TPTP Problem File: SCT171+6.p
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%------------------------------------------------------------------------------
% File : SCT171+6 : TPTP v9.0.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_500_fofpt_l309 [Bla11]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.11 v8.2.0, 0.14 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0
% Syntax : Number of formulae : 614 ( 174 unt; 0 def)
% Number of atoms : 1581 ( 384 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1140 ( 173 ~; 37 |; 63 &)
% ( 120 <=>; 747 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of predicates : 29 ( 28 usr; 0 prp; 1-2 aty)
% Number of functors : 67 ( 67 usr; 31 con; 0-4 aty)
% Number of variables : 1639 (1619 !; 20 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:21:08
% : Encoded with polymorphic tags.
%------------------------------------------------------------------------------
%----Explicit typings (62)
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res,axiom,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res,axiom,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res,axiom,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res,axiom,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity ).
fof(tsy_c_COMBB_res,axiom,
! [X_b,X_c,X_a] : ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a) ).
fof(tsy_c_COMBC_res,axiom,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c) ).
fof(tsy_c_COMBI_res,axiom,
! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a) ).
fof(tsy_c_COMBK_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b) ).
fof(tsy_c_COMBS_res,axiom,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c) ).
fof(tsy_c_Finite__Set_Ocard_res,axiom,
! [X_a] : ti(fun(fun(X_a,bool),nat),finite_card(X_a)) = finite_card(X_a) ).
fof(tsy_c_Finite__Set_Ofinite_res,axiom,
! [X_b] : ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b)) = finite_finite_1(X_b) ).
fof(tsy_c_Finite__Set_Ofold__image_res,axiom,
! [X_a] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)))),finite_fold_image(nat,X_a)) = finite_fold_image(nat,X_a) ).
fof(tsy_c_Finite__Set_Ofolding__image__simple__idem_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b) ).
fof(tsy_c_FunDef_Oin__rel_res,axiom,
! [X_a,X_b] : ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b) ).
fof(tsy_c_Fun_Oinj__on_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),inj_on(X_a,X_b)) = inj_on(X_a,X_b) ).
fof(tsy_c_FuncSet_OPi_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b) ).
fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
! [X_a] :
( one(X_a)
=> ti(X_a,one_one(X_a)) = one_one(X_a) ) ).
fof(tsy_c_Groups_Oplus__class_Oplus_0_res,axiom,
! [X_a] :
( monoid_add(X_a)
=> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ) ).
fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
! [X_a] :
( ab_semigroup_add(X_a)
=> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ) ).
fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ) ).
fof(tsy_c_Groups_Ozero__class_Ozero_res,axiom,
! [X_a] :
( zero(X_a)
=> ti(X_a,zero_zero(X_a)) = zero_zero(X_a) ) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a) ).
fof(tsy_c_Hilbert__Choice_Oinv__into_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),hilbert_inv_into(X_a,X_b)) = hilbert_inv_into(X_a,X_b) ).
fof(tsy_c_If_res,axiom,
! [X_a] : ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a) ).
fof(tsy_c_Int_Oring__1__class_OInts_res,axiom,
! [X_a] :
( ring_1(X_a)
=> ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a) ) ).
fof(tsy_c_Nat_OSuc_res,axiom,
ti(fun(nat,nat),suc) = suc ).
fof(tsy_c_Orderings_Oord__class_Oless_res,axiom,
! [X_a] :
( ord(X_a)
=> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a) ) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
! [X_b] :
( ord(X_b)
=> ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b) ) ).
fof(tsy_c_Orderings_Otop__class_Otop_res,axiom,
! [X_a] :
( top(X_a)
=> ti(X_a,top_top(X_a)) = top_top(X_a) ) ).
fof(tsy_c_Product__Type_OPair_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b) ).
fof(tsy_c_Product__Type_Oprod_Oprod__rec_res,axiom,
! [X_b,X_c,X_a] : ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a) ).
fof(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res,axiom,
! [X_a] :
( linorder(X_a)
=> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)) = ord_atLeastLessThan(X_a) ) ).
fof(tsy_c_Set_OCollect_res,axiom,
! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a) ).
fof(tsy_c_Set_Oimage_res,axiom,
! [X_b,X_a] : ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a)) = image(X_b,X_a) ).
fof(tsy_c_Sum__Type_OPlus_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool))),sum_Plus(X_a,X_b)) = sum_Plus(X_a,X_b) ).
fof(tsy_c_fFalse_res,axiom,
ti(bool,fFalse) = fFalse ).
fof(tsy_c_fNot_res,axiom,
ti(fun(bool,bool),fNot) = fNot ).
fof(tsy_c_fTrue_res,axiom,
ti(bool,fTrue) = fTrue ).
fof(tsy_c_fconj_res,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj ).
fof(tsy_c_fdisj_res,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj ).
fof(tsy_c_fequal_res,axiom,
! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a) ).
fof(tsy_c_hAPP_arg1,axiom,
! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hAPP_res,axiom,
! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [B_1_1] :
( hBOOL(ti(bool,B_1_1))
<=> hBOOL(B_1_1) ) ).
fof(tsy_c_member_res,axiom,
! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a) ).
fof(tsy_v_F_res,hypothesis,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f ).
fof(tsy_v_Lab_____res,axiom,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab ).
fof(tsy_v_Lba_____res,axiom,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba ).
fof(tsy_v_P_____res,hypothesis,
ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p ).
fof(tsy_v_a_____res,axiom,
ti(arrow_490897120le_alt,a) = a ).
fof(tsy_v_b_____res,axiom,
ti(arrow_490897120le_alt,b) = b ).
fof(tsy_v_c_____res,hypothesis,
ti(arrow_490897120le_alt,c) = c ).
fof(tsy_v_d_____res,hypothesis,
ti(arrow_490897120le_alt,d) = d ).
fof(tsy_v_e_____res,axiom,
ti(arrow_490897120le_alt,e) = e ).
fof(tsy_v_h_____res,axiom,
ti(fun(arrow_660593299e_indi,nat),h) = h ).
fof(tsy_v_n_____res,axiom,
ti(nat,n) = n ).
%----Relevant facts (497)
fof(fact_0_assms_I3_J,axiom,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)) ).
fof(fact_1_u,axiom,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)) ).
fof(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
fof(fact_3__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)) ).
fof(fact_4_in__mkbot,axiom,
! [X_1,Y_2,L_3,Z] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),Z)))
<=> ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z)
& ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z)
=> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) )
& ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) ) ) ) ).
fof(fact_5_in__mktop,axiom,
! [X_1,Y_2,L_3,Z] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),Z)))
<=> ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z)
& ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Z)
=> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) )
& ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) ) ) ) ).
fof(fact_6__C2_C,axiom,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ) ) ).
fof(fact_7__C1_C,axiom,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ) ) ).
fof(fact_8__C4_C,axiom,
! [P_1,Pa,Ca,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,Ca)
=> ( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ca)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ) ).
fof(fact_9_pairwise__neutrality,axiom,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ).
fof(fact_10__C3_C,axiom,
! [P_1,Pa,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ).
fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> ( ( hAPP(arrow_660593299e_indi,nat,h,I_2) = n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e))) )
& ( hAPP(arrow_660593299e_indi,nat,h,I_2) != n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) ) ) ) ) ) ).
fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))) ).
fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ).
fof(fact_14_PW,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ) ).
fof(fact_15_split__paired__All,axiom,
! [X_a,X_b,Pa] :
( ! [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
<=> ! [A_3,B_2] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_2))) ) ).
fof(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)) ).
fof(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ).
fof(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ).
fof(fact_19_n_I1_J,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ).
fof(fact_20_injh,axiom,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))) ).
fof(fact_21_Pair__inject,axiom,
! [X_b,X_a,A_2,B_1,A_6,B_4] :
( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_4)
=> ~ ( ti(X_a,A_2) = ti(X_a,A_6)
=> ti(X_b,B_1) != ti(X_b,B_4) ) ) ).
fof(fact_22_Pair__eq,axiom,
! [X_b,X_a,Aa,Ba,A_5,B_3] :
( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_3)
<=> ( ti(X_a,Aa) = ti(X_a,A_5)
& ti(X_b,Ba) = ti(X_b,B_3) ) ) ).
fof(fact_23_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,Fa))
<=> ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> ! [Xa] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Xa),arrow_1111136790e_Prof))
=> ! [A_3,B_2] :
( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa))) ) ) ) ) ) ).
fof(fact_24_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,Fa))
<=> ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> ! [A_3,B_2] :
( ! [I_2] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2)))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) ) ) ) ).
fof(fact_25_top1I,axiom,
! [X_a,X_1] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1)) ).
fof(fact_26_UNIV__I,axiom,
! [X_a,X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool)))) ).
fof(fact_27_iso__tuple__UNIV__I,axiom,
! [X_a,X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool)))) ).
fof(fact_28_prod_Orecs,axiom,
! [X_b,X_c,X_a,F1,Aa,Ba] : hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba) ).
