TPTP Problem File: SCT171+3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT171+3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 1000 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_1000_fofmg_l309 [Bla11]
% Status : Theorem
% Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 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, 0.30 v5.4.0, 0.36 v5.3.0
% Syntax : Number of formulae : 1415 ( 312 unt; 0 def)
% Number of atoms : 4309 ( 585 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 3220 ( 326 ~; 59 |; 316 &)
% ( 243 <=>;2276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 0 prp; 1-2 aty)
% Number of functors : 506 ( 506 usr; 171 con; 0-3 aty)
% Number of variables : 3986 (3965 !; 21 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 17:57:33
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (136)
fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA,axiom,
is_fun158382675l_bool(arrow_1654180089le_IIA) ).
fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin,axiom,
is_fun279392540l_bool(arrow_1681063817le_Lin) ).
fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf,axiom,
is_fun288122577l_bool(arrow_1721807329e_Prof) ).
fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow,axiom,
! [B_1_1,B_2_1,B_3_1] :
( ( is_fun961089132t_bool(B_1_1)
& is_Arr1861959080le_alt(B_2_1)
& is_Arr1861959080le_alt(B_3_1) )
=> is_fun961089132t_bool(arrow_1539419881_below(B_1_1,B_2_1,B_3_1)) ) ).
fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity,axiom,
is_fun158382675l_bool(arrow_1587283740nimity) ).
fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_,axiom,
! [B_1_1,B_2_1] :
( is_fun1236654035i_bool(B_1_1)
=> is_fun288122577l_bool(pi_Arr990697634t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin,axiom,
! [B_1_1,B_2_1] :
( is_fun288122577l_bool(B_1_1)
=> is_fun158382675l_bool(pi_fun150026276t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_1_1)
=> is_fun279392540l_bool(pi_Pro666468413t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt,axiom,
is_Arr1861959080le_alt(undefi462180727le_alt(arrow_107136085le_alt)) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi,axiom,
is_Arr43961803e_indi(undefi237088188e_indi(arrow_1271263838e_indi)) ).
fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
is_fun2093718614t_bool(undefi1931156935t_bool(fun(arrow_107136085le_alt,fun(arrow_107136085le_alt,bool)))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001,axiom,
is_fun1236654035i_bool(undefi1547870882i_bool(fun(arrow_1271263838e_indi,bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J,axiom,
is_fun1568535512t_bool(undefi312741927t_bool(fun(product_unit,bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
is_fun288122577l_bool(undefi203294880l_bool(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
is_fun158382675l_bool(undefi1466315554l_bool(fun(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
is_fun279392540l_bool(undefi871250829l_bool(fun(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool),bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
is_fun961089132t_bool(undefi1481304379t_bool(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool))) ).
fof(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu,axiom,
! [B_1_1,B_2_1] :
( is_fun1236654035i_bool(B_1_1)
=> is_fun1217980910e_indi(hilber693666498di_nat(B_1_1,B_2_1)) ) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,axiom,
is_bool(top_top_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____,axiom,
is_fun2093718614t_bool(top_to178429151t_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002,axiom,
is_fun1236654035i_bool(top_to1576102282i_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL,axiom,
is_fun1568535512t_bool(top_to1257323279t_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira,axiom,
is_fun288122577l_bool(top_to522745736l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,axiom,
is_fun158382675l_bool(top_to1714702858l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,axiom,
is_fun279392540l_bool(top_to1853035173l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,axiom,
is_fun961089132t_bool(top_to565915683t_bool) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob,axiom,
! [B_1_1,B_2_1] :
( is_Arr1861959080le_alt(B_2_1)
=> is_bool(hAPP_A862370221t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc,axiom,
! [B_1_1,B_2_1] :
( is_Arr1861959080le_alt(B_2_1)
=> is_fun279392540l_bool(hAPP_A187815023l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003,axiom,
! [B_1_1,B_2_1] :
( is_Arr1861959080le_alt(B_2_1)
=> is_fun961089132t_bool(hAPP_A568203993t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O,axiom,
! [B_1_1,B_2_1] :
( ( is_fun1236654035i_bool(B_1_1)
& is_Arr43961803e_indi(B_2_1) )
=> is_bool(hAPP_A1785763630i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It,axiom,
! [B_1_1,B_2_1] :
( is_Arr43961803e_indi(B_2_1)
=> is_fun288122577l_bool(hAPP_A1952883197l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004,axiom,
! [B_1_1,B_2_1] :
( is_Arr43961803e_indi(B_2_1)
=> is_fun158382675l_bool(hAPP_A1112981887l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005,axiom,
! [B_1_1,B_2_1] :
( is_Arr43961803e_indi(B_2_1)
=> is_fun279392540l_bool(hAPP_A60074736l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006,axiom,
! [B_1_1,B_2_1] :
( is_Arr43961803e_indi(B_2_1)
=> is_fun961089132t_bool(hAPP_A1677245848t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun1236654035i_bool(hAPP_b1337486384i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun1568535512t_bool(hAPP_b1096750261t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun288122577l_bool(hAPP_b1048178734l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun158382675l_bool(hAPP_b517355696l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun279392540l_bool(hAPP_b1812770943l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun961089132t_bool(hAPP_b1703662281t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi,axiom,
! [B_1_1,B_2_1] :
( is_fun1217980910e_indi(B_1_1)
=> is_Arr43961803e_indi(hAPP_n1951273283e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn,axiom,
! [B_1_1,B_2_1] : is_fun2093718614t_bool(hAPP_n539120590t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007,axiom,
! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_n821919323i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_n454528608t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,axiom,
! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_n2095207769l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____,axiom,
! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_n295497947l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___,axiom,
! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_n1674354836l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_n588788980t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_fun1568535512t_bool(B_1_1)
=> is_bool(hAPP_P1676879539t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order,axiom,
! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_P254387896l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow,axiom,
! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_P1171466554l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro,axiom,
! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_P1294997365l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde,axiom,
! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_P1341894483t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2013399995l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008,axiom,
! [B_1_1,B_2_1] :
( is_fun2093718614t_bool(B_2_1)
=> is_bool(hAPP_f324780729l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_,axiom,
! [B_1_1,B_2_1] :
( is_fun1236654035i_bool(B_2_1)
=> is_bool(hAPP_f1599966040l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009,axiom,
! [B_1_1,B_2_1] :
( is_fun1236654035i_bool(B_2_1)
=> is_fun1236654035i_bool(hAPP_f580451669i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010,axiom,
! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_f836059805e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011,axiom,
! [B_1_1,B_2_1] :
( is_fun288122577l_bool(B_1_1)
=> is_bool(hAPP_f965095724l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012,axiom,
! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f1948454017i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1891021702t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014,axiom,
! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_f1277514478l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015,hypothesis,
! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_f412050202t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____,axiom,
! [B_1_1,B_2_1] : is_fun2093718614t_bool(hAPP_f861874780t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow_____016,axiom,
! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f632777549i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Product__,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1061584978t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,axiom,
! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_f226010187l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___017,axiom,
! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_f1449238989l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___018,axiom,
! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_f769545506l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_,axiom,
! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_f899613158t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__,axiom,
! [B_1_1,B_2_1] :
( is_fun1568535512t_bool(B_2_1)
=> is_bool(hAPP_f2028818269l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I,axiom,
! [B_1_1,B_2_1] :
( is_fun1568535512t_bool(B_2_1)
=> is_fun1568535512t_bool(hAPP_f427533077t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1632652727l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1252760917l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f785974231l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021,axiom,
! [B_1_1,B_2_1] :
( is_fun288122577l_bool(B_2_1)
=> is_bool(hAPP_f777333846l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022,axiom,
! [B_1_1,B_2_1] :
( is_fun288122577l_bool(B_2_1)
=> is_fun288122577l_bool(hAPP_f146009813l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023,axiom,
! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_f1693298207e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024,axiom,
! [B_1_1,B_2_1] :
( is_fun158382675l_bool(B_1_1)
=> is_bool(hAPP_f312250286l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025,axiom,
! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f1552576127i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1866147972t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1837019376l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f67777128l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f599145828l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f651410150l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f817604743l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1351174655l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f795156475l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f537623936l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f339859954l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f844512602l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1508442332l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1846209297l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f415146997l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1725204053l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_028,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f597137892l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_029,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f770608346l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030,axiom,
! [B_1_1,B_2_1] :
( is_fun158382675l_bool(B_2_1)
=> is_bool(hAPP_f250445784l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031,axiom,
! [B_1_1,B_2_1] :
( is_fun158382675l_bool(B_2_1)
=> is_fun158382675l_bool(hAPP_f1765205l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f10461143l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_032,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f859154022l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_033,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1644647260l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f560831258l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_034,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f167218729l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_035,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f866275871l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1306865520l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036,axiom,
! [B_1_1,B_2_1] :
( is_fun279392540l_bool(B_2_1)
=> is_bool(hAPP_f1749234559l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037,axiom,
! [B_1_1,B_2_1] :
( is_fun279392540l_bool(B_2_1)
=> is_fun279392540l_bool(hAPP_f111185985l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f22590837l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_2_1)
=> is_Arr43961803e_indi(hAPP_f1582908258e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039,hypothesis,
! [B_1_1,B_2_1] :
( ( is_fun279392540l_bool(B_1_1)
& is_fun961089132t_bool(B_2_1) )
=> is_bool(hAPP_f592646513l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_2_1)
=> is_fun2093718614t_bool(hAPP_f1617919085t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_2_1)
=> is_fun1236654035i_bool(hAPP_f244157820i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_2_1)
=> is_fun1568535512t_bool(hAPP_f1710744577t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_2_1)
=> is_fun279392540l_bool(hAPP_f863359027l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_2_1)
=> is_fun961089132t_bool(hAPP_f515126293t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_,axiom,
! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_P710098616e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045,axiom,
! [B_1_1,B_2_1] :
( is_fun961089132t_bool(B_1_1)
=> is_bool(hAPP_P606313927t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046,axiom,
! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_P1875867302i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_P332578347t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048,hypothesis,
! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_P229966473l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_Lab____,axiom,
is_fun961089132t_bool(lab) ).
fof(gsy_v_Lba____,axiom,
is_fun961089132t_bool(lba) ).
fof(gsy_v_a____,axiom,
is_Arr1861959080le_alt(a) ).
fof(gsy_v_b____,axiom,
is_Arr1861959080le_alt(b) ).
fof(gsy_v_c____,hypothesis,
is_Arr1861959080le_alt(c) ).
fof(gsy_v_d____,hypothesis,
is_Arr1861959080le_alt(d) ).
fof(gsy_v_e____,axiom,
is_Arr1861959080le_alt(e) ).
%----Relevant facts (1200)
fof(fact_0_assms_I3_J,axiom,
hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,f)) ).
fof(fact_1_u,axiom,
hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,f)) ).
fof(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
fof(fact_3__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,p),arrow_1721807329e_Prof)) ).
fof(fact_4_in__mkbot,axiom,
! [X_2,Y_2,L_3,Z_2] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2)
& is_Arr1861959080le_alt(Z_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),Z_2)))
<=> ( Y_2 != Z_2
& ( X_2 = Z_2
=> X_2 != Y_2 )
& ( X_2 != Z_2
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) ) ) ) ) ).
fof(fact_5_in__mktop,axiom,
! [X_2,Y_2,L_3,Z_2] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2)
& is_Arr1861959080le_alt(Z_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),Z_2)))
<=> ( X_2 != Z_2
& ( Y_2 = Z_2
=> X_2 != Y_2 )
& ( Y_2 != Z_2
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) ) ) ) ) ).
fof(fact_6__C2_C,axiom,
! [P_1,Pa,A_34,B_32,Aa,Ba] :
( ( is_Arr1861959080le_alt(A_34)
& is_Arr1861959080le_alt(B_32)
& is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( A_34 != B_32
=> ( Aa != B_32
=> ( Ba != A_34
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) ) ) ) ) ) ) ) ) ) ).
fof(fact_7__C1_C,axiom,
! [P_1,Pa,A_34,B_32,Aa,Ba] :
( ( is_Arr1861959080le_alt(A_34)
& is_Arr1861959080le_alt(B_32)
& is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( A_34 != B_32
=> ( Aa != B_32
=> ( Ba != A_34
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) ) ) ) ) ) ) ) ) ) ).
fof(fact_8__C4_C,axiom,
! [P_1,Pa,Ca,Aa,Ba] :
( ( is_Arr1861959080le_alt(Ca)
& is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( Ba != Ca
=> ( Aa != Ca
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_f412050202t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).
fof(fact_9_pairwise__neutrality,axiom,
! [P_1,Pa,A_34,B_32,Aa,Ba] :
( ( is_Arr1861959080le_alt(A_34)
& is_Arr1861959080le_alt(B_32)
& is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( A_34 != B_32
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) ) ) ) ) ) ) ) ).
fof(fact_10__C3_C,axiom,
! [P_1,Pa,Aa,Ba] :
( ( is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_f412050202t_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_1] :
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,I_1)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> ( ( hAPP_A1637648121di_nat(h,I_1) = n
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e))) )
& ( hAPP_A1637648121di_nat(h,I_1) != n
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ).
fof(fact_14_PW,axiom,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ) ).
fof(fact_15_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P606313927t_bool(Pa,X1))
<=> ! [A_27,B_25] :
( ( is_Arr1861959080le_alt(A_27)
& is_Arr1861959080le_alt(B_25) )
=> hBOOL(hAPP_P606313927t_bool(Pa,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25))) ) ) ).
