
( ~ bounded_lattice_top(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),top_top(X1)) = top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6824]) ).
cnf(c_0_6825_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ mult_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6825_1,axiom,
( ~ mult_zero(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6825]) ).
cnf(c_0_6826_0,axiom,
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6826]) ).
cnf(c_0_6826_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6826]) ).
cnf(c_0_6829_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X2 != one_one(nat)
| X1 != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6829]) ).
cnf(c_0_6829_1,axiom,
( X2 != one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X1 != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6829]) ).
cnf(c_0_6829_2,axiom,
( X1 != one_one(nat)
| X2 != one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6829]) ).
cnf(c_0_6830_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X2 != one_one(nat)
| X1 != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6830_1,axiom,
( X2 != one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
| X1 != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6830_2,axiom,
( X1 != one_one(nat)
| X2 != one_one(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6830]) ).
cnf(c_0_6831_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_6831]) ).
cnf(c_0_6831_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_6831]) ).
cnf(c_0_6831_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_6831]) ).
cnf(c_0_6833_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6833_1,axiom,
( X1 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6833]) ).
cnf(c_0_6834_0,axiom,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6834_1,axiom,
( X2 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6834]) ).
cnf(c_0_6841_0,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6841]) ).
cnf(c_0_6841_1,axiom,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6841]) ).
cnf(c_0_6842_0,axiom,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6842]) ).
cnf(c_0_6842_1,axiom,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6842]) ).
cnf(c_0_6843_0,axiom,
( X1 = X2
| hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6843]) ).
cnf(c_0_6843_1,axiom,
( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6843]) ).
cnf(c_0_6847_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_6847]) ).
cnf(c_0_6847_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_6847]) ).
cnf(c_0_6850_0,axiom,
( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6850]) ).
cnf(c_0_6850_1,axiom,
( ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6850]) ).
cnf(c_0_6850_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6850]) ).
cnf(c_0_6851_0,axiom,
( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6851]) ).
cnf(c_0_6851_1,axiom,
( ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6851]) ).
cnf(c_0_6851_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1)
| hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6851]) ).
cnf(c_0_6855_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ finite_finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6855]) ).
cnf(c_0_6855_1,axiom,
( ~ finite_finite(X1)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6855]) ).
cnf(c_0_6856_0,axiom,
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
| ~ finite_finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6856]) ).
cnf(c_0_6856_1,axiom,
( ~ finite_finite(X1)
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6856]) ).
cnf(c_0_6862_0,axiom,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6862]) ).
cnf(c_0_6862_1,axiom,
( hBOOL(X1)
| hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6862]) ).
cnf(c_0_6863_0,axiom,
( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6863]) ).
cnf(c_0_6863_1,axiom,
( X1 != X2
| hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6863]) ).
cnf(c_0_6882_0,axiom,
( hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2)
| ~ top(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6882]) ).
cnf(c_0_6882_1,axiom,
( ~ top(X2)
| hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6882]) ).
cnf(c_0_6885_0,axiom,
( ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2)
| ~ comm_monoid_add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6885]) ).
cnf(c_0_6885_1,axiom,
( ~ comm_monoid_add(X2)
| ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6885]) ).
cnf(c_0_6890_0,axiom,
( hAPP(nat,nat,suc,sk1_esk97_1(X1)) = X1
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6890]) ).
cnf(c_0_6890_1,axiom,
( X1 = zero_zero(nat)
| hAPP(nat,nat,suc,sk1_esk97_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6890]) ).
cnf(c_0_6891_0,axiom,
( hAPP(nat,nat,suc,sk1_esk96_1(X1)) = X1
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_6891]) ).
cnf(c_0_6891_1,axiom,
( X1 = zero_zero(nat)
| hAPP(nat,nat,suc,sk1_esk96_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6891]) ).
cnf(c_0_6901_0,axiom,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6901]) ).
cnf(c_0_6901_1,axiom,
( ~ linorder(X1)
| ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6901]) ).
cnf(c_0_6902_0,axiom,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6902]) ).
cnf(c_0_6902_1,axiom,
( ~ linorder(X1)
| ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6902]) ).
cnf(c_0_6903_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_6903]) ).
cnf(c_0_6903_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_6903]) ).
cnf(c_0_6904_0,axiom,
( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6904]) ).
cnf(c_0_6904_1,axiom,
( ~ order(X1)
| ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6904]) ).
cnf(c_0_6909_0,axiom,
( ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1)
| ~ semilattice_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6909]) ).
cnf(c_0_6909_1,axiom,
( ~ semilattice_sup(X1)
| ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6909]) ).
cnf(c_0_6910_0,axiom,
( ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1)
| ~ semilattice_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6910]) ).
cnf(c_0_6910_1,axiom,
( ~ semilattice_inf(X1)
| ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6910]) ).
cnf(c_0_6911_0,axiom,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ no_zero_divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6911]) ).
cnf(c_0_6911_1,axiom,
( ~ no_zero_divisors(X1)
| ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6911]) ).
cnf(c_0_6912_0,axiom,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ mult_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6912]) ).
cnf(c_0_6912_1,axiom,
( ~ mult_zero(X1)
| ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6912]) ).
cnf(c_0_6913_0,axiom,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ ab_semigroup_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6913]) ).
cnf(c_0_6913_1,axiom,
( ~ ab_semigroup_mult(X1)
| ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6913]) ).
cnf(c_0_6914_0,axiom,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6914]) ).
cnf(c_0_6914_1,axiom,
( ~ monoid_mult(X1)
| ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6914]) ).
cnf(c_0_6915_0,axiom,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6915]) ).
cnf(c_0_6915_1,axiom,
( ~ semiring(X1)
| ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6915]) ).
cnf(c_0_6916_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_6916]) ).
cnf(c_0_6916_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_6916]) ).
cnf(c_0_6917_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_6917]) ).
cnf(c_0_6917_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_6917]) ).
cnf(c_0_6918_0,axiom,
( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
| ~ monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6918]) ).
cnf(c_0_6918_1,axiom,
( ~ monoid_add(X1)
| ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6918]) ).
cnf(c_0_6919_0,axiom,
( ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1)
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6919]) ).
cnf(c_0_6919_1,axiom,
( ~ ord(X1)
| ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6919]) ).
cnf(c_0_6920_0,axiom,
( ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1)
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6920]) ).
cnf(c_0_6920_1,axiom,
( ~ ord(X1)
| ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6920]) ).
cnf(c_0_6921_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_6921]) ).
cnf(c_0_6921_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_6921]) ).
cnf(c_0_6922_0,axiom,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6922]) ).
cnf(c_0_6922_1,axiom,
( ~ ord(X1)
| ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6922]) ).
cnf(c_0_6930_0,axiom,
( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
| ~ ring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6930]) ).
cnf(c_0_6930_1,axiom,
( ~ ring_1(X1)
| ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6930]) ).
cnf(c_0_6931_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6931]) ).
cnf(c_0_6931_1,axiom,
( ~ zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6931]) ).
cnf(c_0_6931_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6931]) ).
cnf(c_0_6932_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6932]) ).
cnf(c_0_6932_1,axiom,
( ~ zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6932]) ).
cnf(c_0_6932_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6932]) ).
cnf(c_0_6933_0,axiom,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6933]) ).
cnf(c_0_6933_1,axiom,
( ~ one(X1)
| ti(X1,X2) = one_one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6933]) ).
cnf(c_0_6933_2,axiom,
( ti(X1,X2) != one_one(X1)
| ~ one(X1)
| ti(X1,X2) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6933]) ).
cnf(c_0_6934_0,axiom,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6934]) ).
cnf(c_0_6934_1,axiom,
( ~ one(X1)
| ti(X1,X2) = one_one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6934]) ).
cnf(c_0_6934_2,axiom,
( ti(X1,X2) != one_one(X1)
| ~ one(X1)
| ti(X1,X2) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6934]) ).
cnf(c_0_6937_0,axiom,
( finite_finite(product_prod(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6937]) ).
cnf(c_0_6937_1,axiom,
( ~ finite_finite(X1)
| finite_finite(product_prod(X1,X2))
| ~ finite_finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6937]) ).
cnf(c_0_6937_2,axiom,
( ~ finite_finite(X2)
| ~ finite_finite(X1)
| finite_finite(product_prod(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6937]) ).
cnf(c_0_6938_0,axiom,
( finite_finite(sum_sum(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6938]) ).
cnf(c_0_6938_1,axiom,
( ~ finite_finite(X1)
| finite_finite(sum_sum(X1,X2))
| ~ finite_finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6938]) ).
cnf(c_0_6938_2,axiom,
( ~ finite_finite(X2)
| ~ finite_finite(X1)
| finite_finite(sum_sum(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6938]) ).
cnf(c_0_6939_0,axiom,
( finite_finite(fun(X1,X2))
| ~ finite_finite(X1)
| ~ finite_finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6939]) ).
cnf(c_0_6939_1,axiom,
( ~ finite_finite(X1)
| finite_finite(fun(X1,X2))
| ~ finite_finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6939]) ).
cnf(c_0_6939_2,axiom,
( ~ finite_finite(X2)
| ~ finite_finite(X1)
| finite_finite(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6939]) ).