fof(fact_29_top__apply,axiom,
! [X_b,X_a] :
( top(X_a)
=> ! [X_1] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1) = top_top(X_a) ) ).
fof(fact_30_not__top__less,axiom,
! [X_a] :
( top(X_a)
=> ! [A_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_2)) ) ).
fof(fact_31_less__top,axiom,
! [X_a] :
( top(X_a)
=> ! [Aa] :
( ti(X_a,Aa) != top_top(X_a)
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a))) ) ) ).
fof(fact_32_assms_I1_J,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ).
fof(fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ) ).
fof(fact_34__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)) ).
fof(fact_35__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)) ).
fof(fact_36__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ).
fof(fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ).
fof(fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ).
fof(fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ).
fof(fact_41_PiProf,axiom,
! [Na] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_1111136790e_Prof)) ).
fof(fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
~ ! [Lab] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),Lab))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),Lab),arrow_2064824852le_Lin)) ) ).
fof(fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
~ ! [Lba] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),Lba))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),Lba),arrow_2064824852le_Lin)) ) ).
fof(fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_2] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> ( ( hAPP(arrow_660593299e_indi,nat,h,I_2) = n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e))) )
& ( hAPP(arrow_660593299e_indi,nat,h,I_2) != n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ) ) ) ).
fof(fact_45_n_I2_J,axiom,
! [M] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba)))) ) ).
fof(fact_46_notin__Lin__iff,axiom,
! [X_1,Y_2,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
=> ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Y_2),X_1)),L_3)) ) ) ) ).
fof(fact_47_Lin__irrefl,axiom,
! [Aa,Ba,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),L_3))
=> ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),L_3)) ) ) ).
fof(fact_48_mktop__Lin,axiom,
! [X_1,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),X_1)),arrow_2064824852le_Lin)) ) ).
fof(fact_49_mkbot__Lin,axiom,
! [X_1,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),X_1)),arrow_2064824852le_Lin)) ) ).
fof(fact_50_above__Lin,axiom,
! [L_3,X_1,Y_2] :
( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),X_1),Y_2)),arrow_2064824852le_Lin)) ) ) ).
fof(fact_51_const__Lin__Prof,axiom,
! [L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),L_3)),arrow_1111136790e_Prof)) ) ).
fof(fact_52_linorder__cases,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ( ti(X_a,X) != ti(X_a,Y)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ) ).
fof(fact_53_order__less__asym,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ).
fof(fact_54_xt1_I10_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)) ) ) ) ).
fof(fact_55_order__less__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)) ) ) ) ).
fof(fact_56_xt1_I2_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
=> ( ti(X_a,B_1) = ti(X_a,C)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_2)) ) ) ) ).
fof(fact_57_ord__less__eq__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
=> ( B_1 = C
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C)) ) ) ) ).
fof(fact_58_xt1_I1_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,A_2,B_1] :
( ti(X_a,A_2) = ti(X_a,B_1)
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_2)) ) ) ) ).
fof(fact_59_ord__eq__less__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,A_2,B_1] :
( A_2 = B_1
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C)) ) ) ) ).
fof(fact_60_xt1_I9_J,axiom,
! [X_a] :
( order(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ).
fof(fact_61_order__less__asym_H,axiom,
! [X_a] :
( preorder(X_a)
=> ! [A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) ) ) ).
fof(fact_62_order__less__imp__triv,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Pa,X_1,Y_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))
=> hBOOL(Pa) ) ) ) ).
fof(fact_63_order__less__imp__not__eq2,axiom,
! [X_a] :
( order(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ti(X_a,Y) != ti(X_a,X) ) ) ).
fof(fact_64_order__less__imp__not__eq,axiom,
! [X_a] :
( order(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ti(X_a,X) != ti(X_a,Y) ) ) ).
fof(fact_65_order__less__imp__not__less,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ).
fof(fact_66_order__less__not__sym,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ).
fof(fact_67_less__imp__neq,axiom,
! [X_a] :
( order(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ti(X_a,X) != ti(X_a,Y) ) ) ).
fof(fact_68_linorder__neqE,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( ti(X_a,X) != ti(X_a,Y)
=> ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ) ).
fof(fact_69_linorder__antisym__conv3,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Y_2,X_1] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))
=> ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ).
fof(fact_70_linorder__less__linear,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
| ti(X_a,X) = ti(X_a,Y)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ).
fof(fact_71_not__less__iff__gr__or__eq,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))
| ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ).
fof(fact_72_linorder__neq__iff,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ti(X_a,X_1) != ti(X_a,Y_2)
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) ) ) ) ).
fof(fact_73_order__less__irrefl,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)) ) ).
fof(fact_74_UNIV__def,axiom,
! [X_a] : top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue)) ).
fof(fact_75_ext,axiom,
! [X_a,X_b,F,G] :
( ! [X_2] : hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)
=> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G) ) ).
fof(fact_76_mem__def,axiom,
! [X_a,X_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
<=> hBOOL(hAPP(X_a,bool,A_1,X_1)) ) ).
fof(fact_77_Collect__def,axiom,
! [X_a,Pa] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa) ).
fof(fact_78_in__above,axiom,
! [X_1,Y_2,L_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),Aa),Ba)))
<=> ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
& ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Y_2)),L_3)) )
& ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Ba)
=> ( ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Aa)),L_3)) ) )
& ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) ) ) ) ) ) ) ) ).
fof(fact_79_pred__equals__eq2,axiom,
! [X_a,X_b,S_1,R_1] :
( ! [X_2,Xa] :
( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_1))
<=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S_1)) )
<=> ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S_1) ) ).
fof(fact_80_n_I3_J,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ).
fof(fact_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ) ).
fof(fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_2] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> ( ( hAPP(arrow_660593299e_indi,nat,h,I_2) = n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e))) )
& ( hAPP(arrow_660593299e_indi,nat,h,I_2) != n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ) ) ) ).
fof(fact_83_inv__f__eq,axiom,
! [X_a,X_b,X_1,Y_2,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hAPP(X_a,X_b,F,X_1) = ti(X_b,Y_2)
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_2) = ti(X_a,X_1) ) ) ).
fof(fact_84_inv__f__f,axiom,
! [X_a,X_b,X_1,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_1)) = ti(X_a,X_1) ) ).
fof(fact_85_dictatorI,axiom,
! [I_1,Fa] :
( hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Fa),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
=> ( ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> ! [A_3,B_2] :
( ti(arrow_490897120le_alt,A_3) != ti(arrow_490897120le_alt,B_2)
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1)))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) ) ) )
=> hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1)) ) ) ).
fof(fact_86_PiE,axiom,
! [X_a,X_b,X_1,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
=> ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1)))
=> ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) ).
fof(fact_87_complete__Lin,axiom,
! [Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ? [X_2] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X_2),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),X_2)) ) ) ).
fof(fact_88_Pi__UNIV,axiom,
! [X_a,X_b,A_1] : hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool)) ).
fof(fact_89_inj__fun,axiom,
! [X_c,X_a,X_b,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,fun(X_c,X_b)),fun(fun(X_a,bool),bool),inj_on(X_a,fun(X_c,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_c,X_b)),hAPP(fun(X_b,fun(X_c,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_c,X_b))),combb(X_b,fun(X_c,X_b),X_a),combk(X_b,X_c)),F)),top_top(fun(X_a,bool)))) ) ).
fof(fact_90_order__refl,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X)) ) ).
fof(fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_,axiom,
? [N] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
& ! [M] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba)))) )
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))),lab)),lba)))) ) ).
fof(fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O,axiom,
~ ! [N] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
=> ( ! [M] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba)))) )
=> ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))),lab)),lba)))) ) ) ).
fof(fact_93_linorder__le__cases,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ) ).
fof(fact_94_le__funE,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [X_1,F,G] :
( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))) ) ) ).
fof(fact_95_xt1_I6_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X)) ) ) ) ).
fof(fact_96_xt1_I5_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
=> ti(X_a,X) = ti(X_a,Y) ) ) ) ).
fof(fact_97_order__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) ) ) ) ).
fof(fact_98_order__antisym,axiom,
! [X_a] :
( order(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
=> ti(X_a,X) = ti(X_a,Y) ) ) ) ).
fof(fact_99_xt1_I4_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
=> ( ti(X_a,B_1) = ti(X_a,C)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_2)) ) ) ) ).
fof(fact_100_ord__le__eq__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> ( B_1 = C
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C)) ) ) ) ).
fof(fact_101_xt1_I3_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,A_2,B_1] :
( ti(X_a,A_2) = ti(X_a,B_1)
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_2)) ) ) ) ).
fof(fact_102_ord__eq__le__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,A_2,B_1] :
( A_2 = B_1
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C)) ) ) ) ).
fof(fact_103_order__antisym__conv,axiom,
! [X_a] :
( order(X_a)
=> ! [Y_2,X_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ).
fof(fact_104_le__funD,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [X_1,F,G] :
( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))) ) ) ).
fof(fact_105_order__eq__refl,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X,Y] :
( X = Y
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ) ).