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_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))),arrow_1721807329e_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ).
fof(fact_19_n_I1_J,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ).
fof(fact_20_injh,axiom,
hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(h),top_to1576102282i_bool)) ).
fof(fact_21_Pair__inject,axiom,
! [A_36,B_34,A_35,B_33] :
( ( is_Arr1861959080le_alt(A_36)
& is_Arr1861959080le_alt(B_34)
& is_Arr1861959080le_alt(A_35)
& is_Arr1861959080le_alt(B_33) )
=> ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_36),B_34) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_35),B_33)
=> ~ ( A_36 = A_35
=> B_34 != B_33 ) ) ) ).
fof(fact_22_Pair__eq,axiom,
! [Aa,Ba,A_34,B_32] :
( ( is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba)
& is_Arr1861959080le_alt(A_34)
& is_Arr1861959080le_alt(B_32) )
=> ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)
<=> ( Aa = A_34
& Ba = B_32 ) ) ) ).
fof(fact_23_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,Fa))
<=> ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
=> ! [Xa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Xa),arrow_1721807329e_Prof))
=> ! [A_27,B_25] :
( ( is_Arr1861959080le_alt(A_27)
& is_Arr1861959080le_alt(B_25) )
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(Xa,I_1))) ) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,Xa))) ) ) ) ) ) ) ).
fof(fact_24_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,Fa))
<=> ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
=> ! [A_27,B_25] :
( ( is_Arr1861959080le_alt(A_27)
& is_Arr1861959080le_alt(B_25) )
=> ( ! [I_1] :
( is_Arr43961803e_indi(I_1)
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1))) ) ) ) ) ).
fof(fact_25_top1I,axiom,
! [X_2] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2)) ).
fof(fact_26_top1I,axiom,
! [X_2] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2)) ).
fof(fact_27_top1I,axiom,
! [X_2] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2)) ).
fof(fact_28_top1I,axiom,
! [X_2] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2)) ).
fof(fact_29_top1I,axiom,
! [X_2] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2)) ).
fof(fact_30_top1I,axiom,
! [X_2] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)) ).
fof(fact_31_top1I,axiom,
! [X_2] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)) ).
fof(fact_32_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).
fof(fact_33_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_bool)) ).
fof(fact_34_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)) ).
fof(fact_35_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool)) ).
fof(fact_36_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool)) ).
fof(fact_37_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool)) ).
fof(fact_38_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_bool)) ).
fof(fact_39_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).
fof(fact_40_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).
fof(fact_41_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_bool)) ).
fof(fact_42_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)) ).
fof(fact_43_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool)) ).
fof(fact_44_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool)) ).
fof(fact_45_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool)) ).
fof(fact_46_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_bool)) ).
fof(fact_47_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).
fof(fact_48_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_49_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_50_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_51_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_52_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_53_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_54_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_55_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),Aa)) ).
fof(fact_56_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),Aa)) ).
fof(fact_57_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),Aa)) ).
fof(fact_58_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)) ).
fof(fact_59_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),Aa)) ).
fof(fact_60_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),Aa)) ).
fof(fact_61_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa)) ).
fof(fact_62_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)) ).
fof(fact_63_less__top,axiom,
! [Aa] :
( is_fun279392540l_bool(Aa)
=> ( Aa != top_to1853035173l_bool
<=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),top_to1853035173l_bool)) ) ) ).
fof(fact_64_less__top,axiom,
! [Aa] :
( is_fun288122577l_bool(Aa)
=> ( Aa != top_to522745736l_bool
<=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),top_to522745736l_bool)) ) ) ).
fof(fact_65_less__top,axiom,
! [Aa] :
( is_fun158382675l_bool(Aa)
=> ( Aa != top_to1714702858l_bool
<=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),top_to1714702858l_bool)) ) ) ).
fof(fact_66_less__top,axiom,
! [Aa] :
( ~ ( hBOOL(Aa)
<=> hBOOL(top_top_bool) )
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) ) ).
fof(fact_67_less__top,axiom,
! [Aa] :
( is_fun961089132t_bool(Aa)
=> ( Aa != top_to565915683t_bool
<=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),top_to565915683t_bool)) ) ) ).
fof(fact_68_less__top,axiom,
! [Aa] :
( is_fun1236654035i_bool(Aa)
=> ( Aa != top_to1576102282i_bool
<=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),top_to1576102282i_bool)) ) ) ).
fof(fact_69_less__top,axiom,
! [Aa] :
( Aa != top_top_fun_nat_bool
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool)) ) ).
fof(fact_70_less__top,axiom,
! [Aa] :
( is_fun1568535512t_bool(Aa)
=> ( Aa != top_to1257323279t_bool
<=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool)) ) ) ).
fof(fact_71_assms_I1_J,axiom,
hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,f),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ).
fof(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba)))) ) ).
fof(fact_73_dictator__def,axiom,
! [Fa,I] :
( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I))
<=> ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
=> hAPP_f412050202t_bool(Fa,X_1) = hAPP_A1677245848t_bool(X_1,I) ) ) ).
fof(fact_74__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lab),arrow_1681063817le_Lin)) ).
fof(fact_75__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lba),arrow_1681063817le_Lin)) ).
fof(fact_76__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ).
fof(fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ).
fof(fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ).
fof(fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ).
fof(fact_81_PiProf,axiom,
! [Na] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_1721807329e_Prof)) ).
fof(fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
~ ! [Lab] :
( is_fun961089132t_bool(Lab)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),Lab))
=> ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Lab),arrow_1681063817le_Lin)) ) ) ).
fof(fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
~ ! [Lba] :
( is_fun961089132t_bool(Lba)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),Lba))
=> ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Lba),arrow_1681063817le_Lin)) ) ) ).
fof(fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_1] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> ( ( hAPP_A1637648121di_nat(h,I_1) = n
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e))) )
& ( hAPP_A1637648121di_nat(h,I_1) != n
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ) ) ) ).
fof(fact_85_n_I2_J,axiom,
! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba)))) ) ).
fof(fact_86_notin__Lin__iff,axiom,
! [X_2,Y_2,L_3] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> ( X_2 != Y_2
=> ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_2),X_2)),L_3)) ) ) ) ) ).
fof(fact_87_Lin__irrefl,axiom,
! [Aa,Ba,L_3] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),L_3))
=> ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),L_3)) ) ) ).
fof(fact_88_mktop__Lin,axiom,
! [X_2,L_3] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),X_2)),arrow_1681063817le_Lin)) ) ).
fof(fact_89_mkbot__Lin,axiom,
! [X_2,L_3] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),X_2)),arrow_1681063817le_Lin)) ) ).
fof(fact_90_above__Lin,axiom,
! [L_3,X_2,Y_2] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2) )
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),X_2),Y_2)),arrow_1681063817le_Lin)) ) ) ) ).
fof(fact_91_const__Lin__Prof,axiom,
! [L_3] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,L_3)),arrow_1721807329e_Prof)) ) ).
fof(fact_92_linorder__cases,axiom,
! [X_32,Y_30] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_30))
=> ( X_32 != Y_30
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_32)) ) ) ).
fof(fact_93_order__less__asym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).
fof(fact_94_order__less__asym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).
fof(fact_95_order__less__asym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ) ).
fof(fact_96_order__less__asym,axiom,
! [X_31,Y_29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_29))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_31)) ) ).
fof(fact_97_xt1_I10_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ) ).
fof(fact_98_xt1_I10_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ) ).
fof(fact_99_xt1_I10_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2)) ) ) ).
fof(fact_100_xt1_I10_J,axiom,
! [Z_9,Y_28,X_30] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_28),X_30))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_28))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_30)) ) ) ).
fof(fact_101_order__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ) ).
fof(fact_102_order__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ) ).
fof(fact_103_order__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2)) ) ) ).
fof(fact_104_order__less__trans,axiom,
! [Z_8,X_29,Y_27] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Y_27))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_27),Z_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Z_8)) ) ) ).
fof(fact_105_xt1_I2_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ) ).
fof(fact_106_xt1_I2_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ) ).
fof(fact_107_xt1_I2_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Aa)) ) ) ).
fof(fact_108_xt1_I2_J,axiom,
! [C_24,B_31,A_33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_33))
=> ( B_31 = C_24
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_24),A_33)) ) ) ).
fof(fact_109_ord__less__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ) ).
fof(fact_110_ord__less__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ) ).
fof(fact_111_ord__less__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ca)) ) ) ).
fof(fact_112_ord__less__eq__trans,axiom,
! [C_23,A_32,B_30] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),B_30))
=> ( B_30 = C_23
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),C_23)) ) ) ).
fof(fact_113_xt1_I1_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ) ).
fof(fact_114_xt1_I1_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ) ).
fof(fact_115_xt1_I1_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Aa)) ) ) ).
fof(fact_116_xt1_I1_J,axiom,
! [C_22,A_31,B_29] :
( A_31 = B_29
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),B_29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),A_31)) ) ) ).
fof(fact_117_ord__eq__less__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ) ).
fof(fact_118_ord__eq__less__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ) ).
fof(fact_119_ord__eq__less__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ca)) ) ) ).
fof(fact_120_ord__eq__less__trans,axiom,
! [C_21,A_30,B_28] :
( A_30 = B_28
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_28),C_21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),C_21)) ) ) ).
fof(fact_121_xt1_I9_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ).
fof(fact_122_xt1_I9_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ).
fof(fact_123_xt1_I9_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ) ).
fof(fact_124_xt1_I9_J,axiom,
! [B_27,A_29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_27),A_29))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_27)) ) ).
fof(fact_125_order__less__asym_H,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ).
fof(fact_126_order__less__asym_H,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ).
fof(fact_127_order__less__asym_H,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ) ).
fof(fact_128_order__less__asym_H,axiom,
! [A_28,B_26] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_26))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_26),A_28)) ) ).
fof(fact_129_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_130_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_131_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_132_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_133_order__less__imp__not__eq2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> Y_2 != X_2 ) ).
fof(fact_134_order__less__imp__not__eq2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> Y_2 != X_2 ) ).
fof(fact_135_order__less__imp__not__eq2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> Y_2 != X_2 ) ).
fof(fact_136_order__less__imp__not__eq2,axiom,
! [X_28,Y_26] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_26))
=> Y_26 != X_28 ) ).
fof(fact_137_order__less__imp__not__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_138_order__less__imp__not__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_139_order__less__imp__not__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_140_order__less__imp__not__eq,axiom,
! [X_27,Y_25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_25))
=> X_27 != Y_25 ) ).
fof(fact_141_order__less__imp__not__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).
fof(fact_142_order__less__imp__not__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).
fof(fact_143_order__less__imp__not__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ) ).
fof(fact_144_order__less__imp__not__less,axiom,
! [X_26,Y_24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_24))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_26)) ) ).
fof(fact_145_order__less__not__sym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).
fof(fact_146_order__less__not__sym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).
fof(fact_147_order__less__not__sym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ) ).
fof(fact_148_order__less__not__sym,axiom,
! [X_25,Y_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_23))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_25)) ) ).
fof(fact_149_less__imp__neq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_150_less__imp__neq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_151_less__imp__neq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_152_less__imp__neq,axiom,
! [X_24,Y_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_22))
=> X_24 != Y_22 ) ).
fof(fact_153_linorder__neqE,axiom,
! [X_23,Y_21] :
( X_23 != Y_21
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_23)) ) ) ).