cnf(c_0_6941_0,axiom,
( ord(fun(X1,X2))
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6941]) ).
cnf(c_0_6941_1,axiom,
( ~ ord(X2)
| ord(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6941]) ).
cnf(c_0_6942_0,axiom,
( top(fun(X1,X2))
| ~ top(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6942]) ).
cnf(c_0_6942_1,axiom,
( ~ top(X2)
| top(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6942]) ).
cnf(c_0_6943_0,axiom,
( order(fun(X1,X2))
| ~ order(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6943]) ).
cnf(c_0_6943_1,axiom,
( ~ order(X2)
| order(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6943]) ).
cnf(c_0_6944_0,axiom,
( lattice(fun(X1,X2))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6944]) ).
cnf(c_0_6944_1,axiom,
( ~ lattice(X2)
| lattice(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6944]) ).
cnf(c_0_6945_0,axiom,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6945]) ).
cnf(c_0_6945_1,axiom,
( ~ preorder(X2)
| preorder(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6945]) ).
cnf(c_0_6946_0,axiom,
( distrib_lattice(fun(X1,X2))
| ~ distrib_lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6946]) ).
cnf(c_0_6946_1,axiom,
( ~ distrib_lattice(X2)
| distrib_lattice(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6946]) ).
cnf(c_0_6947_0,axiom,
( semilattice_inf(fun(X1,X2))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6947]) ).
cnf(c_0_6947_1,axiom,
( ~ lattice(X2)
| semilattice_inf(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6947]) ).
cnf(c_0_6948_0,axiom,
( semilattice_sup(fun(X1,X2))
| ~ lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6948]) ).
cnf(c_0_6948_1,axiom,
( ~ lattice(X2)
| semilattice_sup(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6948]) ).
cnf(c_0_6949_0,axiom,
( bounded_lattice_top(fun(X1,X2))
| ~ bounded_lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6949]) ).
cnf(c_0_6949_1,axiom,
( ~ bounded_lattice(X2)
| bounded_lattice_top(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6949]) ).
cnf(c_0_6950_0,axiom,
( bounded_lattice(fun(X1,X2))
| ~ bounded_lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6950]) ).
cnf(c_0_6950_1,axiom,
( ~ bounded_lattice(X2)
| bounded_lattice(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6950]) ).
cnf(c_0_6956_0,axiom,
( ti(X1,top_top(X1)) = top_top(X1)
| ~ top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6956]) ).
cnf(c_0_6956_1,axiom,
( ~ top(X1)
| ti(X1,top_top(X1)) = top_top(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6956]) ).
cnf(c_0_6957_0,axiom,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6957]) ).
cnf(c_0_6957_1,axiom,
( ~ zero(X1)
| ti(X1,zero_zero(X1)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6957]) ).
cnf(c_0_6958_0,axiom,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6958]) ).
cnf(c_0_6958_1,axiom,
( ~ one(X1)
| ti(X1,one_one(X1)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6958]) ).
cnf(c_0_6959_0,axiom,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(literals_permutation,[status(thm)],[c_0_6959]) ).
cnf(c_0_6959_1,axiom,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(literals_permutation,[status(thm)],[c_0_6959]) ).
cnf(c_0_6960_0,axiom,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(literals_permutation,[status(thm)],[c_0_6960]) ).
cnf(c_0_6960_1,axiom,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(literals_permutation,[status(thm)],[c_0_6960]) ).
cnf(c_0_6961_0,axiom,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(literals_permutation,[status(thm)],[c_0_6961]) ).
cnf(c_0_6961_1,axiom,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(literals_permutation,[status(thm)],[c_0_6961]) ).
cnf(c_0_6963_0,axiom,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6963]) ).
cnf(c_0_6963_1,axiom,
( ~ zero_neq_one(X1)
| zero_zero(X1) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6963]) ).
cnf(c_0_6964_0,axiom,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6964]) ).
cnf(c_0_6964_1,axiom,
( ~ zero_neq_one(X1)
| zero_zero(X1) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6964]) ).
cnf(c_0_6965_0,axiom,
( finite_finite(option(X1))
| ~ finite_finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6965]) ).
cnf(c_0_6965_1,axiom,
( ~ finite_finite(X1)
| finite_finite(option(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6965]) ).
cnf(c_0_5825_0,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5826_0,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5956_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_5956]) ).
cnf(c_0_5957_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_5957]) ).
cnf(c_0_6334_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_6334]) ).
cnf(c_0_6620_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_6620]) ).
cnf(c_0_6621_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_6621]) ).
cnf(c_0_6622_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_6622]) ).
cnf(c_0_6632_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6632]) ).
cnf(c_0_6633_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6633]) ).
cnf(c_0_6782_0,axiom,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
inference(literals_permutation,[status(thm)],[c_0_6782]) ).
cnf(c_0_6866_0,axiom,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6866]) ).
cnf(c_0_6867_0,axiom,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6867]) ).
cnf(c_0_6868_0,axiom,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6868]) ).
cnf(c_0_6869_0,axiom,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6869]) ).
cnf(c_0_6870_0,axiom,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6870]) ).
cnf(c_0_6871_0,axiom,
hAPP(nat,nat,suc,X1) != zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6871]) ).
cnf(c_0_6874_0,axiom,
hAPP(nat,nat,suc,X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6874]) ).
cnf(c_0_6875_0,axiom,
hAPP(nat,nat,suc,X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6875]) ).
cnf(c_0_6972_0,axiom,
~ hBOOL(fFalse),
inference(literals_permutation,[status(thm)],[c_0_6972]) ).
cnf(c_0_7023_0,axiom,
b != a,
inference(literals_permutation,[status(thm)],[c_0_7023]) ).
cnf(c_0_7024_0,axiom,
d != c,
inference(literals_permutation,[status(thm)],[c_0_7024]) ).
cnf(c_0_5281_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(literals_permutation,[status(thm)],[c_0_5281]) ).
cnf(c_0_5282_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(literals_permutation,[status(thm)],[c_0_5282]) ).
cnf(c_0_5283_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(literals_permutation,[status(thm)],[c_0_5283]) ).
cnf(c_0_5284_0,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
inference(literals_permutation,[status(thm)],[c_0_5284]) ).
cnf(c_0_5292_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk29_0),one_one(nat))))),lab)),lba)))),
inference(literals_permutation,[status(thm)],[c_0_5292]) ).
cnf(c_0_5293_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5293]) ).
cnf(c_0_5294_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_5294]) ).
cnf(c_0_5298_0,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_301600364e_Prof)),
inference(literals_permutation,[status(thm)],[c_0_5298]) ).
cnf(c_0_5319_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,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X3)),X4)),X5)),X6) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),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),X3))))),
inference(literals_permutation,[status(thm)],[c_0_5319]) ).
cnf(c_0_5382_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_5382]) ).
cnf(c_0_5408_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)),
inference(literals_permutation,[status(thm)],[c_0_5408]) ).
cnf(c_0_5415_0,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5429_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),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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_5429]) ).
cnf(c_0_5470_0,axiom,
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),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))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5471_0,axiom,
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),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))) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5541_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)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5558_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5593_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)),X4),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5731_0,axiom,
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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_5731]) ).
cnf(c_0_5732_0,axiom,
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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_5732]) ).
cnf(c_0_5864_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5865_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5910_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
inference(literals_permutation,[status(thm)],[c_0_5910]) ).
cnf(c_0_5912_0,axiom,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
inference(literals_permutation,[status(thm)],[c_0_5912]) ).
cnf(c_0_5913_0,axiom,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
inference(literals_permutation,[status(thm)],[c_0_5913]) ).
cnf(c_0_5954_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_5954]) ).
cnf(c_0_5982_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5983_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5985_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_5985]) ).
cnf(c_0_5986_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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X2)),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5987_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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X3)),
inference(literals_permutation,[status(thm)],[c_0_5987]) ).
cnf(c_0_5988_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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(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_5988]) ).
cnf(c_0_5989_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_5989]) ).
cnf(c_0_5990_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_5990]) ).
cnf(c_0_6002_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6024_0,axiom,
hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),hAPP(fun(X1,X5),fun(X1,X2),hAPP(fun(X5,X2),fun(fun(X1,X5),fun(X1,X2)),comp(X5,X2,X1),X6),X7)) = hAPP(fun(X1,X5),fun(X1,X3),hAPP(fun(X5,X3),fun(fun(X1,X5),fun(X1,X3)),comp(X5,X3,X1),hAPP(fun(X5,X2),fun(X5,X3),hAPP(fun(X2,X3),fun(fun(X5,X2),fun(X5,X3)),comp(X2,X3,X5),X4),X6)),X7),
inference(literals_permutation,[status(thm)],[c_0_6024]) ).
cnf(c_0_6030_0,axiom,
hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),X6) = hAPP(fun(X1,bool),fun(X1,X3),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X1,X3)),restrict(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X5),X6)),X4),
inference(literals_permutation,[status(thm)],[c_0_6030]) ).
cnf(c_0_6045_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_6045]) ).
cnf(c_0_6060_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),sk1_esk20_0)),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6061_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),sk1_esk19_0)),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6062_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6063_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6064_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)),comp(X3,X2,X1),X4),X5)),X6) = 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),X6)),
inference(literals_permutation,[status(thm)],[c_0_6064]) ).