fof(fact_106_order__eq__iff,axiom,
! [X_a] :
( order(X_a)
=> ! [X_1,Y_2] :
( ti(X_a,X_1) = ti(X_a,Y_2)
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1)) ) ) ) ).
fof(fact_107_linorder__linear,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ) ).
fof(fact_108_le__fun__def,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [F,G] :
( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
<=> ! [X_2] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))) ) ) ).
fof(fact_109_linorder__not__less,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1)) ) ) ).
fof(fact_110_linorder__not__le,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) ) ) ).
fof(fact_111_linorder__le__less__linear,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ).
fof(fact_112_order__less__le,axiom,
! [X_a] :
( order(X_a)
=> ! [X_1,Y_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
& ti(X_a,X_1) != ti(X_a,Y_2) ) ) ) ).
fof(fact_113_less__le__not__le,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X_1,Y_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
& ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1)) ) ) ) ).
fof(fact_114_order__le__less,axiom,
! [X_a] :
( order(X_a)
=> ! [X_1,Y_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ).
fof(fact_115_leI,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X,Y] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ) ).
fof(fact_116_not__leE,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Y,X] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ) ).
fof(fact_117_linorder__antisym__conv1,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ).
fof(fact_118_order__neq__le__trans,axiom,
! [X_a] :
( order(X_a)
=> ! [A_2,B_1] :
( ti(X_a,A_2) != ti(X_a,B_1)
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ) ).
fof(fact_119_xt1_I12_J,axiom,
! [X_a] :
( order(X_a)
=> ! [A_2,B_1] :
( ti(X_a,A_2) != ti(X_a,B_1)
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) ) ) ) ).
fof(fact_120_leD,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ) ).
fof(fact_121_order__less__imp__le,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ) ).
fof(fact_122_linorder__antisym__conv2,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
=> ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ).
fof(fact_123_order__le__imp__less__or__eq,axiom,
! [X_a] :
( order(X_a)
=> ! [X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
| ti(X_a,X) = ti(X_a,Y) ) ) ) ).
fof(fact_124_order__le__neq__trans,axiom,
! [X_a] :
( order(X_a)
=> ! [A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> ( ti(X_a,A_2) != ti(X_a,B_1)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ) ).
fof(fact_125_xt1_I11_J,axiom,
! [X_a] :
( order(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
=> ( ti(X_a,A_2) != ti(X_a,B_1)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) ) ) ) ).
fof(fact_126_order__less__le__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)) ) ) ) ).
fof(fact_127_xt1_I7_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)) ) ) ) ).
fof(fact_128_order__le__less__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)) ) ) ) ).
fof(fact_129_xt1_I8_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)) ) ) ) ).
fof(fact_130_top__greatest,axiom,
! [X_a] :
( top(X_a)
=> ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),top_top(X_a))) ) ).
fof(fact_131_top__unique,axiom,
! [X_a] :
( top(X_a)
=> ! [Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),Aa))
<=> ti(X_a,Aa) = top_top(X_a) ) ) ).
fof(fact_132_top__le,axiom,
! [X_a] :
( top(X_a)
=> ! [A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_2))
=> ti(X_a,A_2) = top_top(X_a) ) ) ).
fof(fact_133_inj__on__def,axiom,
! [X_a,X_b,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
<=> ! [X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ! [Xa] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Xa)
=> ti(X_a,X_2) = ti(X_a,Xa) ) ) ) ) ).
fof(fact_134_inj__on__contraD,axiom,
! [X_a,X_b,X_1,Y_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( ti(X_a,X_1) != ti(X_a,Y_2)
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1))
=> hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,F,Y_2) ) ) ) ) ).
fof(fact_135_inj__on__iff,axiom,
! [X_a,X_b,Y_2,X_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1))
=> ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ) ).
fof(fact_136_inj__onD,axiom,
! [X_a,X_b,X_1,Y_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1))
=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ) ).
fof(fact_137_Pi__mem,axiom,
! [X_a,X_b,X_1,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1))) ) ) ).
fof(fact_138_Prof__def,axiom,
arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)) ).
fof(fact_139_inj__on__id2,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),combi(X_a)),A_1)) ).
fof(fact_140_funcset__mem,axiom,
! [X_a,X_b,X_1,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B)) ) ) ).
fof(fact_141_funcset__id,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1)))) ).
fof(fact_142_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1))
<=> ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1) ) ) ).
fof(fact_143_inj__eq,axiom,
! [X_a,X_b,X_1,Y_2,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ).
fof(fact_144_injD,axiom,
! [X_a,X_b,X_1,Y_2,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ).
fof(fact_145_inv__into__f__f,axiom,
! [X_a,X_b,X_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_1)) = ti(X_a,X_1) ) ) ).
fof(fact_146_inv__into__f__eq,axiom,
! [X_a,X_b,Y_2,X_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ( hAPP(X_a,X_b,F,X_1) = ti(X_b,Y_2)
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_2) = ti(X_a,X_1) ) ) ) ).
fof(fact_147_Pi__I,axiom,
! [X_b,X_a,F,B,A_1] :
( ! [X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ) ).
fof(fact_148_inj__imp__inv__eq,axiom,
! [X_a,X_b,G,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( ! [X_2] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_2)) = ti(X_b,X_2)
=> hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F) = ti(fun(X_b,X_a),G) ) ) ).
fof(fact_149_less__add__one,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a)))) ) ).
fof(fact_150_add__less__le__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,D,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ) ).
fof(fact_151_add__le__less__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,D,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ) ).
fof(fact_152_injI,axiom,
! [X_a,X_b,F] :
( ! [X_2,Y_3] :
( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_3)
=> ti(X_a,X_2) = ti(X_a,Y_3) )
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ) ).
fof(fact_153_dense__le,axiom,
! [X_a] :
( dense_linorder(X_a)
=> ! [Z_1,Y] :
( ! [X_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) ) ) ).
fof(fact_154_dense__le__bounded,axiom,
! [X_a] :
( dense_linorder(X_a)
=> ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ( ! [W] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) ) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) ) ) ) ).
fof(fact_155_less__fun__def,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [F,G] :
( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))
<=> ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
& ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)) ) ) ) ).
fof(fact_156_Pi__anti__mono,axiom,
! [X_b,X_a,B,A_4,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_4),A_1))
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_4),B))) ) ).
fof(fact_157_pred__subset__eq2,axiom,
! [X_a,X_b,R_1,S_1] :
( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_1)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S_1)))
<=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_1),S_1)) ) ).
fof(fact_158_subset__UNIV,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),top_top(fun(X_a,bool)))) ).
fof(fact_159_subset__inj__on,axiom,
! [X_a,X_b,A_1,F,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ) ).
fof(fact_160_linorder__neqE__linordered__idom,axiom,
! [X_a] :
( linordered_idom(X_a)
=> ! [X,Y] :
( ti(X_a,X) != ti(X_a,Y)
=> ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ) ).
fof(fact_161_add__right__imp__eq,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ! [B_1,A_2,C] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2)
=> ti(X_a,B_1) = ti(X_a,C) ) ) ).
fof(fact_162_add__imp__eq,axiom,
! [X_a] :
( cancel146912293up_add(X_a)
=> ! [A_2,B_1,C] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)
=> ti(X_a,B_1) = ti(X_a,C) ) ) ).
fof(fact_163_add__left__imp__eq,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ! [A_2,B_1,C] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)
=> ti(X_a,B_1) = ti(X_a,C) ) ) ).
fof(fact_164_add__right__cancel,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ! [Ba,Aa,Ca] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)
<=> ti(X_a,Ba) = ti(X_a,Ca) ) ) ).
fof(fact_165_add__left__cancel,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ! [Aa,Ba,Ca] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)
<=> ti(X_a,Ba) = ti(X_a,Ca) ) ) ).
fof(fact_166_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X_a] :
( ab_semigroup_add(X_a)
=> ! [A_2,B_1,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)) ) ).
fof(fact_167_one__reorient,axiom,
! [X_a] :
( one(X_a)
=> ! [X_1] :
( one_one(X_a) = ti(X_a,X_1)
<=> ti(X_a,X_1) = one_one(X_a) ) ) ).
fof(fact_168_add__le__imp__le__left,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) ) ) ).
fof(fact_169_add__le__imp__le__right,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [A_2,C,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) ) ) ).
fof(fact_170_add__mono,axiom,
! [X_a] :
( ordere779506340up_add(X_a)
=> ! [C,D,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ) ).
fof(fact_171_add__left__mono,axiom,
! [X_a] :
( ordere779506340up_add(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) ) ) ).
fof(fact_172_add__right__mono,axiom,
! [X_a] :
( ordere779506340up_add(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) ) ) ).
fof(fact_173_add__le__cancel__left,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [Ca,Aa,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ) ).
fof(fact_174_add__le__cancel__right,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [Aa,Ca,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ) ).
fof(fact_175_add__less__imp__less__left,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ).
fof(fact_176_add__less__imp__less__right,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [A_2,C,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ).