fof(fact_154_linorder__antisym__conv3,axiom,
! [Y_2,X_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
<=> X_2 = Y_2 ) ) ).
fof(fact_155_linorder__less__linear,axiom,
! [X_22,Y_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_20))
| X_22 = Y_20
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_22)) ) ).
fof(fact_156_not__less__iff__gr__or__eq,axiom,
! [X_2,Y_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
| X_2 = Y_2 ) ) ).
fof(fact_157_linorder__neq__iff,axiom,
! [X_2,Y_2] :
( X_2 != Y_2
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ) ).
fof(fact_158_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)) ).
fof(fact_159_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)) ).
fof(fact_160_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),X_2)) ).
fof(fact_161_order__less__irrefl,axiom,
! [X_21] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)) ).
fof(fact_162_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
<=> hBOOL(hAPP_A1785763630i_bool(A,X_2)) ) ).
fof(fact_163_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
<=> hBOOL(hAPP_bool_bool(A,X_2)) ) ).
fof(fact_164_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
<=> hBOOL(hAPP_P1676879539t_bool(A,X_2)) ) ).
fof(fact_165_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
<=> hBOOL(hAPP_P606313927t_bool(A,X_2)) ) ).
fof(fact_166_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
<=> hBOOL(hAPP_f965095724l_bool(A,X_2)) ) ).
fof(fact_167_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
<=> hBOOL(hAPP_f312250286l_bool(A,X_2)) ) ).
fof(fact_168_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
<=> hBOOL(hAPP_f592646513l_bool(A,X_2)) ) ).
fof(fact_169_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
<=> hBOOL(hAPP_nat_bool(A,X_2)) ) ).
fof(fact_170_Collect__def,axiom,
! [Pa] :
( is_fun1568535512t_bool(Pa)
=> hAPP_f427533077t_bool(collect_Product_unit,Pa) = Pa ) ).
fof(fact_171_Collect__def,axiom,
! [Pa] :
( is_fun1236654035i_bool(Pa)
=> hAPP_f580451669i_bool(collec1611109369e_indi,Pa) = Pa ) ).
fof(fact_172_Collect__def,axiom,
! [Pa] : hAPP_f800510211t_bool(collect_nat,Pa) = Pa ).
fof(fact_173_UNIV__def,axiom,
top_to1853035173l_bool = hAPP_f111185985l_bool(collec1553055422t_bool,hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,fTrue)) ).
fof(fact_174_UNIV__def,axiom,
top_to522745736l_bool = hAPP_f146009813l_bool(collec1063742455t_bool,hAPP_b1048178734l_bool(cOMBK_272667621t_bool,fTrue)) ).
fof(fact_175_UNIV__def,axiom,
top_to1714702858l_bool = hAPP_f1765205l_bool(collec418781817t_bool,hAPP_b517355696l_bool(cOMBK_1626390631t_bool,fTrue)) ).
fof(fact_176_UNIV__def,axiom,
top_to565915683t_bool = hAPP_f515126293t_bool(collec2096990994le_alt,hAPP_b1703662281t_bool(cOMBK_306730240le_alt,fTrue)) ).
fof(fact_177_UNIV__def,axiom,
top_to1576102282i_bool = hAPP_f580451669i_bool(collec1611109369e_indi,hAPP_b1337486384i_bool(cOMBK_575487463e_indi,fTrue)) ).
fof(fact_178_UNIV__def,axiom,
top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)) ).
fof(fact_179_UNIV__def,axiom,
top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)) ).
fof(fact_180_in__above,axiom,
! [X_2,Y_2,L_3,Aa,Ba] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2)
& is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),Aa),Ba)))
<=> ( X_2 != Y_2
& ( X_2 = Ba
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_2)),L_3)) )
& ( X_2 != Ba
=> ( ( Y_2 = Ba
=> ( X_2 = Aa
| hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Aa)),L_3)) ) )
& ( Y_2 != Ba
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ) ).
fof(fact_181_pred__equals__eq2,axiom,
! [S_1,R_1] :
( ( is_fun961089132t_bool(S_1)
& is_fun961089132t_bool(R_1) )
=> ( ! [X_1,Xa] :
( ( is_Arr1861959080le_alt(X_1)
& is_Arr1861959080le_alt(Xa) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1)) ) )
<=> R_1 = S_1 ) ) ).
fof(fact_182_dictatorI,axiom,
! [I,Fa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Fa),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin))))
=> ( ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
=> ! [A_27,B_25] :
( ( is_Arr1861959080le_alt(A_27)
& is_Arr1861959080le_alt(B_25) )
=> ( A_27 != B_25
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I)))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1))) ) ) ) )
=> hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I)) ) ) ).
fof(fact_183_n_I3_J,axiom,
hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ).
fof(fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ) ).
fof(fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
! [I_1] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
=> ( ( hAPP_A1637648121di_nat(h,I_1) = n
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e))) )
& ( hAPP_A1637648121di_nat(h,I_1) != n
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) ) ) ) ).
fof(fact_186_inv__f__eq,axiom,
! [X_2,Y_2,F] :
( is_Arr43961803e_indi(X_2)
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
=> ( hAPP_A1637648121di_nat(F,X_2) = Y_2
=> hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,F),Y_2) = X_2 ) ) ) ).
fof(fact_187_inv__f__eq,axiom,
! [X_2,Y_2,F] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
=> ( hAPP_nat_nat(F,X_2) = Y_2
=> hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),Y_2) = X_2 ) ) ).
fof(fact_188_inv__f__f,axiom,
! [X_2,F] :
( is_Arr43961803e_indi(X_2)
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
=> hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,F),hAPP_A1637648121di_nat(F,X_2)) = X_2 ) ) ).
fof(fact_189_inv__f__f,axiom,
! [X_2,F] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
=> hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),hAPP_nat_nat(F,X_2)) = X_2 ) ).
fof(fact_190_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ) ).
fof(fact_191_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ) ).
fof(fact_192_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_193_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),hAPP_P1341894483t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_194_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ) ).
fof(fact_195_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_196_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),hAPP_P254387896l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_197_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ) ).
fof(fact_198_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_199_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),hAPP_P1171466554l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_200_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_201_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),hAPP_P1294997365l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_202_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B)))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),hAPP_A2046586321t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ) ).
fof(fact_203_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_204_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_205_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ) ).
fof(fact_206_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),hAPP_P332578347t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ) ).
fof(fact_207_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ) ).
fof(fact_208_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ) ).
fof(fact_209_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),hAPP_f1891021702t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ) ).
fof(fact_210_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ) ).
fof(fact_211_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ) ).
fof(fact_212_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),hAPP_f1866147972t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ) ).
fof(fact_213_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ) ).
fof(fact_214_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ) ).
fof(fact_215_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),hAPP_f1710744577t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ) ).
fof(fact_216_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),hAPP_n821919323i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).
fof(fact_217_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).
fof(fact_218_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).
fof(fact_219_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ) ).
fof(fact_220_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ) ).
fof(fact_221_complete__Lin,axiom,
! [Aa,Ba] :
( ( is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ? [X_1] :
( is_fun961089132t_bool(X_1)
& hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),arrow_1681063817le_Lin))
& hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),X_1)) ) ) ) ).
fof(fact_222_Pi__UNIV,axiom,
! [A] : pi_Pro666468413t_bool(A,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool ).
fof(fact_223_Pi__UNIV,axiom,
! [A] : pi_fun150026276t_bool(A,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool ).
fof(fact_224_Pi__UNIV,axiom,
! [A] : pi_Arr990697634t_bool(A,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool ).
fof(fact_225_in__below,axiom,
! [X_2,Y_2,L_3,Aa,Ba] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2)
& is_Arr1861959080le_alt(Aa)
& is_Arr1861959080le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),arrow_1539419881_below(L_3,Aa,Ba)))
<=> ( X_2 != Y_2
& ( Y_2 = Aa
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Ba)),L_3)) )
& ( Y_2 != Aa
=> ( ( X_2 = Aa
=> ( Y_2 = Ba
| hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Y_2)),L_3)) ) )
& ( X_2 != Aa
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ) ).
fof(fact_226_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),X_2)) ).
fof(fact_227_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),X_2)) ).
fof(fact_228_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),X_2)) ).
fof(fact_229_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),X_2)) ).
fof(fact_230_order__refl,axiom,
! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)) ).
fof(fact_231_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),X_2)) ).
fof(fact_232_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),X_2)) ).
fof(fact_233_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),X_2)) ).
fof(fact_234_order__refl,axiom,
! [X_20] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)) ).
fof(fact_235_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)) ).
fof(fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
? [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
& ! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
& hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba)))) ) ).
fof(fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
~ ! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
=> ( ! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
=> ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba)))) ) ) ).
fof(fact_238_linorder__le__cases,axiom,
! [X_19,Y_19] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_19)) ) ).
fof(fact_239_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f592646513l_bool(G,X_2))) ) ).
fof(fact_240_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f312250286l_bool(G,X_2))) ) ).
fof(fact_241_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f965095724l_bool(G,X_2))) ) ).
fof(fact_242_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P606313927t_bool(G,X_2))) ) ).
fof(fact_243_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_2)),hAPP_A1785763630i_bool(G,X_2))) ) ).
fof(fact_244_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2))) ) ).
fof(fact_245_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
=> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_2)),hAPP_A1664620203t_bool(G,X_2))) ) ).
fof(fact_246_le__funE,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).
fof(fact_247_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),X_2)) ) ) ).
fof(fact_248_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),X_2)) ) ) ).
fof(fact_249_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),X_2)) ) ) ).
fof(fact_250_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),X_2)) ) ) ).
fof(fact_251_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),X_2)) ) ) ).
fof(fact_252_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),X_2)) ) ) ).
fof(fact_253_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),X_2)) ) ) ).
fof(fact_254_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),X_2)) ) ) ).
fof(fact_255_xt1_I6_J,axiom,
! [Z_7,Y_18,X_18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_18))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),X_18)) ) ) ).
fof(fact_256_xt1_I6_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_2)) ) ) ).
fof(fact_257_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun279392540l_bool(Y_2)
& is_fun279392540l_bool(X_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_258_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun158382675l_bool(Y_2)
& is_fun158382675l_bool(X_2) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_259_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun288122577l_bool(Y_2)
& is_fun288122577l_bool(X_2) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_260_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun961089132t_bool(Y_2)
& is_fun961089132t_bool(X_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_261_xt1_I5_J,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_262_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun1236654035i_bool(Y_2)
& is_fun1236654035i_bool(X_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_263_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun1568535512t_bool(Y_2)
& is_fun1568535512t_bool(X_2) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_264_xt1_I5_J,axiom,
! [Y_2,X_2] :
( ( is_fun2093718614t_bool(Y_2)
& is_fun2093718614t_bool(X_2) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_265_xt1_I5_J,axiom,
! [Y_17,X_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_17))
=> X_17 = Y_17 ) ) ).
fof(fact_266_xt1_I5_J,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
=> X_2 = Y_2 ) ) ).
fof(fact_267_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Z_2)) ) ) ).
fof(fact_268_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Z_2)) ) ) ).
fof(fact_269_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Z_2)) ) ) ).
fof(fact_270_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Z_2)) ) ) ).
fof(fact_271_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_2)) ) ) ).
fof(fact_272_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Z_2)) ) ) ).
fof(fact_273_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Z_2)) ) ) ).
fof(fact_274_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Z_2)) ) ) ).
fof(fact_275_order__trans,axiom,
! [Z_6,X_16,Y_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Z_6)) ) ) ).
fof(fact_276_order__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_2)) ) ) ).
fof(fact_277_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun279392540l_bool(X_2)
& is_fun279392540l_bool(Y_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_278_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun158382675l_bool(X_2)
& is_fun158382675l_bool(Y_2) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_279_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun288122577l_bool(X_2)
& is_fun288122577l_bool(Y_2) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_280_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun961089132t_bool(X_2)
& is_fun961089132t_bool(Y_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_281_order__antisym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_282_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun1236654035i_bool(X_2)
& is_fun1236654035i_bool(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_283_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun1568535512t_bool(X_2)
& is_fun1568535512t_bool(Y_2) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_284_order__antisym,axiom,
! [X_2,Y_2] :
( ( is_fun2093718614t_bool(X_2)
& is_fun2093718614t_bool(Y_2) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ) ).
fof(fact_285_order__antisym,axiom,
! [X_15,Y_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_15))
=> X_15 = Y_15 ) ) ).
fof(fact_286_order__antisym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ).