cnf(c_0_6065_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_6065]) ).
cnf(c_0_6094_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6095_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6096_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6123_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_6123]) ).
cnf(c_0_6124_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_6124]) ).
cnf(c_0_6138_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_6138]) ).
cnf(c_0_6184_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6221_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_6221]) ).
cnf(c_0_6222_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_6222]) ).
cnf(c_0_6235_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,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4) = 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_6235]) ).
cnf(c_0_6238_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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2))),
inference(literals_permutation,[status(thm)],[c_0_6238]) ).
cnf(c_0_6239_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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6256_0,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6259_0,axiom,
hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)) = arrow_301600364e_Prof,
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6281_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_6281]) ).
cnf(c_0_6282_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_6282]) ).
cnf(c_0_6300_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_6300]) ).
cnf(c_0_6315_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_6315]) ).
cnf(c_0_6344_0,axiom,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X4)),X5),X6) = ti(X2,X4),
inference(literals_permutation,[status(thm)],[c_0_6344]) ).
cnf(c_0_6347_0,axiom,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
inference(literals_permutation,[status(thm)],[c_0_6347]) ).
cnf(c_0_6348_0,axiom,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
inference(literals_permutation,[status(thm)],[c_0_6348]) ).
cnf(c_0_6408_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6409_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6410_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1))),
inference(literals_permutation,[status(thm)],[c_0_6410]) ).
cnf(c_0_6411_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_6411]) ).
cnf(c_0_6412_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_6412]) ).
cnf(c_0_6414_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_6414]) ).
cnf(c_0_6427_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_6427]) ).
cnf(c_0_6462_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_6462]) ).
cnf(c_0_6463_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_atLeastAtMost(nat),X1),X2))),
inference(literals_permutation,[status(thm)],[c_0_6463]) ).
cnf(c_0_6464_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_gr676655987ssThan(nat),X1),X2))),
inference(literals_permutation,[status(thm)],[c_0_6464]) ).
cnf(c_0_6465_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_gr1471790799AtMost(nat),X1),X2))),
inference(literals_permutation,[status(thm)],[c_0_6465]) ).
cnf(c_0_6466_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_6466]) ).
cnf(c_0_6469_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_6469]) ).
cnf(c_0_6483_0,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sk1_esk66_0),arrow_1568854078le_Lin)),
inference(literals_permutation,[status(thm)],[c_0_6483]) ).
cnf(c_0_6484_0,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sk1_esk20_0),arrow_1568854078le_Lin)),
inference(literals_permutation,[status(thm)],[c_0_6484]) ).
cnf(c_0_6485_0,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sk1_esk19_0),arrow_1568854078le_Lin)),
inference(literals_permutation,[status(thm)],[c_0_6485]) ).
cnf(c_0_6486_0,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
inference(literals_permutation,[status(thm)],[c_0_6486]) ).
cnf(c_0_6487_0,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
inference(literals_permutation,[status(thm)],[c_0_6487]) ).
cnf(c_0_6498_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_6498]) ).
cnf(c_0_6499_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_6499]) ).
cnf(c_0_6500_0,axiom,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
inference(literals_permutation,[status(thm)],[c_0_6500]) ).
cnf(c_0_6501_0,axiom,
hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6502_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,suc,X2)),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6505_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_6505]) ).
cnf(c_0_6560_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_6560]) ).
cnf(c_0_6561_0,axiom,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),hAPP(nat,nat,suc,X4)) = hAPP(nat,X1,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6562_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_6562]) ).
cnf(c_0_6563_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X1)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X1)),
inference(literals_permutation,[status(thm)],[c_0_6563]) ).
cnf(c_0_6565_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X1)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X1)),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6574_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk29_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
inference(literals_permutation,[status(thm)],[c_0_6574]) ).
cnf(c_0_6575_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk28_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6576_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6581_0,axiom,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6582_0,axiom,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2),
inference(literals_permutation,[status(thm)],[c_0_6582]) ).
cnf(c_0_6588_0,axiom,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) = hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),sk1_esk101_0),top_top(fun(arrow_1998540521e_indi,bool))),
inference(literals_permutation,[status(thm)],[c_0_6588]) ).
cnf(c_0_6589_0,axiom,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) = hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))),
inference(literals_permutation,[status(thm)],[c_0_6589]) ).
cnf(c_0_6590_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_6590]) ).
cnf(c_0_6611_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_6611]) ).
cnf(c_0_6615_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_6615]) ).
cnf(c_0_6636_0,axiom,
hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_6636]) ).
cnf(c_0_6647_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2),
inference(literals_permutation,[status(thm)],[c_0_6647]) ).
cnf(c_0_6648_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2),
inference(literals_permutation,[status(thm)],[c_0_6648]) ).
cnf(c_0_6652_0,axiom,
hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6652]) ).
cnf(c_0_6653_0,axiom,
hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2),
inference(literals_permutation,[status(thm)],[c_0_6653]) ).
cnf(c_0_6662_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_6662]) ).
cnf(c_0_6663_0,axiom,
ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6663]) ).
cnf(c_0_6664_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_6664]) ).
cnf(c_0_6665_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_6665]) ).
cnf(c_0_6668_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_6668]) ).
cnf(c_0_6672_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_6672]) ).
cnf(c_0_6673_0,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),sk1_esk101_0),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(literals_permutation,[status(thm)],[c_0_6673]) ).
cnf(c_0_6674_0,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(literals_permutation,[status(thm)],[c_0_6674]) ).
cnf(c_0_6676_0,axiom,
hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk148_1(X1)),top_top(fun(X1,bool)))),
inference(literals_permutation,[status(thm)],[c_0_6676]) ).
cnf(c_0_6677_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_6677]) ).
cnf(c_0_6678_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_6678]) ).
cnf(c_0_6679_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_6679]) ).
cnf(c_0_6680_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_6680]) ).
cnf(c_0_6716_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_6716]) ).
cnf(c_0_6721_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_6721]) ).
cnf(c_0_6722_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_6722]) ).
cnf(c_0_6738_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_6738]) ).
cnf(c_0_6739_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_6739]) ).
cnf(c_0_6740_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_6740]) ).
cnf(c_0_6749_0,axiom,
hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)),
inference(literals_permutation,[status(thm)],[c_0_6749]) ).
cnf(c_0_6750_0,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
inference(literals_permutation,[status(thm)],[c_0_6750]) ).
cnf(c_0_6751_0,axiom,
hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
inference(literals_permutation,[status(thm)],[c_0_6751]) ).
cnf(c_0_6756_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X2) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_6756]) ).
cnf(c_0_6757_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X2) = top_top(fun(X1,bool)),
inference(literals_permutation,[status(thm)],[c_0_6757]) ).
cnf(c_0_6762_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),top_top(fun(X1,bool))) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_6762]) ).
cnf(c_0_6763_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
inference(literals_permutation,[status(thm)],[c_0_6763]) ).
cnf(c_0_6773_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_6773]) ).
cnf(c_0_6774_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_6774]) ).
cnf(c_0_6775_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_6775]) ).
cnf(c_0_6777_0,axiom,
ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6777]) ).
cnf(c_0_6778_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_6778]) ).
cnf(c_0_6779_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_6779]) ).
cnf(c_0_6780_0,axiom,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X1),
inference(literals_permutation,[status(thm)],[c_0_6780]) ).
cnf(c_0_6781_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_6781]) ).
cnf(c_0_6783_0,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
inference(literals_permutation,[status(thm)],[c_0_6783]) ).
cnf(c_0_6784_0,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
inference(literals_permutation,[status(thm)],[c_0_6784]) ).
cnf(c_0_6785_0,axiom,
ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
inference(literals_permutation,[status(thm)],[c_0_6785]) ).
cnf(c_0_6786_0,axiom,
ti(fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)))),compose(X1,X2,X3)) = compose(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_6786]) ).
cnf(c_0_6787_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_6787]) ).
cnf(c_0_6791_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_6791]) ).
cnf(c_0_6827_0,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
inference(literals_permutation,[status(thm)],[c_0_6827]) ).
cnf(c_0_6828_0,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
inference(literals_permutation,[status(thm)],[c_0_6828]) ).
cnf(c_0_6832_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6832]) ).
cnf(c_0_6835_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6835]) ).
cnf(c_0_6836_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_6836]) ).
cnf(c_0_6837_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6837]) ).
cnf(c_0_6838_0,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),one_one(nat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6838]) ).
cnf(c_0_6839_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_6839]) ).
cnf(c_0_6840_0,axiom,
ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6840]) ).
cnf(c_0_6844_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_6844]) ).
cnf(c_0_6845_0,axiom,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_6845]) ).
cnf(c_0_6846_0,axiom,
ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
inference(literals_permutation,[status(thm)],[c_0_6846]) ).
cnf(c_0_6848_0,axiom,
hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
inference(literals_permutation,[status(thm)],[c_0_6848]) ).
cnf(c_0_6849_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_6849]) ).
cnf(c_0_6852_0,axiom,
hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_6852]) ).
cnf(c_0_6853_0,axiom,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_6853]) ).