fof(fact_177_add__strict__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,D,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ) ).
fof(fact_178_add__strict__left__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) ) ) ).
fof(fact_179_add__strict__right__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) ) ) ).
fof(fact_180_add__less__cancel__left,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [Ca,Aa,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) ) ).
fof(fact_181_add__less__cancel__right,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [Aa,Ca,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) ) ).
fof(fact_182_le__funI,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [F,G] :
( ! [X_2] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))
=> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) ) ) ).
fof(fact_183_xt6,axiom,
! [X_b,X_a] :
( ( order(X_a)
& ord(X_b) )
=> ! [Ca,F,Ba,Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),Ba))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_3),X_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_3)),hAPP(X_b,X_a,F,X_2))) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa)) ) ) ) ) ).
fof(fact_184_xt4,axiom,
! [X_b,X_a] :
( ( order(X_a)
& order(X_b) )
=> ! [Ca,F,Ba,Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_3),X_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_3)),hAPP(X_b,X_a,F,X_2))) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa)) ) ) ) ) ).
fof(fact_185_order__le__less__subst1,axiom,
! [X_a,X_b] :
( ( order(X_b)
& order(X_a) )
=> ! [Ca,Aa,F,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba)))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),Ca))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_3))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_3))) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca))) ) ) ) ) ).
fof(fact_186_order__less__le__subst1,axiom,
! [X_a,X_b] :
( ( order(X_b)
& order(X_a) )
=> ! [Ca,Aa,F,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba)))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),Ca))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_3))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_3))) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca))) ) ) ) ) ).
fof(fact_187_order__le__less__subst2,axiom,
! [X_a,X_b] :
( ( order(X_b)
& order(X_a) )
=> ! [F,Ca,Aa,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),Ca))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_3))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_3))) )
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca)) ) ) ) ) ).
fof(fact_188_equalityI,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
=> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ) ).
fof(fact_189_subsetD,axiom,
! [X_a,Ca,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ) ).
fof(fact_190_psubset__eq,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
& ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ) ) ).
fof(fact_191_subset__iff__psubset__eq,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
| ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ) ).
fof(fact_192_psubset__imp__subset,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ).
fof(fact_193_psubset__subset__trans,axiom,
! [X_a,C_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_1)) ) ) ).
fof(fact_194_subset__psubset__trans,axiom,
! [X_a,C_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_1)) ) ) ).
fof(fact_195_rev__predicate2D,axiom,
! [X_b,X_a,Q_1,Pa,X_1,Y_2] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_2))
=> ( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1))
=> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_2)) ) ) ).
fof(fact_196_equalityE,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
=> ~ ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ) ) ).
fof(fact_197_predicate2D,axiom,
! [X_a,X_b,X_1,Y_2,Pa,Q_1] :
( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_2))
=> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_2)) ) ) ).
fof(fact_198_subset__trans,axiom,
! [X_a,C_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_1)) ) ) ).
fof(fact_199_set__mp,axiom,
! [X_a,X_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) ) ) ).
fof(fact_200_set__rev__mp,axiom,
! [X_a,B,X_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) ) ) ).
fof(fact_201_predicate1D,axiom,
! [X_a,X_1,Pa,Q_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1))
=> ( hBOOL(hAPP(X_a,bool,Pa,X_1))
=> hBOOL(hAPP(X_a,bool,Q_1,X_1)) ) ) ).
fof(fact_202_in__mono,axiom,
! [X_a,X_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) ) ) ).
fof(fact_203_equalityD2,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ) ).
fof(fact_204_equalityD1,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ).
fof(fact_205_rev__predicate1D,axiom,
! [X_a,Q_1,Pa,X_1] :
( hBOOL(hAPP(X_a,bool,Pa,X_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1))
=> hBOOL(hAPP(X_a,bool,Q_1,X_1)) ) ) ).
fof(fact_206_set__eq__subset,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ) ) ).
fof(fact_207_subset__refl,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1)) ).
fof(fact_208_pred__subset__eq,axiom,
! [X_a,R_1,S_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S_1)))
<=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_1),S_1)) ) ).
fof(fact_209_predicate2I,axiom,
! [X_b,X_a,Q_1,Pa] :
( ! [X_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_3))
=> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_3)) )
=> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) ) ).
fof(fact_210_Pi__mono,axiom,
! [X_b,X_a,B,C_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_a,fun(X_b,bool),B,X_2)),hAPP(X_a,fun(X_b,bool),C_1,X_2))) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),C_1))) ) ).
fof(fact_211_subsetI,axiom,
! [X_a,B,A_1] :
( ! [X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) )
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ).
fof(fact_212_xt5,axiom,
! [X_b,X_a] :
( ( order(X_a)
& order(X_b) )
=> ! [Ca,F,Ba,Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,Ba)))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_3),X_2))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_3)),hAPP(X_a,X_b,F,X_2))) )
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa))) ) ) ) ) ).
fof(fact_213_xt7,axiom,
! [X_b,X_a] :
( ( order(X_a)
& order(X_b) )
=> ! [Ca,F,Ba,Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Ba)))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_3),X_2))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_3)),hAPP(X_a,X_b,F,X_2))) )
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa))) ) ) ) ) ).
fof(fact_214_psubsetD,axiom,
! [X_a,Ca,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ) ).
fof(fact_215_psubset__trans,axiom,
! [X_a,C_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_1)) ) ) ).
fof(fact_216_order__less__le__subst2,axiom,
! [X_a,X_b] :
( ( order(X_b)
& order(X_a) )
=> ! [F,Ca,Aa,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),Ca))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_3))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_3))) )
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca)) ) ) ) ) ).
fof(fact_217_in__below,axiom,
! [X_1,Y_2,L_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),Aa),Ba)))
<=> ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
& ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Aa)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Ba)),L_3)) )
& ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Aa)
=> ( ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa)
=> ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Y_2)),L_3)) ) )
& ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Aa)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) ) ) ) ) ) ) ) ).
fof(fact_218_add__leE,axiom,
! [M_3,K_1,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_1)),N_1))
=> ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) ) ) ).
fof(fact_219_add__leD1,axiom,
! [M_3,K_1,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_1)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ) ).
fof(fact_220_add__leD2,axiom,
! [M_3,K_1,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_1)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) ) ).
fof(fact_221_less__not__refl,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)) ).
fof(fact_222_nat__neq__iff,axiom,
! [M_2,Na] :
( M_2 != Na
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) ) ) ).
fof(fact_223_linorder__neqE__nat,axiom,
! [X,Y] :
( X != Y
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)) ) ) ).
fof(fact_224_less__irrefl__nat,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)) ).
fof(fact_225_less__not__refl2,axiom,
! [N_1,M_3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_3))
=> M_3 != N_1 ) ).
fof(fact_226_less__not__refl3,axiom,
! [S,T_3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))
=> S != T_3 ) ).
fof(fact_227_nat__less__cases,axiom,
! [Pa,M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) )
=> ( ( M_2 = Na
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) ) ) ) ).
fof(fact_228_nat__add__commute,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_3) ).
fof(fact_229_nat__add__left__commute,axiom,
! [X,Y,Z_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1)) ).
fof(fact_230_nat__add__assoc,axiom,
! [M_3,N_1,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_1)) ).
fof(fact_231_nat__add__left__cancel,axiom,
! [K,M_2,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
<=> M_2 = Na ) ).
fof(fact_232_nat__add__right__cancel,axiom,
! [M_2,K,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
<=> M_2 = Na ) ).
fof(fact_233_le__refl,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1)) ).
fof(fact_234_nat__le__linear,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_3)) ) ).
fof(fact_235_eq__imp__le,axiom,
! [M_3,N_1] :
( M_3 = N_1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ) ).
fof(fact_236_le__trans,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_1)) ) ) ).
fof(fact_237_le__antisym,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_3))
=> M_3 = N_1 ) ) ).
fof(fact_238_below__Lin,axiom,
! [L_3,X_1,Y_2] :
( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),X_1),Y_2)),arrow_2064824852le_Lin)) ) ) ).
fof(fact_239_inj__on__add__nat,axiom,
! [K,N_3] : 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)),K)),N_3)) ).
fof(fact_240_not__add__less1,axiom,
! [I,J_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),I)) ).
fof(fact_241_not__add__less2,axiom,
! [J_2,I] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),I)) ).
fof(fact_242_nat__add__left__cancel__less,axiom,
! [K,M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ).
fof(fact_243_trans__less__add1,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_3))) ) ).
fof(fact_244_trans__less__add2,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_2))) ) ).
fof(fact_245_add__less__mono1,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_1))) ) ).
fof(fact_246_add__less__mono,axiom,
! [K_1,L_2,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_2))) ) ) ).
fof(fact_247_less__add__eq__less,axiom,
! [M_3,N_1,K_1,L_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_2))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),L_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ) ).
fof(fact_248_add__lessD1,axiom,
! [I,J_2,K_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1)) ) ).
fof(fact_249_nat__less__le,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
& M_2 != Na ) ) ).