fof(fact_287_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Aa)) ) ) ).
fof(fact_288_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Aa)) ) ) ).
fof(fact_289_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Aa)) ) ) ).
fof(fact_290_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Aa)) ) ) ).
fof(fact_291_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
=> ( ( hBOOL(Ba)
<=> hBOOL(Ca) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ) ).
fof(fact_292_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Aa)) ) ) ).
fof(fact_293_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa)) ) ) ).
fof(fact_294_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Aa)) ) ) ).
fof(fact_295_xt1_I4_J,axiom,
! [C_20,B_24,A_26] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_26))
=> ( B_24 = C_20
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_26)) ) ) ).
fof(fact_296_xt1_I4_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ) ).
fof(fact_297_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ca)) ) ) ).
fof(fact_298_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ca)) ) ) ).
fof(fact_299_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ca)) ) ) ).
fof(fact_300_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ca)) ) ) ).
fof(fact_301_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
=> ( ( hBOOL(Ba)
<=> hBOOL(Ca) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ) ).
fof(fact_302_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ca)) ) ) ).
fof(fact_303_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca)) ) ) ).
fof(fact_304_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ca)) ) ) ).
fof(fact_305_ord__le__eq__trans,axiom,
! [C_19,A_25,B_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_23))
=> ( B_23 = C_19
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),C_19)) ) ) ).
fof(fact_306_ord__le__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ) ).
fof(fact_307_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Aa)) ) ) ).
fof(fact_308_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Aa)) ) ) ).
fof(fact_309_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Aa)) ) ) ).
fof(fact_310_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Aa)) ) ) ).
fof(fact_311_xt1_I3_J,axiom,
! [Ca,Ba,Aa] :
( ( hBOOL(Aa)
<=> hBOOL(Ba) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ) ).
fof(fact_312_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Aa)) ) ) ).
fof(fact_313_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa)) ) ) ).
fof(fact_314_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Aa)) ) ) ).
fof(fact_315_xt1_I3_J,axiom,
! [C_18,A_24,B_22] :
( A_24 = B_22
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_24)) ) ) ).
fof(fact_316_xt1_I3_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ) ).
fof(fact_317_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ca)) ) ) ).
fof(fact_318_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ca)) ) ) ).
fof(fact_319_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ca)) ) ) ).
fof(fact_320_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ca)) ) ) ).
fof(fact_321_ord__eq__le__trans,axiom,
! [Ca,Ba,Aa] :
( ( hBOOL(Aa)
<=> hBOOL(Ba) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ) ).
fof(fact_322_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ca)) ) ) ).
fof(fact_323_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca)) ) ) ).
fof(fact_324_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ca)) ) ) ).
fof(fact_325_ord__eq__le__trans,axiom,
! [C_17,A_23,B_21] :
( A_23 = B_21
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),C_17)) ) ) ).
fof(fact_326_ord__eq__le__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ) ).
fof(fact_327_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun279392540l_bool(Y_2)
& is_fun279392540l_bool(X_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_328_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun158382675l_bool(Y_2)
& is_fun158382675l_bool(X_2) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_329_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun288122577l_bool(Y_2)
& is_fun288122577l_bool(X_2) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_330_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun961089132t_bool(Y_2)
& is_fun961089132t_bool(X_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_331_order__antisym__conv,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
<=> ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_332_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun1236654035i_bool(Y_2)
& is_fun1236654035i_bool(X_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_333_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun1568535512t_bool(Y_2)
& is_fun1568535512t_bool(X_2) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_334_order__antisym__conv,axiom,
! [Y_2,X_2] :
( ( is_fun2093718614t_bool(Y_2)
& is_fun2093718614t_bool(X_2) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ) ).
fof(fact_335_order__antisym__conv,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
<=> X_2 = Y_2 ) ) ).
fof(fact_336_order__antisym__conv,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
<=> X_2 = Y_2 ) ) ).
fof(fact_337_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f592646513l_bool(G,X_2))) ) ).
fof(fact_338_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f312250286l_bool(G,X_2))) ) ).
fof(fact_339_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f965095724l_bool(G,X_2))) ) ).
fof(fact_340_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P606313927t_bool(G,X_2))) ) ).
fof(fact_341_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_2)),hAPP_A1785763630i_bool(G,X_2))) ) ).
fof(fact_342_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2))) ) ).
fof(fact_343_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
=> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_2)),hAPP_A1664620203t_bool(G,X_2))) ) ).
fof(fact_344_le__funD,axiom,
! [X_2,F,G] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).
fof(fact_345_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) ).
fof(fact_346_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) ).
fof(fact_347_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) ).
fof(fact_348_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) ).
fof(fact_349_order__eq__refl,axiom,
! [Y_2,X_2] :
( ( hBOOL(X_2)
<=> hBOOL(Y_2) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).
fof(fact_350_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) ).
fof(fact_351_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ).
fof(fact_352_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) ).
fof(fact_353_order__eq__refl,axiom,
! [X_14,Y_14] :
( X_14 = Y_14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_14)) ) ).
fof(fact_354_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ).
fof(fact_355_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun279392540l_bool(X_2)
& is_fun279392540l_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
& hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2)) ) ) ) ).
fof(fact_356_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun158382675l_bool(X_2)
& is_fun158382675l_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
& hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2)) ) ) ) ).
fof(fact_357_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun288122577l_bool(X_2)
& is_fun288122577l_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
& hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2)) ) ) ) ).
fof(fact_358_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun961089132t_bool(X_2)
& is_fun961089132t_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
& hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2)) ) ) ) ).
fof(fact_359_order__eq__iff,axiom,
! [Y_2,X_2] :
( ( hBOOL(X_2)
<=> hBOOL(Y_2) )
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
& hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).
fof(fact_360_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun1236654035i_bool(X_2)
& is_fun1236654035i_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
& hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2)) ) ) ) ).
fof(fact_361_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun1568535512t_bool(X_2)
& is_fun1568535512t_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
& hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ) ) ) ).
fof(fact_362_order__eq__iff,axiom,
! [X_2,Y_2] :
( ( is_fun2093718614t_bool(X_2)
& is_fun2093718614t_bool(Y_2) )
=> ( X_2 = Y_2
<=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
& hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2)) ) ) ) ).
fof(fact_363_order__eq__iff,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).
fof(fact_364_order__eq__iff,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ) ) ).
fof(fact_365_linorder__linear,axiom,
! [X_13,Y_13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),Y_13))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13)) ) ).
fof(fact_366_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
<=> ! [X_1] :
( is_fun961089132t_bool(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1))) ) ) ).
fof(fact_367_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
<=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1))) ) ).
fof(fact_368_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
<=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1))) ) ).
fof(fact_369_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
<=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1))) ) ).
fof(fact_370_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
<=> ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1))) ) ) ).
fof(fact_371_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
<=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1))) ) ).
fof(fact_372_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
<=> ! [X_1] :
( is_Arr1861959080le_alt(X_1)
=> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1))) ) ) ).
fof(fact_373_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
<=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))) ) ).
fof(fact_374_linorder__not__less,axiom,
! [X_2,Y_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ).
fof(fact_375_linorder__not__le,axiom,
! [X_2,Y_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ).
fof(fact_376_linorder__le__less__linear,axiom,
! [X_12,Y_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_12)) ) ).
fof(fact_377_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun1568535512t_bool(X_2)
& is_fun1568535512t_bool(Y_2) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_378_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun1236654035i_bool(X_2)
& is_fun1236654035i_bool(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_379_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun279392540l_bool(X_2)
& is_fun279392540l_bool(Y_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_380_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun158382675l_bool(X_2)
& is_fun158382675l_bool(Y_2) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_381_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun288122577l_bool(X_2)
& is_fun288122577l_bool(Y_2) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_382_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun961089132t_bool(X_2)
& is_fun961089132t_bool(Y_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_383_order__less__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
& ~ ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_384_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun2093718614t_bool(X_2)
& is_fun2093718614t_bool(Y_2) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_385_order__less__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ).
fof(fact_386_order__less__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
& X_2 != Y_2 ) ) ).
fof(fact_387_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ) ) ).
fof(fact_388_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2)) ) ) ).
fof(fact_389_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2)) ) ) ).
fof(fact_390_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2)) ) ) ).
fof(fact_391_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2)) ) ) ).
fof(fact_392_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2)) ) ) ).
fof(fact_393_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
& ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).
fof(fact_394_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2)) ) ) ).
fof(fact_395_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ) ) ).
fof(fact_396_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).
fof(fact_397_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun1568535512t_bool(X_2)
& is_fun1568535512t_bool(Y_2) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_398_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun1236654035i_bool(X_2)
& is_fun1236654035i_bool(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_399_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun279392540l_bool(X_2)
& is_fun279392540l_bool(Y_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_400_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun158382675l_bool(X_2)
& is_fun158382675l_bool(Y_2) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_401_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun288122577l_bool(X_2)
& is_fun288122577l_bool(Y_2) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_402_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun961089132t_bool(X_2)
& is_fun961089132t_bool(Y_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_403_order__le__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
| ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_404_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun2093718614t_bool(X_2)
& is_fun2093718614t_bool(Y_2) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_405_order__le__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ).
fof(fact_406_order__le__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
| X_2 = Y_2 ) ) ).
fof(fact_407_leI,axiom,
! [X_11,Y_11] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_11)) ) ).
fof(fact_408_not__leE,axiom,
! [Y_10,X_10] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10)) ) ).
fof(fact_409_linorder__antisym__conv1,axiom,
! [X_2,Y_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
<=> X_2 = Y_2 ) ) ).
fof(fact_410_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun1568535512t_bool(Aa)
& is_fun1568535512t_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ) ).
fof(fact_411_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun1236654035i_bool(Aa)
& is_fun1236654035i_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ) ) ) ).
fof(fact_412_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun279392540l_bool(Aa)
& is_fun279392540l_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),Ba)) ) ) ) ).
fof(fact_413_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun158382675l_bool(Aa)
& is_fun158382675l_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),Ba)) ) ) ) ).
fof(fact_414_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun288122577l_bool(Aa)
& is_fun288122577l_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),Ba)) ) ) ) ).
fof(fact_415_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun961089132t_bool(Aa)
& is_fun961089132t_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),Ba)) ) ) ) ).
fof(fact_416_order__neq__le__trans,axiom,
! [Ba,Aa] :
( ~ ( hBOOL(Aa)
<=> hBOOL(Ba) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ) ).
fof(fact_417_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun2093718614t_bool(Aa)
& is_fun2093718614t_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),Ba)) ) ) ) ).
fof(fact_418_order__neq__le__trans,axiom,
! [Aa,Ba] :
( Aa != Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ) ).
fof(fact_419_order__neq__le__trans,axiom,
! [A_22,B_20] :
( A_22 != B_20
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_22),B_20))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_22),B_20)) ) ) ).
fof(fact_420_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun1568535512t_bool(Aa)
& is_fun1568535512t_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ) ).
fof(fact_421_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun1236654035i_bool(Aa)
& is_fun1236654035i_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ) ) ) ).
fof(fact_422_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun279392540l_bool(Aa)
& is_fun279392540l_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ba),Aa)) ) ) ) ).
fof(fact_423_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun158382675l_bool(Aa)
& is_fun158382675l_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ba),Aa)) ) ) ) ).
fof(fact_424_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun288122577l_bool(Aa)
& is_fun288122577l_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ba),Aa)) ) ) ) ).
fof(fact_425_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun961089132t_bool(Aa)
& is_fun961089132t_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ba),Aa)) ) ) ) ).
fof(fact_426_xt1_I12_J,axiom,
! [Ba,Aa] :
( ~ ( hBOOL(Aa)
<=> hBOOL(Ba) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ) ).
fof(fact_427_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun2093718614t_bool(Aa)
& is_fun2093718614t_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ba),Aa)) ) ) ) ).
fof(fact_428_xt1_I12_J,axiom,
! [Aa,Ba] :
( Aa != Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ) ).
fof(fact_429_xt1_I12_J,axiom,
! [A_21,B_19] :
( A_21 != B_19
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_21)) ) ) ).
fof(fact_430_leD,axiom,
! [Y_9,X_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_9))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9)) ) ).
fof(fact_431_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ).
fof(fact_432_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) ).
fof(fact_433_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) ).
fof(fact_434_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) ).
fof(fact_435_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) ).
fof(fact_436_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) ).
fof(fact_437_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).
fof(fact_438_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) ).
fof(fact_439_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ).