cnf(c_0_6854_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_6854]) ).
cnf(c_0_6857_0,axiom,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_6857]) ).
cnf(c_0_6858_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_6858]) ).
cnf(c_0_6859_0,axiom,
ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),comp(X1,X2,X3)) = comp(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_6859]) ).
cnf(c_0_6860_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_6860]) ).
cnf(c_0_6861_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_6861]) ).
cnf(c_0_6864_0,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
inference(literals_permutation,[status(thm)],[c_0_6864]) ).
cnf(c_0_6865_0,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
inference(literals_permutation,[status(thm)],[c_0_6865]) ).
cnf(c_0_6872_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_6872]) ).
cnf(c_0_6873_0,axiom,
ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6873]) ).
cnf(c_0_6876_0,axiom,
ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6876]) ).
cnf(c_0_6877_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_6877]) ).
cnf(c_0_6878_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_6878]) ).
cnf(c_0_6879_0,axiom,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(literals_permutation,[status(thm)],[c_0_6879]) ).
cnf(c_0_6880_0,axiom,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
inference(literals_permutation,[status(thm)],[c_0_6880]) ).
cnf(c_0_6881_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_6881]) ).
cnf(c_0_6883_0,axiom,
hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
inference(literals_permutation,[status(thm)],[c_0_6883]) ).
cnf(c_0_6884_0,axiom,
ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
inference(literals_permutation,[status(thm)],[c_0_6884]) ).
cnf(c_0_6886_0,axiom,
ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
inference(literals_permutation,[status(thm)],[c_0_6886]) ).
cnf(c_0_6887_0,axiom,
ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6887]) ).
cnf(c_0_6888_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_6888]) ).
cnf(c_0_6889_0,axiom,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6889]) ).
cnf(c_0_6892_0,axiom,
hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6892]) ).
cnf(c_0_6893_0,axiom,
hAPP(nat,nat,size_size(nat),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_6893]) ).
cnf(c_0_6894_0,axiom,
hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6894]) ).
cnf(c_0_6895_0,axiom,
hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
inference(literals_permutation,[status(thm)],[c_0_6895]) ).
cnf(c_0_6896_0,axiom,
ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
inference(literals_permutation,[status(thm)],[c_0_6896]) ).
cnf(c_0_6897_0,axiom,
hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6897]) ).
cnf(c_0_6898_0,axiom,
hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6898]) ).
cnf(c_0_6899_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_6899]) ).
cnf(c_0_6900_0,axiom,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
inference(literals_permutation,[status(thm)],[c_0_6900]) ).
cnf(c_0_6905_0,axiom,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(literals_permutation,[status(thm)],[c_0_6905]) ).
cnf(c_0_6906_0,axiom,
ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
inference(literals_permutation,[status(thm)],[c_0_6906]) ).
cnf(c_0_6907_0,axiom,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(literals_permutation,[status(thm)],[c_0_6907]) ).
cnf(c_0_6908_0,axiom,
ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6908]) ).
cnf(c_0_6923_0,axiom,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(literals_permutation,[status(thm)],[c_0_6923]) ).
cnf(c_0_6924_0,axiom,
ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
inference(literals_permutation,[status(thm)],[c_0_6924]) ).
cnf(c_0_6925_0,axiom,
ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
inference(literals_permutation,[status(thm)],[c_0_6925]) ).
cnf(c_0_6926_0,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
inference(literals_permutation,[status(thm)],[c_0_6926]) ).
cnf(c_0_6927_0,axiom,
ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
inference(literals_permutation,[status(thm)],[c_0_6927]) ).
cnf(c_0_6928_0,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(literals_permutation,[status(thm)],[c_0_6928]) ).
cnf(c_0_6929_0,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(literals_permutation,[status(thm)],[c_0_6929]) ).
cnf(c_0_6935_0,axiom,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_6935]) ).
cnf(c_0_6936_0,axiom,
ti(fun(X1,X1),combi(X1)) = combi(X1),
inference(literals_permutation,[status(thm)],[c_0_6936]) ).
cnf(c_0_6940_0,axiom,
ti(fun(nat,nat),size_size(nat)) = size_size(nat),
inference(literals_permutation,[status(thm)],[c_0_6940]) ).
cnf(c_0_6951_0,axiom,
ti(fun(arrow_1998540521e_indi,nat),h) = h,
inference(literals_permutation,[status(thm)],[c_0_6951]) ).
cnf(c_0_6952_0,axiom,
ti(fun(bool,bool),fNot) = fNot,
inference(literals_permutation,[status(thm)],[c_0_6952]) ).
cnf(c_0_6953_0,axiom,
ti(fun(nat,nat),nat_size) = nat_size,
inference(literals_permutation,[status(thm)],[c_0_6953]) ).
cnf(c_0_6954_0,axiom,
ti(fun(nat,nat),suc) = suc,
inference(literals_permutation,[status(thm)],[c_0_6954]) ).
cnf(c_0_6955_0,axiom,
ti(fun(bool,nat),bool_size) = bool_size,
inference(literals_permutation,[status(thm)],[c_0_6955]) ).
cnf(c_0_6962_0,axiom,
ti(X1,undefined(X1)) = undefined(X1),
inference(literals_permutation,[status(thm)],[c_0_6962]) ).
cnf(c_0_6966_0,axiom,
ti(nat,n) = n,
inference(literals_permutation,[status(thm)],[c_0_6966]) ).
cnf(c_0_6967_0,axiom,
ti(arrow_2142409994le_alt,e) = e,
inference(literals_permutation,[status(thm)],[c_0_6967]) ).
cnf(c_0_6968_0,axiom,
ti(arrow_2142409994le_alt,b) = b,
inference(literals_permutation,[status(thm)],[c_0_6968]) ).
cnf(c_0_6969_0,axiom,
ti(arrow_2142409994le_alt,a) = a,
inference(literals_permutation,[status(thm)],[c_0_6969]) ).
cnf(c_0_6970_0,axiom,
ti(bool,fTrue) = fTrue,
inference(literals_permutation,[status(thm)],[c_0_6970]) ).
cnf(c_0_6971_0,axiom,
ti(bool,fFalse) = fFalse,
inference(literals_permutation,[status(thm)],[c_0_6971]) ).
cnf(c_0_6973_0,axiom,
hBOOL(fTrue),
inference(literals_permutation,[status(thm)],[c_0_6973]) ).
cnf(c_0_6974_0,axiom,
finite_finite(product_unit),
inference(literals_permutation,[status(thm)],[c_0_6974]) ).
cnf(c_0_6975_0,axiom,
ord(bool),
inference(literals_permutation,[status(thm)],[c_0_6975]) ).
cnf(c_0_6976_0,axiom,
top(bool),
inference(literals_permutation,[status(thm)],[c_0_6976]) ).
cnf(c_0_6977_0,axiom,
order(bool),
inference(literals_permutation,[status(thm)],[c_0_6977]) ).
cnf(c_0_6978_0,axiom,
lattice(bool),
inference(literals_permutation,[status(thm)],[c_0_6978]) ).
cnf(c_0_6979_0,axiom,
finite_finite(bool),
inference(literals_permutation,[status(thm)],[c_0_6979]) ).
cnf(c_0_6980_0,axiom,
preorder(bool),
inference(literals_permutation,[status(thm)],[c_0_6980]) ).
cnf(c_0_6981_0,axiom,
distrib_lattice(bool),
inference(literals_permutation,[status(thm)],[c_0_6981]) ).
cnf(c_0_6982_0,axiom,
semilattice_inf(bool),
inference(literals_permutation,[status(thm)],[c_0_6982]) ).
cnf(c_0_6983_0,axiom,
semilattice_sup(bool),
inference(literals_permutation,[status(thm)],[c_0_6983]) ).
cnf(c_0_6984_0,axiom,
bounded_lattice_top(bool),
inference(literals_permutation,[status(thm)],[c_0_6984]) ).
cnf(c_0_6985_0,axiom,
one(nat),
inference(literals_permutation,[status(thm)],[c_0_6985]) ).
cnf(c_0_6986_0,axiom,
zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6986]) ).
cnf(c_0_6987_0,axiom,
ord(nat),
inference(literals_permutation,[status(thm)],[c_0_6987]) ).
cnf(c_0_6988_0,axiom,
semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_6988]) ).
cnf(c_0_6989_0,axiom,
order(nat),
inference(literals_permutation,[status(thm)],[c_0_6989]) ).
cnf(c_0_6990_0,axiom,
mult_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_6990]) ).
cnf(c_0_6991_0,axiom,
lattice(nat),
inference(literals_permutation,[status(thm)],[c_0_6991]) ).
cnf(c_0_6992_0,axiom,
semiring_0(nat),
inference(literals_permutation,[status(thm)],[c_0_6992]) ).
cnf(c_0_6993_0,axiom,
monoid_add(nat),
inference(literals_permutation,[status(thm)],[c_0_6993]) ).
cnf(c_0_6994_0,axiom,
monoid_mult(nat),
inference(literals_permutation,[status(thm)],[c_0_6994]) ).
cnf(c_0_6995_0,axiom,
linorder(nat),
inference(literals_permutation,[status(thm)],[c_0_6995]) ).