fof(fact_250_le__eq__less__or__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| M_2 = Na ) ) ).
fof(fact_251_less__imp__le__nat,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ) ).
fof(fact_252_le__neq__implies__less,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> ( M_3 != N_1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ) ).
fof(fact_253_less__or__eq__imp__le,axiom,
! [M_3,N_1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| M_3 = N_1 )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ) ).
fof(fact_254_le__add2,axiom,
! [N_1,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1))) ).
fof(fact_255_le__add1,axiom,
! [N_1,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_3))) ).
fof(fact_256_le__iff__add,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
<=> ? [K_2] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2) ) ).
fof(fact_257_nat__add__left__cancel__le,axiom,
! [K,M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ).
fof(fact_258_trans__le__add1,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_3))) ) ).
fof(fact_259_trans__le__add2,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_2))) ) ).
fof(fact_260_add__le__mono1,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_1))) ) ).
fof(fact_261_add__le__mono,axiom,
! [K_1,L_2,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_2))) ) ) ).
fof(fact_262_mono__nat__linear__lb,axiom,
! [M_2,K,F] :
( ! [M,N] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M)),hAPP(nat,nat,F,N))) )
=> 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,F,M_2)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K)))) ) ).
fof(fact_263_less__mono__imp__le__mono,axiom,
! [I_1,J_1,F] :
( ! [I_2,J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1))) ) ) ).
fof(fact_264_termination__basic__simps_I3_J,axiom,
! [Z_1,X,Y] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) ) ).
fof(fact_265_termination__basic__simps_I4_J,axiom,
! [Y,X,Z_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) ) ).
fof(fact_266_termination__basic__simps_I2_J,axiom,
! [Y,X,Z_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) ) ).
fof(fact_267_termination__basic__simps_I1_J,axiom,
! [Z_1,X,Y] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) ) ).
fof(fact_268_termination__basic__simps_I5_J,axiom,
! [X,Y] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) ) ).
fof(fact_269_in__rel__def,axiom,
! [X_b,X_a,R_1,X_1,Y_2] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_2))
<=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_2)),R_1)) ) ).
fof(fact_270_funcsetI,axiom,
! [X_b,X_a,F,B,A_1] :
( ! [X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B)) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ) ).
fof(fact_271_linear__alt,axiom,
? [L_1] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) ).
fof(fact_272_Pi__cong,axiom,
! [X_b,X_a,B,F,G,A_1] :
( ! [W] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1))
=> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W) )
=> ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
<=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ) ) ).
fof(fact_273_Pi__I_H,axiom,
! [X_b,X_a,F,B,A_1] :
( ! [X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ) ).
fof(fact_274_card__inj,axiom,
! [X_a,X_b,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))) ) ) ) ).
fof(fact_275_inj__onI,axiom,
! [X_b,X_a,F,A_1] :
( ! [X_2,Y_3] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_3),A_1))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_3)
=> ti(X_a,X_2) = ti(X_a,Y_3) ) ) )
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ).
fof(fact_276_inj__on__cong,axiom,
! [X_b,X_a,F,G,A_1] :
( ! [A_3] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
=> hAPP(X_a,X_b,F,A_3) = hAPP(X_a,X_b,G,A_3) )
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
<=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1)) ) ) ).
fof(fact_277_finite__indi,axiom,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ).
fof(fact_278_card__bij,axiom,
! [X_a,X_b,G,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(fun(X_b,X_a),bool),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,X_a),bool),bool),member(fun(X_b,X_a)),G),hAPP(fun(X_b,fun(X_a,bool)),fun(fun(X_b,X_a),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_a,bool)),fun(fun(X_b,X_a),bool)),pi(X_b,X_a),B),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),combk(fun(X_a,bool),X_b),A_1))))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),G),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
=> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_b,bool),nat,finite_card(X_b),B) ) ) ) ) ) ) ).
fof(fact_279_finite__Collect__subsets,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1)))) ) ).
fof(fact_280_card__psubset,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ) ) ) ).
fof(fact_281_psubset__card__mono,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B))) ) ) ).
fof(fact_282_card__mono,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B))) ) ) ).
fof(fact_283_finite__Collect__conjI,axiom,
! [X_a,Q_1,Pa] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)))
| hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) )
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),Pa)),Q_1)))) ) ).
fof(fact_284_finite__Collect__less__nat,axiom,
! [K] : 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)),K)))) ).
fof(fact_285_finite__Collect__le__nat,axiom,
! [K] : 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)),K)))) ).
fof(fact_286_finite,axiom,
! [X_a] :
( finite_finite(X_a)
=> ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ).
fof(fact_287_finite__code,axiom,
! [X_a] :
( finite_finite(X_a)
=> ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ).
fof(fact_288_card__UNIV__unit,axiom,
hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat) ).
fof(fact_289_finite__Collect__disjI,axiom,
! [X_a,Pa,Q_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),Pa)),Q_1))))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)))
& hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) ) ) ).
fof(fact_290_card__Collect__less__nat,axiom,
! [Na] : 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)),Na))) = Na ).
fof(fact_291_finite__subset,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ) ).
fof(fact_292_rev__finite__subset,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ) ).
fof(fact_293_finite__UNIV,axiom,
! [X_a] :
( finite_finite(X_a)
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ).
fof(fact_294_finite__Prod__UNIV,axiom,
! [X_b,X_a] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,finite_finite_1(product_prod(X_a,X_b)),top_top(fun(product_prod(X_a,X_b),bool)))) ) ) ).
fof(fact_295_finite__Plus__UNIV__iff,axiom,
! [X_a,X_b] :
( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),top_top(fun(sum_sum(X_a,X_b),bool))))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
& hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool)))) ) ) ).
fof(fact_296_finite__option__UNIV,axiom,
! [X_a] :
( hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite_1(option(X_a)),top_top(fun(option(X_a),bool))))
<=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ).
fof(fact_297_finite__Collect__not,axiom,
! [X_a,Pa] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),Pa))))
<=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ) ).
fof(fact_298_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
=> ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,finite_card(X_a),top_top(fun(X_a,bool)))
=> ti(fun(X_a,bool),A_1) = top_top(fun(X_a,bool)) ) ) ).
fof(fact_299_finite__fun__UNIVD2,axiom,
! [X_a,X_b] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite_1(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool))))
=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool)))) ) ).
fof(fact_300_card__seteq,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)))
=> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ) ) ).
fof(fact_301_ex__new__if__finite,axiom,
! [X_a,A_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ? [A_3] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) ) ) ).
fof(fact_302_card__Plus,axiom,
! [X_b,X_a,B,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
=> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)) ) ) ).
fof(fact_303_folding__image__simple__idem_Osubset__idem,axiom,
! [X_b,X_a,B,A_1,F,Z,G,Fa] :
( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1))
=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,B)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1) ) ) ) ).
fof(fact_304_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))) ).
fof(fact_305_folding__image__simple__idem_Oidem,axiom,
! [X_b,X_a,X_1,F,Z,G,Fa] :
( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa))
=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),X_1) = ti(X_a,X_1) ) ).
fof(fact_306_finite__Plus__iff,axiom,
! [X_a,X_b,A_1,B] :
( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
& hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) ) ) ).
fof(fact_307_finite__Plus,axiom,
! [X_b,X_a,B,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
=> hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B))) ) ) ).
fof(fact_308_finite__PlusD_I1_J,axiom,
! [X_a,X_b,A_1,B] :
( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ).
fof(fact_309_finite__PlusD_I2_J,axiom,
! [X_a,X_b,A_1,B] :
( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) ) ).
fof(fact_310_folding__image__simple__idem_Oin__idem,axiom,
! [X_b,X_a,X_1,A_1,F,Z,G,Fa] :
( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_1)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1) ) ) ) ).
fof(fact_311_UNIV__Plus__UNIV,axiom,
! [X_b,X_a] : hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),top_top(fun(X_a,bool))),top_top(fun(X_b,bool))) = top_top(fun(sum_sum(X_a,X_b),bool)) ).
fof(fact_312_finite__M__bounded__by__nat,axiom,
! [Pa,I_1] : 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),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))) ).
fof(fact_313_finite__nat__set__iff__bounded__le,axiom,
! [N_3] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
<=> ? [M] :
! [X_2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M)) ) ) ).
fof(fact_314_finite__nat__set__iff__bounded,axiom,
! [N_3] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
<=> ? [M] :
! [X_2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M)) ) ) ).
fof(fact_315_finite__less__ub,axiom,
! [U,F] :
( ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,F,N)))
=> 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)),F)),U)))) ) ).
fof(fact_316_bounded__nat__set__is__finite,axiom,
! [Na,N_3] :
( ! [X_2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) ) ).
fof(fact_317_card__Plus__conv__if,axiom,
! [X_b,X_a,B,A_1] :
( ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
& hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) )
=> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)) )
& ( ~ ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
& hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) )
=> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = zero_zero(nat) ) ) ).
fof(fact_318_less__zeroE,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))) ).
fof(fact_319_le0,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1)) ).