fof(fact_440_order__less__imp__le,axiom,
! [X_8,Y_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_8)) ) ).
fof(fact_441_linorder__antisym__conv2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
<=> X_2 = Y_2 ) ) ).
fof(fact_442_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun1568535512t_bool(X_2)
& is_fun1568535512t_bool(Y_2) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_443_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun1236654035i_bool(X_2)
& is_fun1236654035i_bool(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_444_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun279392540l_bool(X_2)
& is_fun279392540l_bool(Y_2) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_445_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun158382675l_bool(X_2)
& is_fun158382675l_bool(Y_2) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_446_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun288122577l_bool(X_2)
& is_fun288122577l_bool(Y_2) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_447_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun961089132t_bool(X_2)
& is_fun961089132t_bool(Y_2) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_448_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
| ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_449_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun2093718614t_bool(X_2)
& is_fun2093718614t_bool(Y_2) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_450_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ).
fof(fact_451_order__le__imp__less__or__eq,axiom,
! [X_7,Y_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_7))
| X_7 = Y_7 ) ) ).
fof(fact_452_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun1568535512t_bool(Aa)
& is_fun1568535512t_bool(Ba) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ) ).
fof(fact_453_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun1236654035i_bool(Aa)
& is_fun1236654035i_bool(Ba) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ) ) ) ).
fof(fact_454_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun279392540l_bool(Aa)
& is_fun279392540l_bool(Ba) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),Ba)) ) ) ) ).
fof(fact_455_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun158382675l_bool(Aa)
& is_fun158382675l_bool(Ba) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),Ba)) ) ) ) ).
fof(fact_456_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun288122577l_bool(Aa)
& is_fun288122577l_bool(Ba) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),Ba)) ) ) ) ).
fof(fact_457_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun961089132t_bool(Aa)
& is_fun961089132t_bool(Ba) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),Ba)) ) ) ) ).
fof(fact_458_order__le__neq__trans,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
=> ( ~ ( hBOOL(Aa)
<=> hBOOL(Ba) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ) ).
fof(fact_459_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun2093718614t_bool(Aa)
& is_fun2093718614t_bool(Ba) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),Ba)) ) ) ) ).
fof(fact_460_order__le__neq__trans,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ) ).
fof(fact_461_order__le__neq__trans,axiom,
! [A_20,B_18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_18))
=> ( A_20 != B_18
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_20),B_18)) ) ) ).
fof(fact_462_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun1568535512t_bool(Ba)
& is_fun1568535512t_bool(Aa) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ) ).
fof(fact_463_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun1236654035i_bool(Ba)
& is_fun1236654035i_bool(Aa) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ) ) ) ).
fof(fact_464_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun279392540l_bool(Ba)
& is_fun279392540l_bool(Aa) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ba),Aa)) ) ) ) ).
fof(fact_465_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun158382675l_bool(Ba)
& is_fun158382675l_bool(Aa) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ba),Aa)) ) ) ) ).
fof(fact_466_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun288122577l_bool(Ba)
& is_fun288122577l_bool(Aa) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ba),Aa)) ) ) ) ).
fof(fact_467_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun961089132t_bool(Ba)
& is_fun961089132t_bool(Aa) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ba),Aa)) ) ) ) ).
fof(fact_468_xt1_I11_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
=> ( ~ ( hBOOL(Aa)
<=> hBOOL(Ba) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ) ).
fof(fact_469_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun2093718614t_bool(Ba)
& is_fun2093718614t_bool(Aa) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ba),Aa)) ) ) ) ).
fof(fact_470_xt1_I11_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ) ).
fof(fact_471_xt1_I11_J,axiom,
! [B_17,A_19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_19))
=> ( A_19 != B_17
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_19)) ) ) ).
fof(fact_472_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ) ).
fof(fact_473_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2)) ) ) ).
fof(fact_474_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Z_2)) ) ) ).
fof(fact_475_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Z_2)) ) ) ).
fof(fact_476_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Z_2)) ) ) ).
fof(fact_477_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Z_2)) ) ) ).
fof(fact_478_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2)) ) ) ).
fof(fact_479_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Z_2)) ) ) ).
fof(fact_480_order__less__le__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ) ).
fof(fact_481_order__less__le__trans,axiom,
! [Z_5,X_6,Y_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_6))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Z_5)) ) ) ).
fof(fact_482_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ) ).
fof(fact_483_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2)) ) ) ).
fof(fact_484_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),X_2)) ) ) ).
fof(fact_485_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),X_2)) ) ) ).
fof(fact_486_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),X_2)) ) ) ).
fof(fact_487_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),X_2)) ) ) ).
fof(fact_488_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2)) ) ) ).
fof(fact_489_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),X_2)) ) ) ).
fof(fact_490_xt1_I7_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ) ).
fof(fact_491_xt1_I7_J,axiom,
! [Z_4,Y_5,X_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_5),X_5))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_4),Y_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_5)) ) ) ).
fof(fact_492_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ) ).
fof(fact_493_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2)) ) ) ).
fof(fact_494_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Z_2)) ) ) ).
fof(fact_495_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Z_2)) ) ) ).
fof(fact_496_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Y_2),Z_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Z_2)) ) ) ).
fof(fact_497_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Z_2)) ) ) ).
fof(fact_498_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2)) ) ) ).
fof(fact_499_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Z_2)) ) ) ).
fof(fact_500_order__le__less__trans,axiom,
! [Z_2,X_2,Y_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ) ).
fof(fact_501_order__le__less__trans,axiom,
! [Z_3,X_4,Y_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_4))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),Z_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Z_3)) ) ) ).
fof(fact_502_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ) ).
fof(fact_503_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2)) ) ) ).
fof(fact_504_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),X_2)) ) ) ).
fof(fact_505_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),X_2)) ) ) ).
fof(fact_506_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),Y_2))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),X_2)) ) ) ).
fof(fact_507_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),X_2)) ) ) ).
fof(fact_508_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2)) ) ) ).
fof(fact_509_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),X_2)) ) ) ).
fof(fact_510_xt1_I8_J,axiom,
! [Z_2,Y_2,X_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ) ).
fof(fact_511_xt1_I8_J,axiom,
! [Z_1,Y_3,X_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),Y_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),X_3)) ) ) ).
fof(fact_512_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),top_to1853035173l_bool)) ).
fof(fact_513_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),top_to522745736l_bool)) ).
fof(fact_514_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),top_to1714702858l_bool)) ).
fof(fact_515_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)) ).
fof(fact_516_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),top_to565915683t_bool)) ).
fof(fact_517_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),top_to178429151t_bool)) ).
fof(fact_518_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),top_to1576102282i_bool)) ).
fof(fact_519_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)) ).
fof(fact_520_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)) ).
fof(fact_521_top__unique,axiom,
! [Aa] :
( is_fun279392540l_bool(Aa)
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa))
<=> Aa = top_to1853035173l_bool ) ) ).
fof(fact_522_top__unique,axiom,
! [Aa] :
( is_fun288122577l_bool(Aa)
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))
<=> Aa = top_to522745736l_bool ) ) ).
fof(fact_523_top__unique,axiom,
! [Aa] :
( is_fun158382675l_bool(Aa)
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa))
<=> Aa = top_to1714702858l_bool ) ) ).
fof(fact_524_top__unique,axiom,
! [Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
<=> ( hBOOL(Aa)
<=> hBOOL(top_top_bool) ) ) ).
fof(fact_525_top__unique,axiom,
! [Aa] :
( is_fun961089132t_bool(Aa)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa))
<=> Aa = top_to565915683t_bool ) ) ).
fof(fact_526_top__unique,axiom,
! [Aa] :
( is_fun2093718614t_bool(Aa)
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa))
<=> Aa = top_to178429151t_bool ) ) ).
fof(fact_527_top__unique,axiom,
! [Aa] :
( is_fun1236654035i_bool(Aa)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa))
<=> Aa = top_to1576102282i_bool ) ) ).
fof(fact_528_top__unique,axiom,
! [Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
<=> Aa = top_top_fun_nat_bool ) ).
fof(fact_529_top__unique,axiom,
! [Aa] :
( is_fun1568535512t_bool(Aa)
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
<=> Aa = top_to1257323279t_bool ) ) ).
fof(fact_530_top__le,axiom,
! [Aa] :
( is_fun279392540l_bool(Aa)
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa))
=> Aa = top_to1853035173l_bool ) ) ).
fof(fact_531_top__le,axiom,
! [Aa] :
( is_fun288122577l_bool(Aa)
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))
=> Aa = top_to522745736l_bool ) ) ).
fof(fact_532_top__le,axiom,
! [Aa] :
( is_fun158382675l_bool(Aa)
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa))
=> Aa = top_to1714702858l_bool ) ) ).
fof(fact_533_top__le,axiom,
! [Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
=> ( hBOOL(Aa)
<=> hBOOL(top_top_bool) ) ) ).
fof(fact_534_top__le,axiom,
! [Aa] :
( is_fun961089132t_bool(Aa)
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa))
=> Aa = top_to565915683t_bool ) ) ).
fof(fact_535_top__le,axiom,
! [Aa] :
( is_fun2093718614t_bool(Aa)
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa))
=> Aa = top_to178429151t_bool ) ) ).
fof(fact_536_top__le,axiom,
! [Aa] :
( is_fun1236654035i_bool(Aa)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa))
=> Aa = top_to1576102282i_bool ) ) ).
fof(fact_537_top__le,axiom,
! [Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
=> Aa = top_top_fun_nat_bool ) ).
fof(fact_538_top__le,axiom,
! [Aa] :
( is_fun1568535512t_bool(Aa)
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
=> Aa = top_to1257323279t_bool ) ) ).
fof(fact_539_inj__on__def,axiom,
! [F,A] :
( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
<=> ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
=> ! [Xa] :
( is_Arr43961803e_indi(Xa)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Xa),A))
=> ( hAPP_A1637648121di_nat(F,X_1) = hAPP_A1637648121di_nat(F,Xa)
=> X_1 = Xa ) ) ) ) ) ) ).
fof(fact_540_inj__on__def,axiom,
! [F,A] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
<=> ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
=> ! [Xa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A))
=> ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Xa)
=> X_1 = Xa ) ) ) ) ).
fof(fact_541_inj__on__contraD,axiom,
! [X_2,Y_2,F,A] :
( ( is_Arr43961803e_indi(X_2)
& is_Arr43961803e_indi(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
=> hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2) ) ) ) ) ) ).
fof(fact_542_inj__on__contraD,axiom,
! [X_2,Y_2,F,A] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
=> hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2) ) ) ) ) ).
fof(fact_543_inj__on__iff,axiom,
! [Y_2,X_2,F,A] :
( ( is_Arr43961803e_indi(Y_2)
& is_Arr43961803e_indi(X_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
=> ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
<=> X_2 = Y_2 ) ) ) ) ) ).
fof(fact_544_inj__on__iff,axiom,
! [Y_2,X_2,F,A] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
=> ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
<=> X_2 = Y_2 ) ) ) ) ).
fof(fact_545_inj__onD,axiom,
! [X_2,Y_2,F,A] :
( ( is_Arr43961803e_indi(X_2)
& is_Arr43961803e_indi(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
=> ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
=> X_2 = Y_2 ) ) ) ) ) ).
fof(fact_546_inj__onD,axiom,
! [X_2,Y_2,F,A] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
=> ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
=> X_2 = Y_2 ) ) ) ) ).
fof(fact_547_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B)))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B,X_2))) ) ) ).
fof(fact_548_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B)))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B,X_2))) ) ) ).
fof(fact_549_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B)))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),hAPP_P332578347t_bool(B,X_2))) ) ) ).
fof(fact_550_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B)))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B,X_2))) ) ) ).
fof(fact_551_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B)))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B,X_2))) ) ) ).
fof(fact_552_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B)))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),hAPP_f1891021702t_bool(B,X_2))) ) ) ).
fof(fact_553_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B)))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B,X_2))) ) ) ).
fof(fact_554_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B)))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B,X_2))) ) ) ).
fof(fact_555_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B)))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),hAPP_f1866147972t_bool(B,X_2))) ) ) ).
fof(fact_556_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B)))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B,X_2))) ) ) ).
fof(fact_557_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B)))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B,X_2))) ) ) ).
fof(fact_558_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B)))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),hAPP_f1710744577t_bool(B,X_2))) ) ) ).
fof(fact_559_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),hAPP_n821919323i_bool(B,X_2))) ) ) ).
fof(fact_560_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2))) ) ) ).
fof(fact_561_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2))) ) ) ).