cnf(c_0_6996_0,axiom,
preorder(nat),
inference(literals_permutation,[status(thm)],[c_0_6996]) ).
cnf(c_0_6997_0,axiom,
zero_neq_one(nat),
inference(literals_permutation,[status(thm)],[c_0_6997]) ).
cnf(c_0_6998_0,axiom,
comm_semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_6998]) ).
cnf(c_0_6999_0,axiom,
comm_semiring_1(nat),
inference(literals_permutation,[status(thm)],[c_0_6999]) ).
cnf(c_0_7000_0,axiom,
comm_monoid_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7000]) ).
cnf(c_0_7001_0,axiom,
no_zero_divisors(nat),
inference(literals_permutation,[status(thm)],[c_0_7001]) ).
cnf(c_0_7002_0,axiom,
ordered_semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_7002]) ).
cnf(c_0_7003_0,axiom,
ab_semigroup_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7003]) ).
cnf(c_0_7004_0,axiom,
comm_monoid_mult(nat),
inference(literals_permutation,[status(thm)],[c_0_7004]) ).
cnf(c_0_7005_0,axiom,
ab_semigroup_mult(nat),
inference(literals_permutation,[status(thm)],[c_0_7005]) ).
cnf(c_0_7006_0,axiom,
distrib_lattice(nat),
inference(literals_permutation,[status(thm)],[c_0_7006]) ).
cnf(c_0_7007_0,axiom,
semilattice_inf(nat),
inference(literals_permutation,[status(thm)],[c_0_7007]) ).
cnf(c_0_7008_0,axiom,
semilattice_sup(nat),
inference(literals_permutation,[status(thm)],[c_0_7008]) ).
cnf(c_0_7009_0,axiom,
linordered_semidom(nat),
inference(literals_permutation,[status(thm)],[c_0_7009]) ).
cnf(c_0_7010_0,axiom,
linordered_semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_7010]) ).
cnf(c_0_7011_0,axiom,
cancel_semigroup_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7011]) ).
cnf(c_0_7012_0,axiom,
ordere1490568538miring(nat),
inference(literals_permutation,[status(thm)],[c_0_7012]) ).
cnf(c_0_7013_0,axiom,
ordere453448008miring(nat),
inference(literals_permutation,[status(thm)],[c_0_7013]) ).
cnf(c_0_7014_0,axiom,
cancel146912293up_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7014]) ).
cnf(c_0_7015_0,axiom,
ordere216010020id_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7015]) ).
cnf(c_0_7016_0,axiom,
ordere779506340up_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7016]) ).
cnf(c_0_7017_0,axiom,
linord20386208strict(nat),
inference(literals_permutation,[status(thm)],[c_0_7017]) ).
cnf(c_0_7018_0,axiom,
linord893533164strict(nat),
inference(literals_permutation,[status(thm)],[c_0_7018]) ).
cnf(c_0_7019_0,axiom,
ordere236663937imp_le(nat),
inference(literals_permutation,[status(thm)],[c_0_7019]) ).
cnf(c_0_7020_0,axiom,
ordere223160158up_add(nat),
inference(literals_permutation,[status(thm)],[c_0_7020]) ).
cnf(c_0_7021_0,axiom,
semiri456707255roduct(nat),
inference(literals_permutation,[status(thm)],[c_0_7021]) ).
cnf(c_0_7022_0,axiom,
bounded_lattice(bool),
inference(literals_permutation,[status(thm)],[c_0_7022]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
file('<stdin>',conj_0) ).
fof(c_0_1_002,hypothesis,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
file('<stdin>',tsy_v_F_res) ).
fof(c_0_2_003,hypothesis,
ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_2142409994le_alt,d) = d,
file('<stdin>',tsy_v_d_____res) ).
fof(c_0_5_006,hypothesis,
ti(arrow_2142409994le_alt,c) = c,
file('<stdin>',tsy_v_c_____res) ).
fof(c_0_6_007,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
c_0_1 ).
fof(c_0_8_009,hypothesis,
ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_2142409994le_alt,d) = d,
c_0_4 ).
fof(c_0_11_012,hypothesis,
ti(arrow_2142409994le_alt,c) = c,
c_0_5 ).
fof(c_0_12_013,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
c_0_6 ).
fof(c_0_13_014,hypothesis,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
c_0_7 ).
fof(c_0_14_015,hypothesis,
ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_2142409994le_alt,d) = d,
c_0_10 ).
fof(c_0_17_018,hypothesis,
ti(arrow_2142409994le_alt,c) = c,
c_0_11 ).
cnf(c_0_18_019,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19_020,hypothesis,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20_021,hypothesis,
ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_2142409994le_alt,d) = d,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24_025,hypothesis,
ti(arrow_2142409994le_alt,c) = c,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25_026,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
c_0_18,
[final] ).
cnf(c_0_26_027,hypothesis,
ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
c_0_19,
[final] ).
cnf(c_0_27_028,hypothesis,
ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_2142409994le_alt,d) = d,
c_0_23,
[final] ).
cnf(c_0_31_032,hypothesis,
ti(arrow_2142409994le_alt,c) = c,
c_0_24,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_269,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52e4f7.p',c_0_5283_0) ).
cnf(c_4938,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52e4f7.p',c_0_5275_0) ).
cnf(c_5009,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
file('/export/starexec/sandbox2/tmp/iprover_modulo_52e4f7.p',c_0_25) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_269,c_4938,c_5009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171+7 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 06:41:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running in mono-core mode
% 0.94/1.10 % Orienting using strategy Equiv(ClausalAll)
% 0.94/1.10 % FOF problem with conjecture
% 0.94/1.10 % 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/sandbox2/tmp/iprover_proof_c5af18.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_52e4f7.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_8d80a4 | grep -v "SZS"
% 0.94/1.11
% 0.94/1.11 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.94/1.11
% 0.94/1.11 %
% 0.94/1.11 % ------ iProver source info
% 0.94/1.11
% 0.94/1.11 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.94/1.11 % git: non_committed_changes: true
% 0.94/1.11 % git: last_make_outside_of_git: true
% 0.94/1.11
% 0.94/1.11 %
% 0.94/1.11 % ------ Input Options
% 0.94/1.11
% 0.94/1.11 % --out_options all
% 0.94/1.11 % --tptp_safe_out true
% 0.94/1.11 % --problem_path ""
% 0.94/1.11 % --include_path ""
% 0.94/1.11 % --clausifier .//eprover
% 0.94/1.11 % --clausifier_options --tstp-format
% 0.94/1.11 % --stdin false
% 0.94/1.11 % --dbg_backtrace false
% 0.94/1.11 % --dbg_dump_prop_clauses false
% 0.94/1.11 % --dbg_dump_prop_clauses_file -
% 0.94/1.11 % --dbg_out_stat false
% 0.94/1.11
% 0.94/1.11 % ------ General Options
% 0.94/1.11
% 0.94/1.11 % --fof false
% 0.94/1.11 % --time_out_real 150.
% 0.94/1.11 % --time_out_prep_mult 0.2
% 0.94/1.11 % --time_out_virtual -1.