fof(fact_320_gr0I,axiom,
! [N_1] :
( N_1 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) ) ).
fof(fact_321_gr__implies__not0,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> N_1 != zero_zero(nat) ) ).
fof(fact_322_less__nat__zero__code,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))) ).
fof(fact_323_neq0__conv,axiom,
! [Na] :
( Na != zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ) ).
fof(fact_324_not__less0,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))) ).
fof(fact_325_plus__nat_Oadd__0,axiom,
! [N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1) = N_1 ).
fof(fact_326_Nat_Oadd__0__right,axiom,
! [M_3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),zero_zero(nat)) = M_3 ).
fof(fact_327_add__is__0,axiom,
! [M_2,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) = zero_zero(nat)
<=> ( M_2 = zero_zero(nat)
& Na = zero_zero(nat) ) ) ).
fof(fact_328_add__eq__self__zero,axiom,
! [M_3,N_1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1) = M_3
=> N_1 = zero_zero(nat) ) ).
fof(fact_329_le__0__eq,axiom,
! [Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat)))
<=> Na = zero_zero(nat) ) ).
fof(fact_330_less__eq__nat_Osimps_I1_J,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1)) ).
fof(fact_331_zero__reorient,axiom,
! [X_a] :
( zero(X_a)
=> ! [X_1] :
( zero_zero(X_a) = ti(X_a,X_1)
<=> ti(X_a,X_1) = zero_zero(X_a) ) ) ).
fof(fact_332_zero__neq__one,axiom,
! [X_a] :
( zero_neq_one(X_a)
=> zero_zero(X_a) != one_one(X_a) ) ).
fof(fact_333_one__neq__zero,axiom,
! [X_a] :
( zero_neq_one(X_a)
=> one_one(X_a) != zero_zero(X_a) ) ).
fof(fact_334_add_Ocomm__neutral,axiom,
! [X_a] :
( comm_monoid_add(X_a)
=> ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2) ) ).
fof(fact_335_add__0__right,axiom,
! [X_a] :
( monoid_add(X_a)
=> ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2) ) ).
fof(fact_336_double__zero__sym,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [Aa] :
( zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)
<=> ti(X_a,Aa) = zero_zero(X_a) ) ) ).
fof(fact_337_add__0,axiom,
! [X_a] :
( comm_monoid_add(X_a)
=> ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2) ) ).
fof(fact_338_add__0__left,axiom,
! [X_a] :
( monoid_add(X_a)
=> ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2) ) ).
fof(fact_339_add__nonpos__nonpos,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ) ).
fof(fact_340_add__increasing2,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2,C] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C))) ) ) ) ).
fof(fact_341_add__increasing,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,C,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C))) ) ) ) ).
fof(fact_342_add__nonneg__eq__0__iff,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [Y_2,X_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_2))
=> ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_2) = zero_zero(X_a)
<=> ( ti(X_a,X_1) = zero_zero(X_a)
& ti(X_a,Y_2) = zero_zero(X_a) ) ) ) ) ) ).
fof(fact_343_add__nonneg__nonneg,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ) ).
fof(fact_344_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) ) ) ).
fof(fact_345_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) ) ) ).
fof(fact_346_add__neg__neg,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ) ).
fof(fact_347_pos__add__strict,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> ! [B_1,C,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C))) ) ) ) ).
fof(fact_348_add__pos__pos,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ) ).
fof(fact_349_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) ) ) ).
fof(fact_350_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)) ) ) ).
fof(fact_351_zero__le__one,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))) ) ).
fof(fact_352_not__one__le__zero,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))) ) ).
fof(fact_353_zero__less__one,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))) ) ).
fof(fact_354_not__one__less__zero,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))) ) ).
fof(fact_355_add__gr__0,axiom,
! [M_2,Na] :
( 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),M_2),Na)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ) ) ).
fof(fact_356_card__infinite,axiom,
! [X_a,A_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat) ) ).
fof(fact_357_add__nonpos__neg,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ) ).
fof(fact_358_add__neg__nonpos,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ) ).
fof(fact_359_add__strict__increasing2,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,C,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C))) ) ) ) ).
fof(fact_360_add__strict__increasing,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,C,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C))) ) ) ) ).
fof(fact_361_add__nonneg__pos,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ) ).
fof(fact_362_add__pos__nonneg,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ) ).
fof(fact_363_zero__less__two,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) ) ).
fof(fact_364_card__ge__0__finite,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ).
fof(fact_365_finite__UNIV__card__ge__0,axiom,
! [X_a] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),top_top(fun(X_a,bool))))) ) ).
fof(fact_366_ex__least__nat__less,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,Pa,Na))
=> ? [K_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na))
& ! [I_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_2))
=> ~ hBOOL(hAPP(nat,bool,Pa,I_2)) )
& hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat)))) ) ) ) ).
fof(fact_367_card_Oneutral,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( ( ? [X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> one_one(nat) = zero_zero(nat) )
=> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat) ) ) ).
fof(fact_368_ex__least__nat__le,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,Pa,Na))
=> ? [K_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
& ! [I_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2))
=> ~ hBOOL(hAPP(nat,bool,Pa,I_2)) )
& hBOOL(hAPP(nat,bool,Pa,K_2)) ) ) ) ).
fof(fact_369_less__imp__add__positive,axiom,
! [I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> ? [K_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))
& hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2) = J_2 ) ) ).
fof(fact_370_even__less__0__iff,axiom,
! [X_a] :
( linordered_idom(X_a)
=> ! [Aa] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) ) ) ).
fof(fact_371_double__eq__0__iff,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [Aa] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a)
<=> ti(X_a,Aa) = zero_zero(X_a) ) ) ).
fof(fact_372_finite__fun__UNIVD1,axiom,
! [X_a,X_b] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite_1(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool))))
=> ( hAPP(fun(X_b,bool),nat,finite_card(X_b),top_top(fun(X_b,bool))) != hAPP(nat,nat,suc,zero_zero(nat))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ) ).
fof(fact_373_add__0__iff,axiom,
! [X_a] :
( semiri456707255roduct(X_a)
=> ! [Ba,Aa] :
( ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)
<=> ti(X_a,Aa) = zero_zero(X_a) ) ) ).
fof(fact_374_lessI,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1))) ).
fof(fact_375_Suc__mono,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N_1))) ) ).
fof(fact_376_zero__less__Suc,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))) ).
fof(fact_377_Suc__n__not__le__n,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1)) ).
fof(fact_378_not__less__eq__eq,axiom,
! [M_2,Na] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2)) ) ).
fof(fact_379_le__Suc__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
| M_2 = hAPP(nat,nat,suc,Na) ) ) ).
fof(fact_380_Suc__le__mono,axiom,
! [Na,M_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_2)) ) ).
fof(fact_381_le__SucI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N_1))) ) ).
fof(fact_382_le__SucE,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N_1)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> M_3 = hAPP(nat,nat,suc,N_1) ) ) ).
fof(fact_383_Suc__leD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ) ).
fof(fact_384_Suc__inject,axiom,
! [X,Y] :
( hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y)
=> X = Y ) ).
fof(fact_385_nat_Oinject,axiom,
! [Nat_4,Nat_3] :
( hAPP(nat,nat,suc,Nat_4) = hAPP(nat,nat,suc,Nat_3)
<=> Nat_4 = Nat_3 ) ).
fof(fact_386_Suc__n__not__n,axiom,
! [N_1] : hAPP(nat,nat,suc,N_1) != N_1 ).
fof(fact_387_n__not__Suc__n,axiom,
! [N_1] : N_1 != hAPP(nat,nat,suc,N_1) ).
fof(fact_388_add__Suc__shift,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N_1)) ).
fof(fact_389_add__Suc,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)) ).
fof(fact_390_add__Suc__right,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)) ).
fof(fact_391_not__less__eq,axiom,
! [M_2,Na] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2))) ) ).
fof(fact_392_less__Suc__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| M_2 = Na ) ) ).
fof(fact_393_Suc__less__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,Na)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ).
fof(fact_394_not__less__less__Suc__eq,axiom,
! [Na,M_2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
<=> Na = M_2 ) ) ).
fof(fact_395_less__antisym,axiom,
! [N_1,M_3] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_3))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_3)))
=> M_3 = N_1 ) ) ).
fof(fact_396_less__SucI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1))) ) ).
fof(fact_397_Suc__lessI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> ( hAPP(nat,nat,suc,M_3) != N_1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N_1)) ) ) ).
fof(fact_398_less__trans__Suc,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_1)) ) ) ).
fof(fact_399_less__SucE,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> M_3 = N_1 ) ) ).
fof(fact_400_Suc__lessD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ).
fof(fact_401_Suc__less__SucD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N_1)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ).
fof(fact_402_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)) ).
fof(fact_403_Suc__le__lessD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ).
fof(fact_404_le__less__Suc__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
<=> Na = M_2 ) ) ).
fof(fact_405_Suc__leI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1)) ) ).
fof(fact_406_le__imp__less__Suc,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1))) ) ).