fof(fact_562_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B,X_2))) ) ) ).
fof(fact_563_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B,X_2))) ) ) ).
fof(fact_564_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),hAPP_P1341894483t_bool(B,X_2))) ) ) ).
fof(fact_565_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B,X_2))) ) ) ).
fof(fact_566_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B,X_2))) ) ) ).
fof(fact_567_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),hAPP_P254387896l_bool(B,X_2))) ) ) ).
fof(fact_568_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B,X_2))) ) ) ).
fof(fact_569_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B,X_2))) ) ) ).
fof(fact_570_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),hAPP_P1171466554l_bool(B,X_2))) ) ) ).
fof(fact_571_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B,X_2))) ) ) ).
fof(fact_572_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),hAPP_P1294997365l_bool(B,X_2))) ) ) ).
fof(fact_573_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),hAPP_A2046586321t_bool(B,X_2))) ) ) ).
fof(fact_574_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2))) ) ) ).
fof(fact_575_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2))) ) ) ).
fof(fact_576_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B)))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B,X_2))) ) ) ).
fof(fact_577_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B,X_2))) ) ) ).
fof(fact_578_below__Lin,axiom,
! [L_3,X_2,Y_2] :
( ( is_Arr1861959080le_alt(X_2)
& is_Arr1861959080le_alt(Y_2) )
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(L_3,X_2,Y_2)),arrow_1681063817le_Lin)) ) ) ) ).
fof(fact_579_Prof__def,axiom,
arrow_1721807329e_Prof = pi_Arr990697634t_bool(top_to1576102282i_bool,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,arrow_1681063817le_Lin)) ).
fof(fact_580_inj__on__id2,axiom,
! [A] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)) ).
fof(fact_581_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,B))))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),B)) ) ) ).
fof(fact_582_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,B))))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),B)) ) ) ).
fof(fact_583_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,B))))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),B)) ) ) ).
fof(fact_584_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,B))))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),B)) ) ) ).
fof(fact_585_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,hAPP_f746617550l_bool(cOMBK_370033373t_bool,B))))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),B)) ) ) ).
fof(fact_586_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,B))))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),B)) ) ) ).
fof(fact_587_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,B))))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),B)) ) ) ).
fof(fact_588_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,B))))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),B)) ) ) ).
fof(fact_589_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,B))))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),B)) ) ) ).
fof(fact_590_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,B))))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),B)) ) ) ).
fof(fact_591_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,B))))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),B)) ) ) ).
fof(fact_592_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,B))))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),B)) ) ) ).
fof(fact_593_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,B))))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),B)) ) ) ).
fof(fact_594_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,B))))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),B)) ) ) ).
fof(fact_595_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,B))))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),B)) ) ) ).
fof(fact_596_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,B))))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),B)) ) ) ).
fof(fact_597_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,hAPP_f340261009t_bool(cOMBK_545135096l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),B)) ) ) ).
fof(fact_598_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,B))))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),B)) ) ) ).
fof(fact_599_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,B))))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),B)) ) ) ).
fof(fact_600_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),B)) ) ) ).
fof(fact_601_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,hAPP_f512628453l_bool(cOMBK_295807955t_unit,B))))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),B)) ) ) ).
fof(fact_602_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,B))))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),B)) ) ) ).
fof(fact_603_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),B)) ) ) ).
fof(fact_604_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,B))))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),B)) ) ) ).
fof(fact_605_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,hAPP_f256804927l_bool(cOMBK_69806648l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),B)) ) ) ).
fof(fact_606_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,B))))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),B)) ) ) ).
fof(fact_607_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,B))))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),B)) ) ) ).
fof(fact_608_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),B)) ) ) ).
fof(fact_609_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,B))))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),B)) ) ) ).
fof(fact_610_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,B))))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),B)) ) ) ).
fof(fact_611_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,B))))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),B)) ) ) ).
fof(fact_612_inj__eq,axiom,
! [X_2,Y_2,F] :
( ( is_Arr43961803e_indi(X_2)
& is_Arr43961803e_indi(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
=> ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
<=> X_2 = Y_2 ) ) ) ).
fof(fact_613_inj__eq,axiom,
! [X_2,Y_2,F] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
=> ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
<=> X_2 = Y_2 ) ) ).
fof(fact_614_injD,axiom,
! [X_2,Y_2,F] :
( ( is_Arr43961803e_indi(X_2)
& is_Arr43961803e_indi(Y_2) )
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
=> ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
=> X_2 = Y_2 ) ) ) ).
fof(fact_615_injD,axiom,
! [X_2,Y_2,F] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
=> ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
=> X_2 = Y_2 ) ) ).
fof(fact_616_inv__into__f__f,axiom,
! [X_2,F,A] :
( is_Arr43961803e_indi(X_2)
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> hAPP_n1951273283e_indi(hilber693666498di_nat(A,F),hAPP_A1637648121di_nat(F,X_2)) = X_2 ) ) ) ).
fof(fact_617_inv__into__f__f,axiom,
! [X_2,F,A] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hAPP_nat_nat(hilber195283148at_nat(A,F),hAPP_nat_nat(F,X_2)) = X_2 ) ) ).
fof(fact_618_inv__into__f__eq,axiom,
! [Y_2,X_2,F,A] :
( is_Arr43961803e_indi(X_2)
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
=> ( hAPP_A1637648121di_nat(F,X_2) = Y_2
=> hAPP_n1951273283e_indi(hilber693666498di_nat(A,F),Y_2) = X_2 ) ) ) ) ).
fof(fact_619_inv__into__f__eq,axiom,
! [Y_2,X_2,F,A] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> ( hAPP_nat_nat(F,X_2) = Y_2
=> hAPP_nat_nat(hilber195283148at_nat(A,F),Y_2) = X_2 ) ) ) ).
fof(fact_620_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_1)),hAPP_P1875867302i_bool(B,X_1))) )
=> hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B))) ) ).
fof(fact_621_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_1)),hAPP_P332578347t_bool(B,X_1))) )
=> hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B))) ) ).
fof(fact_622_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_1)),hAPP_f1948454017i_bool(B,X_1))) )
=> hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B))) ) ).
fof(fact_623_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f839832464l_bool(B,X_1))) )
=> hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B))) ) ).
fof(fact_624_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_1)),hAPP_f1891021702t_bool(B,X_1))) )
=> hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B))) ) ).
fof(fact_625_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_1)),hAPP_f1552576127i_bool(B,X_1))) )
=> hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B))) ) ).
fof(fact_626_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f1624277646l_bool(B,X_1))) )
=> hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B))) ) ).
fof(fact_627_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_1)),hAPP_f1866147972t_bool(B,X_1))) )
=> hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B))) ) ).
fof(fact_628_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_fun961089132t_bool(X_1)
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_1)),hAPP_f244157820i_bool(B,X_1))) ) )
=> hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B))) ) ).
fof(fact_629_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_fun961089132t_bool(X_1)
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f210572555l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B))) ) ).
fof(fact_630_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_fun961089132t_bool(X_1)
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_1)),hAPP_f1710744577t_bool(B,X_1))) ) )
=> hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B))) ) ).
fof(fact_631_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_1)),hAPP_n821919323i_bool(B,X_1))) )
=> hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B))) ) ).
fof(fact_632_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_1)),hAPP_n1006566506l_bool(B,X_1))) )
=> hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B))) ) ).
fof(fact_633_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_1)),hAPP_n454528608t_bool(B,X_1))) )
=> hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B))) ) ).
fof(fact_634_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_1)),hAPP_A1677245848t_bool(B,X_1))) ) )
=> hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B))) ) ).
fof(fact_635_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_bool(X_1)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_1)),hAPP_b1703662281t_bool(B,X_1))) ) )
=> hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B))) ) ).
fof(fact_636_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_1)),hAPP_P1341894483t_bool(B,X_1))) )
=> hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B))) ) ).
fof(fact_637_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_1)),hAPP_A1952883197l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B))) ) ).
fof(fact_638_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_bool(X_1)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_1)),hAPP_b1048178734l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B))) ) ).
fof(fact_639_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_1)),hAPP_P254387896l_bool(B,X_1))) )
=> hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B))) ) ).
fof(fact_640_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_1)),hAPP_A1112981887l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B))) ) ).
fof(fact_641_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_bool(X_1)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_1)),hAPP_b517355696l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B))) ) ).
fof(fact_642_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_1)),hAPP_P1171466554l_bool(B,X_1))) )
=> hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B))) ) ).
fof(fact_643_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_bool(X_1)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_1)),hAPP_b1812770943l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B))) ) ).
fof(fact_644_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_1)),hAPP_P1294997365l_bool(B,X_1))) )
=> hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B))) ) ).
fof(fact_645_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_1)),hAPP_A2046586321t_bool(B,X_1))) ) )
=> hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B))) ) ).
fof(fact_646_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_bool(X_1)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_1)),hAPP_b1013836512t_bool(B,X_1))) ) )
=> hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B))) ) ).
fof(fact_647_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_1)),hAPP_P32877782t_bool(B,X_1))) )
=> hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B))) ) ).
fof(fact_648_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P324742453l_bool(B,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B))) ) ).
fof(fact_649_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_1)),hAPP_f1277514478l_bool(B,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B))) ) ).
fof(fact_650_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_1)),hAPP_A60074736l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B))) ) ).
fof(fact_651_inj__imp__inv__eq,axiom,
! [G,F] :
( is_fun1217980910e_indi(G)
=> ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
=> ( ! [X_1] : hAPP_A1637648121di_nat(F,hAPP_n1951273283e_indi(G,X_1)) = X_1
=> hilber693666498di_nat(top_to1576102282i_bool,F) = G ) ) ) ).
fof(fact_652_inj__imp__inv__eq,axiom,
! [G,F] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
=> ( ! [X_1] : hAPP_nat_nat(F,hAPP_nat_nat(G,X_1)) = X_1
=> hilber195283148at_nat(top_top_fun_nat_bool,F) = G ) ) ).
fof(fact_653_less__add__one,axiom,
! [A_18] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),one_one_nat))) ).
fof(fact_654_add__less__le__mono,axiom,
! [C_16,D_3,A_17,B_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_17),B_16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_16),D_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3))) ) ) ).
fof(fact_655_add__le__less__mono,axiom,
! [C_15,D_2,A_16,B_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_16),B_15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_15),D_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_16),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2))) ) ) ).
fof(fact_656_injI,axiom,
! [F] :
( ! [X_1,Y_1] :
( ( is_Arr43961803e_indi(X_1)
& is_Arr43961803e_indi(Y_1) )
=> ( hAPP_A1637648121di_nat(F,X_1) = hAPP_A1637648121di_nat(F,Y_1)
=> X_1 = Y_1 ) )
=> hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool)) ) ).
fof(fact_657_injI,axiom,
! [F] :
( ! [X_1,Y_1] :
( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1)
=> X_1 = Y_1 )
=> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ) ).
fof(fact_658_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa))) ) ) ) ).
fof(fact_659_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa))) ) ) ) ).
fof(fact_660_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f2026336507t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Aa))) ) ) ) ).
fof(fact_661_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa))) ) ) ) ).
fof(fact_662_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa))) ) ) ) ).
fof(fact_663_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),hAPP_n821919323i_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Aa))) ) ) ) ).
fof(fact_664_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),hAPP_n1674354836l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Aa))) ) ) ) ).
fof(fact_665_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),hAPP_n295497947l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Aa))) ) ) ) ).
fof(fact_666_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),hAPP_n2095207769l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Aa))) ) ) ) ).
fof(fact_667_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),hAPP_n588788980t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Aa))) ) ) ) ).
fof(fact_668_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_nat_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa))) ) ) ) ).
fof(fact_669_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),hAPP_n539120590t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Aa))) ) ) ) ).
fof(fact_670_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f22106695ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f22106695ol_nat(F,Aa))) ) ) ) ).
fof(fact_671_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa))) ) ) ) ).
fof(fact_672_xt5,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2120083535ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Aa))) ) ) ) ).
fof(fact_673_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa))) ) ) ) ).
fof(fact_674_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa))) ) ) ) ).
fof(fact_675_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Aa))) ) ) ) ).
fof(fact_676_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Aa))) ) ) ) ).
fof(fact_677_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Aa))) ) ) ) ).
fof(fact_678_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Aa))) ) ) ) ).
fof(fact_679_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Aa))) ) ) ) ).
fof(fact_680_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa))) ) ) ) ).