% 0.94/1.11 % --schedule none
% 0.94/1.11 % --ground_splitting input
% 0.94/1.11 % --splitting_nvd 16
% 0.94/1.11 % --non_eq_to_eq false
% 0.94/1.11 % --prep_gs_sim true
% 0.94/1.11 % --prep_unflatten false
% 0.94/1.11 % --prep_res_sim true
% 0.94/1.11 % --prep_upred true
% 0.94/1.11 % --res_sim_input true
% 0.94/1.11 % --clause_weak_htbl true
% 0.94/1.11 % --gc_record_bc_elim false
% 0.94/1.11 % --symbol_type_check false
% 0.94/1.11 % --clausify_out false
% 0.94/1.11 % --large_theory_mode false
% 0.94/1.11 % --prep_sem_filter none
% 0.94/1.11 % --prep_sem_filter_out false
% 0.94/1.11 % --preprocessed_out false
% 0.94/1.11 % --sub_typing false
% 0.94/1.11 % --brand_transform false
% 0.94/1.11 % --pure_diseq_elim true
% 0.94/1.11 % --min_unsat_core false
% 0.94/1.11 % --pred_elim true
% 0.94/1.11 % --add_important_lit false
% 0.94/1.11 % --soft_assumptions false
% 0.94/1.11 % --reset_solvers false
% 0.94/1.11 % --bc_imp_inh []
% 0.94/1.11 % --conj_cone_tolerance 1.5
% 0.94/1.11 % --prolific_symb_bound 500
% 0.94/1.11 % --lt_threshold 2000
% 0.94/1.11
% 0.94/1.11 % ------ SAT Options
% 0.94/1.11
% 0.94/1.11 % --sat_mode false
% 0.94/1.11 % --sat_fm_restart_options ""
% 0.94/1.11 % --sat_gr_def false
% 0.94/1.11 % --sat_epr_types true
% 0.94/1.11 % --sat_non_cyclic_types false
% 0.94/1.11 % --sat_finite_models false
% 0.94/1.11 % --sat_fm_lemmas false
% 0.94/1.11 % --sat_fm_prep false
% 0.94/1.11 % --sat_fm_uc_incr true
% 0.94/1.11 % --sat_out_model small
% 0.94/1.11 % --sat_out_clauses false
% 0.94/1.11
% 0.94/1.11 % ------ QBF Options
% 0.94/1.11
% 0.94/1.11 % --qbf_mode false
% 0.94/1.11 % --qbf_elim_univ true
% 0.94/1.11 % --qbf_sk_in true
% 0.94/1.11 % --qbf_pred_elim true
% 0.94/1.11 % --qbf_split 32
% 0.94/1.11
% 0.94/1.11 % ------ BMC1 Options
% 0.94/1.11
% 0.94/1.11 % --bmc1_incremental false
% 0.94/1.11 % --bmc1_axioms reachable_all
% 0.94/1.11 % --bmc1_min_bound 0
% 0.94/1.11 % --bmc1_max_bound -1
% 0.94/1.11 % --bmc1_max_bound_default -1
% 0.94/1.11 % --bmc1_symbol_reachability true
% 0.94/1.11 % --bmc1_property_lemmas false
% 0.94/1.11 % --bmc1_k_induction false
% 0.94/1.11 % --bmc1_non_equiv_states false
% 0.94/1.11 % --bmc1_deadlock false
% 0.94/1.11 % --bmc1_ucm false
% 0.94/1.11 % --bmc1_add_unsat_core none
% 0.94/1.11 % --bmc1_unsat_core_children false
% 0.94/1.11 % --bmc1_unsat_core_extrapolate_axioms false
% 0.94/1.11 % --bmc1_out_stat full
% 0.94/1.11 % --bmc1_ground_init false
% 0.94/1.11 % --bmc1_pre_inst_next_state false
% 0.94/1.11 % --bmc1_pre_inst_state false
% 0.94/1.11 % --bmc1_pre_inst_reach_state false
% 0.94/1.11 % --bmc1_out_unsat_core false
% 0.94/1.11 % --bmc1_aig_witness_out false
% 0.94/1.11 % --bmc1_verbose false
% 0.94/1.11 % --bmc1_dump_clauses_tptp false
% 0.97/1.27 % --bmc1_dump_unsat_core_tptp false
% 0.97/1.27 % --bmc1_dump_file -
% 0.97/1.27 % --bmc1_ucm_expand_uc_limit 128
% 0.97/1.27 % --bmc1_ucm_n_expand_iterations 6
% 0.97/1.27 % --bmc1_ucm_extend_mode 1
% 0.97/1.27 % --bmc1_ucm_init_mode 2
% 0.97/1.27 % --bmc1_ucm_cone_mode none
% 0.97/1.27 % --bmc1_ucm_reduced_relation_type 0
% 0.97/1.27 % --bmc1_ucm_relax_model 4
% 0.97/1.27 % --bmc1_ucm_full_tr_after_sat true
% 0.97/1.27 % --bmc1_ucm_expand_neg_assumptions false
% 0.97/1.27 % --bmc1_ucm_layered_model none
% 0.97/1.27 % --bmc1_ucm_max_lemma_size 10
% 0.97/1.27
% 0.97/1.27 % ------ AIG Options
% 0.97/1.27
% 0.97/1.27 % --aig_mode false
% 0.97/1.27
% 0.97/1.27 % ------ Instantiation Options
% 0.97/1.27
% 0.97/1.27 % --instantiation_flag true
% 0.97/1.27 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.97/1.27 % --inst_solver_per_active 750
% 0.97/1.27 % --inst_solver_calls_frac 0.5
% 0.97/1.27 % --inst_passive_queue_type priority_queues
% 0.97/1.27 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.97/1.27 % --inst_passive_queues_freq [25;2]
% 0.97/1.27 % --inst_dismatching true
% 0.97/1.27 % --inst_eager_unprocessed_to_passive true
% 0.97/1.27 % --inst_prop_sim_given true
% 0.97/1.27 % --inst_prop_sim_new false
% 0.97/1.27 % --inst_orphan_elimination true
% 0.97/1.27 % --inst_learning_loop_flag true
% 0.97/1.27 % --inst_learning_start 3000
% 0.97/1.27 % --inst_learning_factor 2
% 0.97/1.27 % --inst_start_prop_sim_after_learn 3
% 0.97/1.27 % --inst_sel_renew solver
% 0.97/1.27 % --inst_lit_activity_flag true
% 0.97/1.27 % --inst_out_proof true
% 0.97/1.27
% 0.97/1.27 % ------ Resolution Options
% 0.97/1.27
% 0.97/1.27 % --resolution_flag true
% 0.97/1.27 % --res_lit_sel kbo_max
% 0.97/1.27 % --res_to_prop_solver none
% 0.97/1.27 % --res_prop_simpl_new false
% 0.97/1.27 % --res_prop_simpl_given false
% 0.97/1.27 % --res_passive_queue_type priority_queues
% 0.97/1.27 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.97/1.27 % --res_passive_queues_freq [15;5]
% 0.97/1.27 % --res_forward_subs full
% 0.97/1.27 % --res_backward_subs full
% 0.97/1.27 % --res_forward_subs_resolution true
% 0.97/1.27 % --res_backward_subs_resolution true
% 0.97/1.27 % --res_orphan_elimination false
% 0.97/1.27 % --res_time_limit 1000.
% 0.97/1.27 % --res_out_proof true
% 0.97/1.27 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_c5af18.s
% 0.97/1.27 % --modulo true
% 0.97/1.27
% 0.97/1.27 % ------ Combination Options
% 0.97/1.27
% 0.97/1.27 % --comb_res_mult 1000
% 0.97/1.27 % --comb_inst_mult 300
% 0.97/1.27 % ------
% 0.97/1.27
% 0.97/1.27 % ------ Parsing...%
% 0.97/1.27
% 0.97/1.27
% 0.97/1.27 % ------ Statistics
% 0.97/1.27
% 0.97/1.27 % ------ General
% 0.97/1.27
% 0.97/1.27 % num_of_input_clauses: 1028
% 0.97/1.27 % num_of_input_neg_conjectures: 0
% 0.97/1.27 % num_of_splits: 0
% 0.97/1.27 % num_of_split_atoms: 0
% 0.97/1.27 % num_of_sem_filtered_clauses: 0
% 0.97/1.27 % num_of_subtypes: 0
% 0.97/1.27 % monotx_restored_types: 0
% 0.97/1.27 % sat_num_of_epr_types: 0
% 0.97/1.27 % sat_num_of_non_cyclic_types: 0
% 0.97/1.27 % sat_guarded_non_collapsed_types: 0
% 0.97/1.27 % is_epr: 0
% 0.97/1.27 % is_horn: 0
% 0.97/1.27 % has_eq: 0
% 0.97/1.27 % num_pure_diseq_elim: 0
% 0.97/1.27 % simp_replaced_by: 0
% 0.97/1.27 % res_preprocessed: 0
% 0.97/1.27 % prep_upred: 0
% 0.97/1.27 % prep_unflattend: 0
% 0.97/1.27 % pred_elim_cands: 0
% 0.97/1.27 % pred_elim: 0
% 0.97/1.27 % pred_elim_cl: 0
% 0.97/1.27 % pred_elim_cycles: 0
% 0.97/1.27 % forced_gc_time: 0
% 0.97/1.27 % gc_basic_clause_elim: 0
% 0.97/1.27 % parsing_time: 0.
% 0.97/1.27 % sem_filter_time: 0.
% 0.97/1.27 % pred_elim_time: 0.
% 0.97/1.27 % out_proof_time: 0.
% 0.97/1.27 % monotx_time: 0.
% 0.97/1.27 % subtype_inf_time: 0.
% 0.97/1.27 % unif_index_cands_time: 0.
% 0.97/1.27 %Fatal error: exception Failure("Parse error in: /export/starexec/sandbox2/tmp/iprover_modulo_52e4f7.p line: 1031 near token: '!='")
% 0.97/1.27 unif_index_add_time: 0.
% 0.97/1.27 % total_time: 0.163
% 0.97/1.27 % num_of_symbols: 208
% 0.97/1.27 % num_of_terms: 3056
% 0.97/1.27
% 0.97/1.27 % ------ Propositional Solver
% 0.97/1.27
% 0.97/1.27 % prop_solver_calls: 0
% 0.97/1.27 % prop_fast_solver_calls: 0
% 0.97/1.27 % prop_num_of_clauses: 0
% 0.97/1.27 % prop_preprocess_simplified: 0
% 0.97/1.27 % prop_fo_subsumed: 0
% 0.97/1.27 % prop_solver_time: 0.
% 0.97/1.27 % prop_fast_solver_time: 0.
% 0.97/1.27 % prop_unsat_core_time: 0.
% 0.97/1.27
% 0.97/1.27 % ------ QBF
% 0.97/1.27
% 0.97/1.27 % qbf_q_res: 0
% 0.97/1.27 % qbf_num_tautologies: 0
% 0.97/1.27 % qbf_prep_cycles: 0
% 0.97/1.27
% 0.97/1.27 % ------ BMC1
% 0.97/1.27
% 0.97/1.27 % bmc1_current_bound: -1
% 0.97/1.27 % bmc1_last_solved_bound: -1
% 0.97/1.27 % bmc1_unsat_core_size: -1
% 0.97/1.27 % bmc1_unsat_core_parents_size: -1
% 0.97/1.27 % bmc1_merge_next_fun: 0
% 0.97/1.27 % bmc1_unsat_core_clauses_time: 0.