fof(fact_407_Suc__le__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),Na))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ).
fof(fact_408_less__Suc__eq__le,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ).
fof(fact_409_less__eq__Suc__le,axiom,
! [Na,M_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2)) ) ).
fof(fact_410_less__iff__Suc__add,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
<=> ? [K_2] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2)) ) ).
fof(fact_411_less__add__Suc2,axiom,
! [I,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),I)))) ).
fof(fact_412_less__add__Suc1,axiom,
! [I,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M_3)))) ).
fof(fact_413_one__is__add,axiom,
! [M_2,Na] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na)
<=> ( ( M_2 = hAPP(nat,nat,suc,zero_zero(nat))
& Na = zero_zero(nat) )
| ( M_2 = zero_zero(nat)
& Na = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ) ).
fof(fact_414_add__is__1,axiom,
! [M_2,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( M_2 = hAPP(nat,nat,suc,zero_zero(nat))
& Na = zero_zero(nat) )
| ( M_2 = zero_zero(nat)
& Na = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ) ).
fof(fact_415_gr0__conv__Suc,axiom,
! [Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
<=> ? [M] : Na = hAPP(nat,nat,suc,M) ) ).
fof(fact_416_less__Suc0,axiom,
! [Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))
<=> Na = zero_zero(nat) ) ).
fof(fact_417_less__Suc__eq__0__disj,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> ( M_2 = zero_zero(nat)
| ? [J] :
( M_2 = hAPP(nat,nat,suc,J)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),Na)) ) ) ) ).
fof(fact_418_inj__Suc,axiom,
! [N_3] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),N_3)) ).
fof(fact_419_Suc__neq__Zero,axiom,
! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat) ).
fof(fact_420_Zero__neq__Suc,axiom,
! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3) ).
fof(fact_421_nat_Osimps_I3_J,axiom,
! [Nat_2] : hAPP(nat,nat,suc,Nat_2) != zero_zero(nat) ).
fof(fact_422_Suc__not__Zero,axiom,
! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat) ).
fof(fact_423_nat_Osimps_I2_J,axiom,
! [Nat_1] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_1) ).
fof(fact_424_Zero__not__Suc,axiom,
! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3) ).
fof(fact_425_less__eq__Suc__le__raw,axiom,
! [X_2] : hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)) ).
fof(fact_426_card__Collect__le__nat,axiom,
! [Na] : 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)),Na))) = hAPP(nat,nat,suc,Na) ).
fof(fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2) ) ).
fof(fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,C,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D)) ) ).
fof(fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,C,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),D) ) ).
fof(fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,B_1,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)) ) ).
fof(fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,B_1,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),B_1) ) ).
fof(fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,B_1,C,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)) ) ).
fof(fact_433_card__less__Suc,axiom,
! [I_1,M_4] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4))
=> 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)),M_4))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))) = 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)),M_4))),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,I_1))))) ) ).
fof(fact_434_card__less,axiom,
! [I_1,M_4] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4))
=> 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)),M_4))),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,I_1))))) != zero_zero(nat) ) ).
fof(fact_435_card__less__Suc2,axiom,
! [I_1,M_4] :
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4))
=> 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)),M_4))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))) = 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)),M_4))),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,I_1))))) ) ).
fof(fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2) ) ).
fof(fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2) ) ).
fof(fact_438_inc__induct,axiom,
! [Pa,I_1,J_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
=> ( hBOOL(hAPP(nat,bool,Pa,J_1))
=> ( ! [I_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
=> ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I_2)))
=> hBOOL(hAPP(nat,bool,Pa,I_2)) ) )
=> hBOOL(hAPP(nat,bool,Pa,I_1)) ) ) ) ).
fof(fact_439_less__imp__Suc__add,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> ? [K_2] : N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)) ) ).
fof(fact_440_gr0__implies__Suc,axiom,
! [N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))
=> ? [M] : N_1 = hAPP(nat,nat,suc,M) ) ).
fof(fact_441_lift__Suc__mono__le,axiom,
! [X_a] :
( order(X_a)
=> ! [Na,N_2,F] :
( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_2))) ) ) ) ).
fof(fact_442_lift__Suc__mono__less,axiom,
! [X_a] :
( order(X_a)
=> ! [Na,N_2,F] :
( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_2))) ) ) ) ).
fof(fact_443_lift__Suc__mono__less__iff,axiom,
! [X_a] :
( order(X_a)
=> ! [Na,M_2,F] :
( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N))))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,M_2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) ) ) ) ).
fof(fact_444_Suc__eq__plus1__left,axiom,
! [N_1] : hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1) ).
fof(fact_445_Suc__eq__plus1,axiom,
! [N_1] : hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)) ).
fof(fact_446_Suc__le__D,axiom,
! [N_1,M_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1))
=> ? [M] : M_1 = hAPP(nat,nat,suc,M) ) ).
fof(fact_447_lessE,axiom,
! [I,K_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1))
=> ( K_1 != hAPP(nat,nat,suc,I)
=> ~ ! [J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))
=> K_1 != hAPP(nat,nat,suc,J) ) ) ) ).
fof(fact_448_Suc__lessE,axiom,
! [I,K_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_1))
=> ~ ! [J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))
=> K_1 != hAPP(nat,nat,suc,J) ) ) ).
fof(fact_449_not0__implies__Suc,axiom,
! [N_1] :
( N_1 != zero_zero(nat)
=> ? [M] : N_1 = hAPP(nat,nat,suc,M) ) ).
fof(fact_450_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero(nat)
=> ~ ! [Nat] : Y != hAPP(nat,nat,suc,Nat) ) ).
fof(fact_451_zero__induct,axiom,
! [Pa,K] :
( hBOOL(hAPP(nat,bool,Pa,K))
=> ( ! [N] :
( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N)))
=> hBOOL(hAPP(nat,bool,Pa,N)) )
=> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ) ) ).
fof(fact_452_nat__induct,axiom,
! [Na,Pa] :
( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
=> ( ! [N] :
( hBOOL(hAPP(nat,bool,Pa,N))
=> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) )
=> hBOOL(hAPP(nat,bool,Pa,Na)) ) ) ).
fof(fact_453_field__le__epsilon,axiom,
! [X_a] :
( linordered_field(X_a)
=> ! [X,Y] :
( ! [E] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ) ).
fof(fact_454_card_Oeq__fold__g,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(nat,fun(fun(X_a,bool),nat),hAPP(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat))),finite_fold_image(nat,X_a),plus_plus(nat)),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),zero_zero(nat)),A_1) ) ).
fof(fact_455_card__def,axiom,
! [X_a,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(nat,fun(fun(X_a,bool),nat),hAPP(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat))),finite_fold_image(nat,X_a),plus_plus(nat)),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),zero_zero(nat)),A_1) )
& ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat) ) ) ).
fof(fact_456_surjh,axiom,
hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ).
fof(fact_457_Ints__odd__less__0,axiom,
! [X_a] :
( linordered_idom(X_a)
=> ! [Aa] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))
<=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) ) ) ) ).
fof(fact_458_image__eqI,axiom,
! [X_a,X_b,A_1,Ba,F,X_1] :
( ti(X_a,Ba) = hAPP(X_b,X_a,F,X_1)
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ) ).
fof(fact_459_finite__imageI,axiom,
! [X_b,X_a,Ha,Fa] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa))
=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),Ha),Fa))) ) ).
fof(fact_460_finite__atLeastLessThan,axiom,
! [L,U] : 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),L),U))) ).
fof(fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123,axiom,
~ ! [H] :
( hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),H),top_top(fun(arrow_660593299e_indi,bool))))
=> hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),H),top_top(fun(arrow_660593299e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ) ).
fof(fact_462_atLeastLessThan__subset__iff,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Aa,Ba,Ca,Da] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))
| ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da)) ) ) ) ) ).
fof(fact_463_funcset__image,axiom,
! [X_a,X_b,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B)) ) ).
fof(fact_464_finite__surj__inj,axiom,
! [X_a,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1)) ) ) ).
fof(fact_465_endo__inj__surj,axiom,
! [X_a,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))
=> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1) = ti(fun(X_a,bool),A_1) ) ) ) ).
fof(fact_466_finite__UNIV__inj__surj,axiom,
! [X_a,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool))))
=> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool)) ) ) ).
fof(fact_467_finite__UNIV__surj__inj,axiom,
! [X_a,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
=> ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool)))) ) ) ).
fof(fact_468_inj__image__subset__iff,axiom,
! [X_a,X_b,A_1,B,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))
<=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ) ).
fof(fact_469_card__image__le,axiom,
! [X_b,X_a,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1))) ) ).
fof(fact_470_eq__card__imp__inj__on,axiom,
! [X_b,X_a,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ) ).
fof(fact_471_inj__on__iff__eq__card,axiom,
! [X_b,X_a,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
<=> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) ) ) ).
fof(fact_472_pigeonhole,axiom,
! [X_a,X_b,F,A_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)))
=> ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1)) ) ).