fof(fact_681_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Aa))) ) ) ) ).
fof(fact_682_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa))) ) ) ) ).
fof(fact_683_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Aa))) ) ) ) ).
fof(fact_684_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_f632777549i_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,Y_1)),hAPP_f632777549i_bool(F,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_f632777549i_bool(F,Aa))) ) ) ) ).
fof(fact_685_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_f769545506l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,Y_1)),hAPP_f769545506l_bool(F,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_f769545506l_bool(F,Aa))) ) ) ) ).
fof(fact_686_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_f1449238989l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,Y_1)),hAPP_f1449238989l_bool(F,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_f1449238989l_bool(F,Aa))) ) ) ) ).
fof(fact_687_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_f226010187l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,Y_1)),hAPP_f226010187l_bool(F,X_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_f226010187l_bool(F,Aa))) ) ) ) ).
fof(fact_688_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_f899613158t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,Y_1)),hAPP_f899613158t_bool(F,X_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_f899613158t_bool(F,Aa))) ) ) ) ).
fof(fact_689_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Aa))) ) ) ) ).
fof(fact_690_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_f861874780t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,Y_1)),hAPP_f861874780t_bool(F,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_f861874780t_bool(F,Aa))) ) ) ) ).
fof(fact_691_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f464145314t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,Y_1)),hAPP_f464145314t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f464145314t_bool(F,Aa))) ) ) ) ).
fof(fact_692_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f839525755t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,Y_1)),hAPP_f839525755t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f839525755t_bool(F,Aa))) ) ) ) ).
fof(fact_693_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f985923321t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,Y_1)),hAPP_f985923321t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f985923321t_bool(F,Aa))) ) ) ) ).
fof(fact_694_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f856106132t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,Y_1)),hAPP_f856106132t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f856106132t_bool(F,Aa))) ) ) ) ).
fof(fact_695_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Aa))) ) ) ) ).
fof(fact_696_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Aa))) ) ) ) ).
fof(fact_697_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa))) ) ) ) ).
fof(fact_698_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1363542492t_bool(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,Y_1)),hAPP_f1363542492t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1363542492t_bool(F,Aa))) ) ) ) ).
fof(fact_699_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1313392232ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,Y_1)),hAPP_f1313392232ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1313392232ol_nat(F,Aa))) ) ) ) ).
fof(fact_700_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1695077327ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,Y_1)),hAPP_f1695077327ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1695077327ol_nat(F,Aa))) ) ) ) ).
fof(fact_701_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f897066961ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,Y_1)),hAPP_f897066961ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f897066961ol_nat(F,Aa))) ) ) ) ).
fof(fact_702_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f816335862ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,Y_1)),hAPP_f816335862ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f816335862ol_nat(F,Aa))) ) ) ) ).
fof(fact_703_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Aa))) ) ) ) ).
fof(fact_704_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Aa))) ) ) ) ).
fof(fact_705_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa))) ) ) ) ).
fof(fact_706_xt7,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1358350510ol_nat(F,Ba)))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,Y_1)),hAPP_f1358350510ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1358350510ol_nat(F,Aa))) ) ) ) ).
fof(fact_707_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G))
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
& ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F)) ) ) ).
fof(fact_708_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,F),G))
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
& ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,G),F)) ) ) ).
fof(fact_709_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,F),G))
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
& ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,G),F)) ) ) ).
fof(fact_710_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,F),G))
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
& ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,G),F)) ) ) ).
fof(fact_711_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,F),G))
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
& ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,G),F)) ) ) ).
fof(fact_712_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,F),G))
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
& ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,G),F)) ) ) ).
fof(fact_713_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,F),G))
<=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
& ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,G),F)) ) ) ).
fof(fact_714_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F)) ) ) ).
fof(fact_715_Pi__anti__mono,axiom,
! [B,A_15,A] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_15),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(A,B)),pi_Pro666468413t_bool(A_15,B))) ) ).
fof(fact_716_Pi__anti__mono,axiom,
! [B,A_15,A] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_15),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(A,B)),pi_fun150026276t_bool(A_15,B))) ) ).
fof(fact_717_Pi__anti__mono,axiom,
! [B,A_15,A] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_15),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(A,B)),pi_Arr990697634t_bool(A_15,B))) ) ).
fof(fact_718_pred__subset__eq2,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),R_1)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),S_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)) ) ).
fof(fact_719_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),top_to1853035173l_bool)) ).
fof(fact_720_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),top_to522745736l_bool)) ).
fof(fact_721_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),top_to1714702858l_bool)) ).
fof(fact_722_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),top_to565915683t_bool)) ).
fof(fact_723_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),top_to1576102282i_bool)) ).
fof(fact_724_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)) ).
fof(fact_725_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)) ).
fof(fact_726_subset__inj__on,axiom,
! [A,F,B] :
( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),B))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
=> hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A)) ) ) ).
fof(fact_727_subset__inj__on,axiom,
! [A,F,B] :
( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) ) ).
fof(fact_728_add__right__imp__eq,axiom,
! [B_14,A_14,C_14] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_14)
=> B_14 = C_14 ) ).
fof(fact_729_add__imp__eq,axiom,
! [A_13,B_13,C_13] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_13)
=> B_13 = C_13 ) ).
fof(fact_730_add__left__imp__eq,axiom,
! [A_12,B_12,C_12] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_12)
=> B_12 = C_12 ) ).
fof(fact_731_add__right__cancel,axiom,
! [Ba,Aa,Ca] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)
<=> Ba = Ca ) ).
fof(fact_732_add__left__cancel,axiom,
! [Aa,Ba,Ca] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)
<=> Ba = Ca ) ).
fof(fact_733_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_11,B_11,C_11] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)) ).
fof(fact_734_one__reorient,axiom,
! [X_2] :
( one_one_nat = X_2
<=> X_2 = one_one_nat ) ).
fof(fact_735_add__le__imp__le__left,axiom,
! [C_10,A_10,B_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_10)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),B_10)) ) ).
fof(fact_736_add__le__imp__le__right,axiom,
! [A_9,C_9,B_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_9)) ) ).
fof(fact_737_add__mono,axiom,
! [C_8,D_1,A_8,B_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_8))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_8),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1))) ) ) ).
fof(fact_738_add__left__mono,axiom,
! [C_7,A_7,B_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))) ) ).
fof(fact_739_add__right__mono,axiom,
! [C_6,A_6,B_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))) ) ).
fof(fact_740_add__le__cancel__left,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ) ).
fof(fact_741_add__le__cancel__right,axiom,
! [Aa,Ca,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ) ).
fof(fact_742_add__less__imp__less__left,axiom,
! [C_5,A_5,B_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),A_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),B_5)) ) ).
fof(fact_743_add__less__imp__less__right,axiom,
! [A_4,C_4,B_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),B_4)) ) ).
fof(fact_744_add__strict__mono,axiom,
! [C_3,D,A_3,B_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),D))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_3),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D))) ) ) ).
fof(fact_745_add__strict__left__mono,axiom,
! [C_2,A_2,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))) ) ).
fof(fact_746_add__strict__right__mono,axiom,
! [C_1,A_1,B_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))) ) ).
fof(fact_747_add__less__cancel__left,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).
fof(fact_748_add__less__cancel__right,axiom,
! [Aa,Ca,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).
fof(fact_749_le__funI,axiom,
! [F,G] :
( ! [X_1] :
( is_fun961089132t_bool(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) ) ).
fof(fact_750_le__funI,axiom,
! [F,G] :
( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1)))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) ) ).
fof(fact_751_le__funI,axiom,
! [F,G] :
( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1)))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) ) ).
fof(fact_752_le__funI,axiom,
! [F,G] :
( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1)))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) ) ).
fof(fact_753_le__funI,axiom,
! [F,G] :
( ! [X_1] :
( is_Arr43961803e_indi(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) ) ).
fof(fact_754_le__funI,axiom,
! [F,G] :
( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1)))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ) ).
fof(fact_755_le__funI,axiom,
! [F,G] :
( ! [X_1] :
( is_Arr1861959080le_alt(X_1)
=> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) ) ).
fof(fact_756_le__funI,axiom,
! [F,G] :
( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ) ).
fof(fact_757_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_758_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_759_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_760_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_761_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_762_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_763_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_764_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_765_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_766_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_767_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_768_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_769_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_770_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_771_xt6,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_772_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_773_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_774_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_775_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_776_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_777_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_778_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_779_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_780_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_781_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_782_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_783_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,Y_1)),hAPP_f632777549i_bool(F,X_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_784_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,Y_1)),hAPP_f769545506l_bool(F,X_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_785_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,Y_1)),hAPP_f1449238989l_bool(F,X_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_786_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,Y_1)),hAPP_f226010187l_bool(F,X_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_787_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,Y_1)),hAPP_f899613158t_bool(F,X_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_788_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_789_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,Y_1)),hAPP_f861874780t_bool(F,X_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_790_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,Y_1)),hAPP_f464145314t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_791_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,Y_1)),hAPP_f839525755t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_792_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,Y_1)),hAPP_f985923321t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_793_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,Y_1)),hAPP_f856106132t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_794_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_795_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_796_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_797_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ba)),Aa))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,Y_1)),hAPP_f1363542492t_bool(F,X_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ca)),Aa)) ) ) ) ).
fof(fact_798_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,Y_1)),hAPP_f1313392232ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_799_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,Y_1)),hAPP_f1695077327ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_800_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,Y_1)),hAPP_f897066961ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_801_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,Y_1)),hAPP_f816335862ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_802_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_803_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_804_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_805_xt4,axiom,
! [Ca,F,Ba,Aa] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ba)),Aa))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,Y_1)),hAPP_f1358350510ol_nat(F,X_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ca)),Aa)) ) ) ) ).
fof(fact_806_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f800510211t_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca))) ) ) ) ).
fof(fact_807_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f543204480t_bool(F,Ba)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca))) ) ) ) ).
fof(fact_808_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f2026336507t_bool(F,Ba)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ca))) ) ) ) ).
fof(fact_809_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_n1699378549t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca))) ) ) ) ).
fof(fact_810_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),hAPP_n454528608t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca))) ) ) ) ).
fof(fact_811_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),hAPP_n821919323i_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ca))) ) ) ) ).
fof(fact_812_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),hAPP_n1674354836l_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ca))) ) ) ) ).
fof(fact_813_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),hAPP_n295497947l_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ca))) ) ) ) ).
fof(fact_814_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),hAPP_n2095207769l_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ca))) ) ) ) ).
fof(fact_815_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),hAPP_n588788980t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ca))) ) ) ) ).
fof(fact_816_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),hAPP_nat_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca))) ) ) ) ).
fof(fact_817_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),hAPP_n539120590t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ca))) ) ) ) ).
fof(fact_818_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f22106695ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f22106695ol_nat(F,Ca))) ) ) ) ).
fof(fact_819_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2030293770ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca))) ) ) ) ).
fof(fact_820_order__le__less__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2120083535ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ca))) ) ) ) ).
fof(fact_821_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca))) ) ) ) ).
fof(fact_822_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca))) ) ) ) ).
fof(fact_823_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ca))) ) ) ) ).
fof(fact_824_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ca))) ) ) ) ).
fof(fact_825_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ca))) ) ) ) ).
fof(fact_826_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ca))) ) ) ) ).
fof(fact_827_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ca))) ) ) ) ).
fof(fact_828_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca))) ) ) ) ).
fof(fact_829_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ba)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ca))) ) ) ) ).
fof(fact_830_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca))) ) ) ) ).
fof(fact_831_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ca))) ) ) ) ).
fof(fact_832_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_f632777549i_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,X_1)),hAPP_f632777549i_bool(F,Y_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_f632777549i_bool(F,Ca))) ) ) ) ).
fof(fact_833_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_f769545506l_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,X_1)),hAPP_f769545506l_bool(F,Y_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_f769545506l_bool(F,Ca))) ) ) ) ).
fof(fact_834_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_f1449238989l_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,X_1)),hAPP_f1449238989l_bool(F,Y_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_f1449238989l_bool(F,Ca))) ) ) ) ).
fof(fact_835_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_f226010187l_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,X_1)),hAPP_f226010187l_bool(F,Y_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_f226010187l_bool(F,Ca))) ) ) ) ).
fof(fact_836_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_f899613158t_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,X_1)),hAPP_f899613158t_bool(F,Y_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_f899613158t_bool(F,Ca))) ) ) ) ).
fof(fact_837_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ca))) ) ) ) ).