% 0.97/1.27
% 0.97/1.27 % ------ Instantiation
% 0.97/1.27
% 0.97/1.27 % inst_num_of_clauses: undef
% 0.97/1.27 % inst_num_in_passive: undef
% 0.97/1.27 % inst_num_in_active: 0
% 0.97/1.27 % inst_num_in_unprocessed: 0
% 0.97/1.27 % inst_num_of_loops: 0
% 0.97/1.27 % inst_num_of_learning_restarts: 0
% 0.97/1.27 % inst_num_moves_active_passive: 0
% 0.97/1.27 % inst_lit_activity: 0
% 0.97/1.27 % inst_lit_activity_moves: 0
% 0.97/1.27 % inst_num_tautologies: 0
% 0.97/1.27 % inst_num_prop_implied: 0
% 0.97/1.27 % inst_num_existing_simplified: 0
% 0.97/1.27 % inst_num_eq_res_simplified: 0
% 0.97/1.27 % inst_num_child_elim: 0
% 0.97/1.27 % inst_num_of_dismatching_blockings: 0
% 0.97/1.27 % inst_num_of_non_proper_insts: 0
% 0.97/1.27 % inst_num_of_duplicates: 0
% 0.97/1.27 % inst_inst_num_from_inst_to_res: 0
% 0.97/1.27 % inst_dismatching_checking_time: 0.
% 0.97/1.27
% 0.97/1.27 % ------ Resolution
% 0.97/1.27
% 0.97/1.27 % res_num_of_clauses: undef
% 0.97/1.27 % res_num_in_passive: undef
% 0.97/1.27 % res_num_in_active: 0
% 0.97/1.27 % res_num_of_loops: 0
% 0.97/1.27 % res_forward_subset_subsumed: 0
% 0.97/1.27 % res_backward_subset_subsumed: 0
% 0.97/1.27 % res_forward_subsumed: 0
% 0.97/1.27 % res_backward_subsumed: 0
% 0.97/1.27 % res_forward_subsumption_resolution: 0
% 0.97/1.27 % res_backward_subsumption_resolution: 0
% 0.97/1.27 % res_clause_to_clause_subsumption: 0
% 0.97/1.27 % res_orphan_elimination: 0
% 0.97/1.27 % res_tautology_del: 0
% 0.97/1.27 % res_num_eq_res_simplified: 0
% 0.97/1.27 % res_num_sel_changes: 0
% 0.97/1.27 % res_moves_from_active_to_pass: 0
% 0.97/1.27
% 0.97/1.27 % Status Unknown
% 1.81/1.90 % Orienting using strategy ClausalAll
% 1.81/1.90 % FOF problem with conjecture
% 1.81/1.90 % 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/sandbox2/tmp/iprover_proof_c5af18.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_52e4f7.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_f2a59c | grep -v "SZS"
% 1.81/1.92
% 1.81/1.92 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 1.81/1.92
% 1.81/1.92 %
% 1.81/1.92 % ------ iProver source info
% 1.81/1.92
% 1.81/1.92 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 1.81/1.92 % git: non_committed_changes: true
% 1.81/1.92 % git: last_make_outside_of_git: true
% 1.81/1.92
% 1.81/1.92 %
% 1.81/1.92 % ------ Input Options
% 1.81/1.92
% 1.81/1.92 % --out_options all
% 1.81/1.92 % --tptp_safe_out true
% 1.81/1.92 % --problem_path ""
% 1.81/1.92 % --include_path ""
% 1.81/1.92 % --clausifier .//eprover
% 1.81/1.92 % --clausifier_options --tstp-format
% 1.81/1.92 % --stdin false
% 1.81/1.92 % --dbg_backtrace false
% 1.81/1.92 % --dbg_dump_prop_clauses false
% 1.81/1.92 % --dbg_dump_prop_clauses_file -
% 1.81/1.92 % --dbg_out_stat false
% 1.81/1.92
% 1.81/1.92 % ------ General Options
% 1.81/1.92
% 1.81/1.92 % --fof false
% 1.81/1.92 % --time_out_real 150.
% 1.81/1.92 % --time_out_prep_mult 0.2
% 1.81/1.92 % --time_out_virtual -1.
% 1.81/1.92 % --schedule none
% 1.81/1.92 % --ground_splitting input
% 1.81/1.92 % --splitting_nvd 16
% 1.81/1.92 % --non_eq_to_eq false
% 1.81/1.92 % --prep_gs_sim true
% 1.81/1.92 % --prep_unflatten false
% 1.81/1.92 % --prep_res_sim true
% 1.81/1.92 % --prep_upred true
% 1.81/1.92 % --res_sim_input true
% 1.81/1.92 % --clause_weak_htbl true
% 1.81/1.92 % --gc_record_bc_elim false
% 1.81/1.92 % --symbol_type_check false
% 1.81/1.92 % --clausify_out false
% 1.81/1.92 % --large_theory_mode false
% 1.81/1.92 % --prep_sem_filter none
% 1.81/1.92 % --prep_sem_filter_out false
% 1.81/1.92 % --preprocessed_out false
% 1.81/1.92 % --sub_typing false
% 1.81/1.92 % --brand_transform false
% 1.81/1.92 % --pure_diseq_elim true
% 1.81/1.92 % --min_unsat_core false
% 1.81/1.92 % --pred_elim true
% 1.81/1.92 % --add_important_lit false
% 1.81/1.92 % --soft_assumptions false
% 1.81/1.92 % --reset_solvers false
% 1.81/1.92 % --bc_imp_inh []
% 1.81/1.92 % --conj_cone_tolerance 1.5
% 1.81/1.92 % --prolific_symb_bound 500
% 1.81/1.92 % --lt_threshold 2000
% 1.81/1.92
% 1.81/1.92 % ------ SAT Options
% 1.81/1.92
% 1.81/1.92 % --sat_mode false
% 1.81/1.92 % --sat_fm_restart_options ""
% 1.81/1.92 % --sat_gr_def false
% 1.81/1.92 % --sat_epr_types true
% 1.81/1.92 % --sat_non_cyclic_types false
% 1.81/1.92 % --sat_finite_models false
% 1.81/1.92 % --sat_fm_lemmas false
% 1.81/1.92 % --sat_fm_prep false
% 1.81/1.92 % --sat_fm_uc_incr true
% 1.81/1.92 % --sat_out_model small
% 1.81/1.92 % --sat_out_clauses false
% 1.81/1.92
% 1.81/1.92 % ------ QBF Options
% 1.81/1.92
% 1.81/1.92 % --qbf_mode false
% 1.81/1.92 % --qbf_elim_univ true
% 1.81/1.92 % --qbf_sk_in true
% 1.81/1.92 % --qbf_pred_elim true
% 1.81/1.92 % --qbf_split 32
% 1.81/1.92
% 1.81/1.92 % ------ BMC1 Options
% 1.81/1.92
% 1.81/1.92 % --bmc1_incremental false
% 1.81/1.92 % --bmc1_axioms reachable_all
% 1.81/1.92 % --bmc1_min_bound 0
% 1.81/1.92 % --bmc1_max_bound -1
% 1.81/1.92 % --bmc1_max_bound_default -1
% 1.81/1.92 % --bmc1_symbol_reachability true
% 1.81/1.92 % --bmc1_property_lemmas false
% 1.81/1.92 % --bmc1_k_induction false
% 1.81/1.92 % --bmc1_non_equiv_states false
% 1.81/1.92 % --bmc1_deadlock false
% 1.81/1.92 % --bmc1_ucm false
% 1.81/1.92 % --bmc1_add_unsat_core none
% 1.81/1.92 % --bmc1_unsat_core_children false
% 1.81/1.92 % --bmc1_unsat_core_extrapolate_axioms false
% 1.81/1.92 % --bmc1_out_stat full
% 1.81/1.92 % --bmc1_ground_init false
% 1.81/1.92 % --bmc1_pre_inst_next_state false
% 1.81/1.92 % --bmc1_pre_inst_state false
% 1.81/1.92 % --bmc1_pre_inst_reach_state false
% 1.81/1.92 % --bmc1_out_unsat_core false
% 1.81/1.92 % --bmc1_aig_witness_out false
% 1.81/1.92 % --bmc1_verbose false
% 1.81/1.92 % --bmc1_dump_clauses_tptp false
% 2.51/2.61 % --bmc1_dump_unsat_core_tptp false
% 2.51/2.61 % --bmc1_dump_file -
% 2.51/2.61 % --bmc1_ucm_expand_uc_limit 128
% 2.51/2.61 % --bmc1_ucm_n_expand_iterations 6
% 2.51/2.61 % --bmc1_ucm_extend_mode 1
% 2.51/2.61 % --bmc1_ucm_init_mode 2
% 2.51/2.61 % --bmc1_ucm_cone_mode none
% 2.51/2.61 % --bmc1_ucm_reduced_relation_type 0
% 2.51/2.61 % --bmc1_ucm_relax_model 4
% 2.51/2.61 % --bmc1_ucm_full_tr_after_sat true
% 2.51/2.61 % --bmc1_ucm_expand_neg_assumptions false
% 2.51/2.61 % --bmc1_ucm_layered_model none
% 2.51/2.61 % --bmc1_ucm_max_lemma_size 10
% 2.51/2.61
% 2.51/2.61 % ------ AIG Options
% 2.51/2.61
% 2.51/2.61 % --aig_mode false
% 2.51/2.61
% 2.51/2.61 % ------ Instantiation Options
% 2.51/2.61
% 2.51/2.61 % --instantiation_flag true
% 2.51/2.61 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 2.51/2.61 % --inst_solver_per_active 750
% 2.51/2.61 % --inst_solver_calls_frac 0.5
% 2.51/2.61 % --inst_passive_queue_type priority_queues
% 2.51/2.61 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.51/2.61 % --inst_passive_queues_freq [25;2]
% 2.51/2.61 % --inst_dismatching true
% 2.51/2.61 % --inst_eager_unprocessed_to_passive true
% 2.51/2.61 % --inst_prop_sim_given true
% 2.51/2.61 % --inst_prop_sim_new false
% 2.51/2.61 % --inst_orphan_elimination true
% 2.51/2.61 % --inst_learning_loop_flag true
% 2.51/2.61 % --inst_learning_start 3000
% 2.51/2.61 % --inst_learning_factor 2
% 2.51/2.61 % --inst_start_prop_sim_after_learn 3
% 2.51/2.61 % --inst_sel_renew solver
% 2.51/2.61 % --inst_lit_activity_flag true
% 2.51/2.61 % --inst_out_proof true
% 2.51/2.61
% 2.51/2.61 % ------ Resolution Options
% 2.51/2.61
% 2.51/2.61 % --resolution_flag true
% 2.51/2.61 % --res_lit_sel kbo_max
% 2.51/2.61 % --res_to_prop_solver none
% 2.51/2.61 % --res_prop_simpl_new false
% 2.51/2.61 % --res_prop_simpl_given false
% 2.51/2.61 % --res_passive_queue_type priority_queues
% 2.51/2.61 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.51/2.61 % --res_passive_queues_freq [15;5]
% 2.51/2.61 % --res_forward_subs full
% 2.51/2.61 % --res_backward_subs full
% 2.51/2.61 % --res_forward_subs_resolution true
% 2.51/2.61 % --res_backward_subs_resolution true
% 2.51/2.61 % --res_orphan_elimination false
% 2.51/2.61 % --res_time_limit 1000.