fof(fact_473_Ints__double__eq__0__iff,axiom,
! [X_a] :
( ring_char_0(X_a)
=> ! [Aa] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
=> ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a)
<=> ti(X_a,Aa) = zero_zero(X_a) ) ) ) ).
fof(fact_474_Ints__0,axiom,
! [X_a] :
( ring_1(X_a)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))) ) ).
fof(fact_475_Ints__1,axiom,
! [X_a] :
( ring_1(X_a)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))) ) ).
fof(fact_476_Ints__add,axiom,
! [X_a] :
( ring_1(X_a)
=> ! [Ba,Aa] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a))) ) ) ) ).
fof(fact_477_inv__into__injective,axiom,
! [X_b,X_a,A_1,F,X_1,Y_2] :
( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),X_1) = hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_2)
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
=> ti(X_b,X_1) = ti(X_b,Y_2) ) ) ) ).
fof(fact_478_inv__into__into,axiom,
! [X_a,X_b,X_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F),X_1)),A_1)) ) ).
fof(fact_479_f__inv__into__f,axiom,
! [X_a,X_b,Y_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
=> hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F),Y_2)) = ti(X_a,Y_2) ) ).
fof(fact_480_rev__image__eqI,axiom,
! [X_b,X_a,Ba,F,X_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ( ti(X_b,Ba) = hAPP(X_a,X_b,F,X_1)
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ) ) ).
fof(fact_481_imageI,axiom,
! [X_b,X_a,F,X_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ) ).
fof(fact_482_image__iff,axiom,
! [X_a,X_b,Z,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
<=> ? [X_2] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
& ti(X_a,Z) = hAPP(X_b,X_a,F,X_2) ) ) ).
fof(fact_483_image__image,axiom,
! [X_b,X_a,X_c,F,G,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_1) ).
fof(fact_484_image__ident,axiom,
! [X_a,Y_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_1) = ti(fun(X_a,bool),Y_1) ).
fof(fact_485_subset__image__iff,axiom,
! [X_a,X_b,B,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
<=> ? [AA] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1))
& ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA) ) ) ).
fof(fact_486_image__mono,axiom,
! [X_b,X_a,F,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))) ) ).
fof(fact_487_atLeastLessThan__eq__iff,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Ca,Da,Aa,Ba] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
=> ( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
<=> ( ti(X_a,Aa) = ti(X_a,Ca)
& ti(X_a,Ba) = ti(X_a,Da) ) ) ) ) ) ).
fof(fact_488_atLeastLessThan__inj_I1_J,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Aa,Ba,Ca,Da] :
( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
=> ti(X_a,Aa) = ti(X_a,Ca) ) ) ) ) ).
fof(fact_489_atLeastLessThan__inj_I2_J,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Aa,Ba,Ca,Da] :
( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
=> ti(X_a,Ba) = ti(X_a,Da) ) ) ) ) ).
fof(fact_490_range__composition,axiom,
! [X_b,X_a,X_c,F,G] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_c),fun(X_b,X_a),hAPP(fun(X_c,X_a),fun(fun(X_b,X_c),fun(X_b,X_a)),combb(X_c,X_a,X_b),F),G)),top_top(fun(X_b,bool))) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),F),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),top_top(fun(X_b,bool)))) ).
fof(fact_491_range__eqI,axiom,
! [X_a,X_b,Ba,F,X_1] :
( ti(X_a,Ba) = hAPP(X_b,X_a,F,X_1)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))) ) ).
fof(fact_492_rangeI,axiom,
! [X_a,X_b,F,X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))) ).
fof(fact_493_finite__range__imageI,axiom,
! [X_c,X_a,X_b,F,G] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool)))))
=> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),combb(X_a,X_c,X_b),F),G)),top_top(fun(X_b,bool))))) ) ).
fof(fact_494_subset__card__intvl__is__intvl,axiom,
! [A_1,K] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_1)))))
=> A_1 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_1))) ) ).
fof(fact_495_inj__on__strict__subset,axiom,
! [X_a,X_b,A_1,F,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))) ) ) ).
fof(fact_496_image__surj__f__inv__f,axiom,
! [X_b,X_a,A_1,F] :
( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
=> hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F)),A_1)) = ti(fun(X_a,bool),A_1) ) ).
%----Arities (33)
fof(arity_fun___Orderings_Opreorder,axiom,
! [T_2,T_1] :
( preorder(T_1)
=> preorder(fun(T_2,T_1)) ) ).
fof(arity_fun___Finite__Set_Ofinite,axiom,
! [T_2,T_1] :
( ( finite_finite(T_1)
& finite_finite(T_2) )
=> finite_finite(fun(T_2,T_1)) ) ).
fof(arity_fun___Orderings_Oorder,axiom,
! [T_2,T_1] :
( order(T_1)
=> order(fun(T_2,T_1)) ) ).
fof(arity_fun___Orderings_Otop,axiom,
! [T_2,T_1] :
( top(T_1)
=> top(fun(T_2,T_1)) ) ).
fof(arity_fun___Orderings_Oord,axiom,
! [T_2,T_1] :
( ord(T_1)
=> ord(fun(T_2,T_1)) ) ).
fof(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
semiri456707255roduct(nat) ).
fof(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
ordere223160158up_add(nat) ).
fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(nat) ).
fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
ordere779506340up_add(nat) ).
fof(arity_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
ordere216010020id_add(nat) ).
fof(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add(nat) ).
fof(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat) ).
fof(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
linordered_semidom(nat) ).
fof(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add(nat) ).
fof(arity_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
comm_monoid_add(nat) ).
fof(arity_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(nat) ).
fof(arity_Nat_Onat___Rings_Ozero__neq__one,axiom,
zero_neq_one(nat) ).
fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
preorder(nat) ).
fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat) ).
fof(arity_Nat_Onat___Groups_Omonoid__add,axiom,
monoid_add(nat) ).
fof(arity_Nat_Onat___Orderings_Oorder,axiom,
order(nat) ).
fof(arity_Nat_Onat___Orderings_Oord,axiom,
ord(nat) ).
fof(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat) ).
fof(arity_Nat_Onat___Groups_Oone,axiom,
one(nat) ).
fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
preorder(bool) ).
fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite(bool) ).
fof(arity_HOL_Obool___Orderings_Oorder,axiom,
order(bool) ).
fof(arity_HOL_Obool___Orderings_Otop,axiom,
top(bool) ).
fof(arity_HOL_Obool___Orderings_Oord,axiom,
ord(bool) ).
fof(arity_sum___Finite__Set_Ofinite,axiom,
! [T_2,T_1] :
( ( finite_finite(T_1)
& finite_finite(T_2) )
=> finite_finite(sum_sum(T_2,T_1)) ) ).
fof(arity_Option_Ooption___Finite__Set_Ofinite,axiom,
! [T_1] :
( finite_finite(T_1)
=> finite_finite(option(T_1)) ) ).
fof(arity_prod___Finite__Set_Ofinite,axiom,
! [T_2,T_1] :
( ( finite_finite(T_1)
& finite_finite(T_2) )
=> finite_finite(product_prod(T_2,T_1)) ) ).
fof(arity_Product__Type_Ounit___Finite__Set_Ofinite,axiom,
finite_finite(product_unit) ).
%----Helper facts (21)
fof(help_ti_idem,axiom,
! [T,A] : ti(T,ti(T,A)) = ti(T,A) ).
fof(help_If_1_1_T,axiom,
! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X) ).
fof(help_If_2_1_T,axiom,
! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y) ).
fof(help_If_3_1_T,axiom,
! [P] :
( ti(bool,P) = fTrue
| ti(bool,P) = fFalse ) ).
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(hAPP(bool,bool,fNot,P))
| ~ hBOOL(P) ) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(P)
| hBOOL(hAPP(bool,bool,fNot,P)) ) ).
fof(help_COMBB_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)) ).
fof(help_COMBC_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) ).
fof(help_COMBI_1_1_U,axiom,
! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P) ).
fof(help_COMBK_1_1_U,axiom,
! [X_b,X_a,P,Q] : hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ).
fof(help_COMBS_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)) ).
fof(help_fTrue_1_1_U,axiom,
hBOOL(fTrue) ).
fof(help_fTrue_1_1_T,axiom,
! [P] :
( ti(bool,P) = fTrue
| ti(bool,P) = fFalse ) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))
| hBOOL(P) ) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))
| hBOOL(Q) ) ).
fof(help_fdisj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ) ).
fof(help_fdisj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ) ).
fof(help_fdisj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
| hBOOL(P)
| hBOOL(Q) ) ).
fof(help_fequal_1_1_T,axiom,
! [X_a,X,Y] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y))
| ti(X_a,X) = ti(X_a,Y) ) ).
fof(help_fequal_2_1_T,axiom,
! [X_a,X,Y] :
( ti(X_a,X) != ti(X_a,Y)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) ) ).
%----Conjectures (1)
fof(conj_0,conjecture,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ).
%------------------------------------------------------------------------------