% 2.51/2.61 % --res_out_proof true
% 2.51/2.61 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_c5af18.s
% 2.51/2.61 % --modulo true
% 2.51/2.61
% 2.51/2.61 % ------ Combination Options
% 2.51/2.61
% 2.51/2.61 % --comb_res_mult 1000
% 2.51/2.61 % --comb_inst_mult 300
% 2.51/2.61 % ------
% 2.51/2.61
% 2.51/2.61 % ------ Parsing...% successful
% 2.51/2.61
% 2.51/2.61 %
% 2.51/2.61
% 2.51/2.61
% 2.51/2.61 % ------ Statistics
% 2.51/2.61
% 2.51/2.61 % ------ General
% 2.51/2.61
% 2.51/2.61 % num_of_input_clauses: 5014
% 2.51/2.61 % num_of_input_neg_conjectures: 1
% 2.51/2.61 % num_of_splits: 0
% 2.51/2.61 % num_of_split_atoms: 0
% 2.51/2.61 % num_of_sem_filtered_clauses: 0
% 2.51/2.61 % num_of_subtypes: 0
% 2.51/2.61 % monotx_restored_types: 0
% 2.51/2.61 % sat_num_of_epr_types: 0
% 2.51/2.61 % sat_num_of_non_cyclic_types: 0
% 2.51/2.61 % sat_guarded_non_collapsed_types: 0
% 2.51/2.61 % is_epr: 0
% 2.51/2.61 % is_horn: 0
% 2.51/2.61 % has_eq: 0
% 2.51/2.61 % num_pure_diseq_elim: 0
% 2.51/2.61 % simp_replaced_by: 0
% 2.51/2.61 % res_preprocessed: 0
% 2.51/2.61 % prep_upred: 0
% 2.51/2.61 % prep_unflattend: 0
% 2.51/2.61 % pred_elim_cands: 0
% 2.51/2.61 % pred_elim: 0
% 2.51/2.61 % pred_elim_cl: 0
% 2.51/2.61 % pred_elim_cycles: 0
% 2.51/2.61 % forced_gc_time: 0
% 2.51/2.61 % gc_basic_clause_elim: 0
% 2.51/2.61 % parsing_time: 0.566
% 2.51/2.61 % sem_filter_time: 0.
% 2.51/2.61 % pred_elim_time: 0.
% 2.51/2.61 % out_proof_time: 0.003
% 2.51/2.61 % monotx_time: 0.
% 2.51/2.61 % subtype_inf_time: 0.
% 2.51/2.61 % unif_index_cands_time: 0.
% 2.51/2.61 % unif_index_add_time: 0.
% 2.51/2.61 % total_time: 0.706
% 2.51/2.61 % num_of_symbols: 349
% 2.51/2.61 % num_of_terms: 14031
% 2.51/2.61
% 2.51/2.61 % ------ Propositional Solver
% 2.51/2.61
% 2.51/2.61 % prop_solver_calls: 0
% 2.51/2.61 % prop_fast_solver_calls: 0
% 2.51/2.61 % prop_num_of_clauses: 3012
% 2.51/2.61 % prop_preprocess_simplified: 6452
% 2.51/2.61 % prop_fo_subsumed: 0
% 2.51/2.61 % prop_solver_time: 0.
% 2.51/2.61 % prop_fast_solver_time: 0.
% 2.51/2.61 % prop_unsat_core_time: 0.
% 2.51/2.61
% 2.51/2.61 % ------ QBF
% 2.51/2.61
% 2.51/2.61 % qbf_q_res: 0
% 2.51/2.61 % qbf_num_tautologies: 0
% 2.51/2.61 % qbf_prep_cycles: 0
% 2.51/2.61
% 2.51/2.61 % ------ BMC1
% 2.51/2.61
% 2.51/2.61 % bmc1_current_bound: -1
% 2.51/2.61 % bmc1_last_solved_bound: -1
% 2.51/2.61 % bmc1_unsat_core_size: -1
% 2.51/2.61 % bmc1_unsat_core_parents_size: -1
% 2.51/2.61 % bmc1_merge_next_fun: 0
% 2.51/2.61 % bmc1_unsat_core_clauses_time: 0.
% 2.51/2.61
% 2.51/2.61 % ------ Instantiation
% 2.51/2.61
% 2.51/2.61 % inst_num_of_clauses: undef
% 2.51/2.61 % inst_num_in_passive: undef
% 2.51/2.61 % inst_num_in_active: 0
% 2.51/2.61 % inst_num_in_unprocessed: 0
% 2.51/2.61 % inst_num_of_loops: 0
% 2.51/2.61 % inst_num_of_learning_restarts: 0
% 2.51/2.61 % inst_num_moves_active_passive: 0
% 2.51/2.61 % inst_lit_activity: 0
% 2.51/2.61 % inst_lit_activity_moves: 0
% 2.51/2.61 % inst_num_tautologies: 0
% 2.51/2.61 % inst_num_prop_implied: 0
% 2.51/2.61 % inst_num_existing_simplified: 0
% 2.51/2.61 % inst_num_eq_res_simplified: 0
% 2.51/2.61 % inst_num_child_elim: 0
% 2.51/2.61 % inst_num_of_dismatching_blockings: 0
% 2.51/2.61 % inst_num_of_non_proper_insts: 0
% 2.51/2.61 % inst_num_of_duplicates: 0
% 2.51/2.61 % inst_inst_num_from_inst_to_res: 0
% 2.51/2.61 % inst_dismatching_checking_time: 0.
% 2.51/2.61
% 2.51/2.61 % ------ Resolution
% 2.51/2.61
% 2.51/2.61 % res_num_of_clauses: undef
% 2.51/2.61 % res_num_in_passive: undef
% 2.51/2.61 % res_num_in_active: 0
% 2.51/2.61 % res_num_of_loops: 0
% 2.51/2.61 % res_forward_subset_subsumed: 0
% 2.51/2.61 % res_backward_subset_subsumed: 0
% 2.51/2.61 % res_forward_subsumed: 0
% 2.51/2.61 % res_backward_subsumed: 0
% 2.51/2.61 % res_forward_subsumption_resolution: 0
% 2.51/2.61 % res_backward_subsumption_resolution: 0
% 2.51/2.61 % res_clause_to_clause_subsumption: 0
% 2.51/2.61 % res_orphan_elimination: 0
% 2.51/2.61 % res_tautology_del: 0
% 2.51/2.61 % res_num_eq_res_simplified: 0
% 2.51/2.61 % res_num_sel_changes: 0
% 2.51/2.61 % res_moves_from_active_to_pass: 0
% 2.51/2.61
% 2.51/2.61 % Status Unsatisfiable
% 2.51/2.61 % SZS status Theorem
% 2.51/2.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------