fof(fact_838_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_f861874780t_bool(F,Ba)))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,X_1)),hAPP_f861874780t_bool(F,Y_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_f861874780t_bool(F,Ca))) ) ) ) ).
fof(fact_839_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f464145314t_bool(F,Ba)))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,X_1)),hAPP_f464145314t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f464145314t_bool(F,Ca))) ) ) ) ).
fof(fact_840_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f839525755t_bool(F,Ba)))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,X_1)),hAPP_f839525755t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f839525755t_bool(F,Ca))) ) ) ) ).
fof(fact_841_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f985923321t_bool(F,Ba)))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,X_1)),hAPP_f985923321t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f985923321t_bool(F,Ca))) ) ) ) ).
fof(fact_842_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f856106132t_bool(F,Ba)))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,X_1)),hAPP_f856106132t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f856106132t_bool(F,Ca))) ) ) ) ).
fof(fact_843_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ba)))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ca))) ) ) ) ).
fof(fact_844_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ba)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ca))) ) ) ) ).
fof(fact_845_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ba)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca))) ) ) ) ).
fof(fact_846_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1363542492t_bool(F,Ba)))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,X_1)),hAPP_f1363542492t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1363542492t_bool(F,Ca))) ) ) ) ).
fof(fact_847_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1313392232ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,X_1)),hAPP_f1313392232ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1313392232ol_nat(F,Ca))) ) ) ) ).
fof(fact_848_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1695077327ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,X_1)),hAPP_f1695077327ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1695077327ol_nat(F,Ca))) ) ) ) ).
fof(fact_849_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f897066961ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,X_1)),hAPP_f897066961ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f897066961ol_nat(F,Ca))) ) ) ) ).
fof(fact_850_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f816335862ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f816335862ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f816335862ol_nat(F,Ca))) ) ) ) ).
fof(fact_851_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ba)))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ca))) ) ) ) ).
fof(fact_852_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ca))) ) ) ) ).
fof(fact_853_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca))) ) ) ) ).
fof(fact_854_order__less__le__subst1,axiom,
! [Ca,Aa,F,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1358350510ol_nat(F,Ba)))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,X_1)),hAPP_f1358350510ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1358350510ol_nat(F,Ca))) ) ) ) ).
fof(fact_855_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_856_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_857_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_858_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_859_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_860_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_861_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_862_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_863_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_864_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_865_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_866_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,X_1)),hAPP_f632777549i_bool(F,Y_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_867_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,X_1)),hAPP_f769545506l_bool(F,Y_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_868_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,X_1)),hAPP_f1449238989l_bool(F,Y_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_869_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,X_1)),hAPP_f226010187l_bool(F,Y_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_870_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,X_1)),hAPP_f899613158t_bool(F,Y_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_871_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_872_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,X_1)),hAPP_f861874780t_bool(F,Y_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_873_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,X_1)),hAPP_f464145314t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_874_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,X_1)),hAPP_f839525755t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_875_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,X_1)),hAPP_f985923321t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_876_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,X_1)),hAPP_f856106132t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_877_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_878_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_879_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_880_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,X_1)),hAPP_f1363542492t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_881_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun279392540l_bool(X_1)
& is_fun279392540l_bool(Y_1) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,X_1)),hAPP_f1313392232ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_882_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun158382675l_bool(X_1)
& is_fun158382675l_bool(Y_1) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,X_1)),hAPP_f1695077327ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_883_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun288122577l_bool(X_1)
& is_fun288122577l_bool(Y_1) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,X_1)),hAPP_f897066961ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_884_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun961089132t_bool(X_1)
& is_fun961089132t_bool(Y_1) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f816335862ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_885_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_886_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_887_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_888_order__le__less__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun2093718614t_bool(X_1)
& is_fun2093718614t_bool(Y_1) )
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,X_1)),hAPP_f1358350510ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_889_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_890_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_891_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_892_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_893_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_894_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_895_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_896_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_897_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_898_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_899_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_900_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
=> hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Aa)),Ca)) ) ) ) ).
fof(fact_901_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_902_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1568535512t_bool(X_1)
& is_fun1568535512t_bool(Y_1) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_903_order__less__le__subst2,axiom,
! [F,Ca,Aa,Ba] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Ba)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_fun1236654035i_bool(X_1)
& is_fun1236654035i_bool(Y_1) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Aa)),Ca)) ) ) ) ).
fof(fact_904_add__leE,axiom,
! [M_2,K_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ) ).
fof(fact_905_equalityI,axiom,
! [A,B] :
( ( is_fun279392540l_bool(A)
& is_fun279392540l_bool(B) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,B),A))
=> A = B ) ) ) ).
fof(fact_906_equalityI,axiom,
! [A,B] :
( ( is_fun158382675l_bool(A)
& is_fun158382675l_bool(B) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,B),A))
=> A = B ) ) ) ).
fof(fact_907_equalityI,axiom,
! [A,B] :
( ( is_fun288122577l_bool(A)
& is_fun288122577l_bool(B) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,B),A))
=> A = B ) ) ) ).
fof(fact_908_equalityI,axiom,
! [A,B] :
( ( is_fun961089132t_bool(A)
& is_fun961089132t_bool(B) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,B),A))
=> A = B ) ) ) ).
fof(fact_909_equalityI,axiom,
! [A,B] :
( ( is_fun1236654035i_bool(A)
& is_fun1236654035i_bool(B) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,B),A))
=> A = B ) ) ) ).
fof(fact_910_equalityI,axiom,
! [A,B] :
( ( is_fun1568535512t_bool(A)
& is_fun1568535512t_bool(B) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),A))
=> A = B ) ) ) ).
fof(fact_911_equalityI,axiom,
! [A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
=> A = B ) ) ).
fof(fact_912_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),A))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),B)) ) ) ).
fof(fact_913_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B)) ) ) ).
fof(fact_914_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B)) ) ) ).
fof(fact_915_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),B)) ) ) ).
fof(fact_916_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),B)) ) ) ).
fof(fact_917_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),B)) ) ) ).
fof(fact_918_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),B)) ) ) ).
fof(fact_919_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) ) ) ).
fof(fact_920_psubset__eq,axiom,
! [A,B] :
( ( is_fun1568535512t_bool(A)
& is_fun1568535512t_bool(B) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
& A != B ) ) ) ).
fof(fact_921_psubset__eq,axiom,
! [A,B] :
( ( is_fun1236654035i_bool(A)
& is_fun1236654035i_bool(B) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
& A != B ) ) ) ).
fof(fact_922_psubset__eq,axiom,
! [A,B] :
( ( is_fun279392540l_bool(A)
& is_fun279392540l_bool(B) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
& A != B ) ) ) ).
fof(fact_923_psubset__eq,axiom,
! [A,B] :
( ( is_fun158382675l_bool(A)
& is_fun158382675l_bool(B) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
& A != B ) ) ) ).
fof(fact_924_psubset__eq,axiom,
! [A,B] :
( ( is_fun288122577l_bool(A)
& is_fun288122577l_bool(B) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
& A != B ) ) ) ).
fof(fact_925_psubset__eq,axiom,
! [A,B] :
( ( is_fun961089132t_bool(A)
& is_fun961089132t_bool(B) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
& A != B ) ) ) ).
fof(fact_926_psubset__eq,axiom,
! [A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
& A != B ) ) ).
fof(fact_927_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun1568535512t_bool(A)
& is_fun1568535512t_bool(B) )
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
<=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
| A = B ) ) ) ).
fof(fact_928_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun1236654035i_bool(A)
& is_fun1236654035i_bool(B) )
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
<=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
| A = B ) ) ) ).
fof(fact_929_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun279392540l_bool(A)
& is_fun279392540l_bool(B) )
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
<=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
| A = B ) ) ) ).
fof(fact_930_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun158382675l_bool(A)
& is_fun158382675l_bool(B) )
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
<=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
| A = B ) ) ) ).
fof(fact_931_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun288122577l_bool(A)
& is_fun288122577l_bool(B) )
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
<=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
| A = B ) ) ) ).
fof(fact_932_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun961089132t_bool(A)
& is_fun961089132t_bool(B) )
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
| A = B ) ) ) ).
fof(fact_933_subset__iff__psubset__eq,axiom,
! [A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
| A = B ) ) ).
fof(fact_934_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) ).
fof(fact_935_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) ) ).
fof(fact_936_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ) ).
fof(fact_937_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ) ).
fof(fact_938_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ) ).
fof(fact_939_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ) ).
fof(fact_940_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).
fof(fact_941_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),C))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).
fof(fact_942_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,B),C))
=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),C)) ) ) ).
fof(fact_943_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,B),C))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),C)) ) ) ).
fof(fact_944_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,B),C))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),C)) ) ) ).
fof(fact_945_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,B),C))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),C)) ) ) ).
fof(fact_946_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,B),C))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),C)) ) ) ).
fof(fact_947_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).
fof(fact_948_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,B),C))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),C)) ) ) ).
fof(fact_949_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,B),C))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),C)) ) ) ).
fof(fact_950_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,B),C))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),C)) ) ) ).
fof(fact_951_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,B),C))
=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),C)) ) ) ).
fof(fact_952_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).
fof(fact_953_equalityE,axiom,
! [A,B] :
( A = B
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).
fof(fact_954_subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C)) ) ) ).
fof(fact_955_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).
fof(fact_956_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B)) ) ) ).
fof(fact_957_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B)) ) ) ).
fof(fact_958_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B)) ) ) ).
fof(fact_959_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B)) ) ) ).
fof(fact_960_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).
fof(fact_961_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B)) ) ) ).
fof(fact_962_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B)) ) ) ).
fof(fact_963_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B)) ) ) ).
fof(fact_964_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B)) ) ) ).
fof(fact_965_predicate1D,axiom,
! [X_2,Pa,Q_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
=> ( hBOOL(hAPP_nat_bool(Pa,X_2))
=> hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ) ).
fof(fact_966_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).
fof(fact_967_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
=> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B)) ) ) ).
fof(fact_968_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
=> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B)) ) ) ).
fof(fact_969_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
=> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B)) ) ) ).
fof(fact_970_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B)) ) ) ).
fof(fact_971_equalityD2,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ).
fof(fact_972_equalityD1,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).
fof(fact_973_rev__predicate1D,axiom,
! [Q_1,Pa,X_2] :
( hBOOL(hAPP_nat_bool(Pa,X_2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
=> hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ) ).
fof(fact_974_set__eq__subset,axiom,
! [A,B] :
( A = B
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).
fof(fact_975_subset__refl,axiom,
! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)) ).
fof(fact_976_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) ) ).
fof(fact_977_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),R_1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),S_1)))
<=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,R_1),S_1)) ) ).
fof(fact_978_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),R_1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),S_1)))
<=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,R_1),S_1)) ) ).
fof(fact_979_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),R_1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),S_1)))
<=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,R_1),S_1)) ) ).
fof(fact_980_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),R_1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),S_1)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)) ) ).
fof(fact_981_less__not__refl,axiom,
! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ).
fof(fact_982_nat__neq__iff,axiom,
! [M_1,Na] :
( M_1 != Na
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ) ).
fof(fact_983_linorder__neqE__nat,axiom,
! [X,Y] :
( X != Y
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).
fof(fact_984_less__irrefl__nat,axiom,
! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ).
fof(fact_985_less__not__refl2,axiom,
! [N,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2))
=> M_2 != N ) ).
fof(fact_986_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ) ).
fof(fact_987_nat__less__cases,axiom,
! [Pa,M_1,Na] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
=> ( ( M_1 = Na
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) ) ) ) ).
fof(fact_988_nat__add__commute,axiom,
! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2) ).
fof(fact_989_nat__add__left__commute,axiom,
! [X,Y,Z] : 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)) = 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)) ).
fof(fact_990_nat__add__assoc,axiom,
! [M_2,N,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_2)) ).
fof(fact_991_nat__add__left__cancel,axiom,
! [K,M_1,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
<=> M_1 = Na ) ).
fof(fact_992_nat__add__right__cancel,axiom,
! [M_1,K,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
<=> M_1 = Na ) ).
fof(fact_993_le__refl,axiom,
! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)) ).
fof(fact_994_nat__le__linear,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2)) ) ).
fof(fact_995_eq__imp__le,axiom,
! [M_2,N] :
( M_2 = N
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).
fof(fact_996_le__trans,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) ) ) ).
fof(fact_997_le__antisym,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2))
=> M_2 = N ) ) ).
fof(fact_998_inj__on__add__nat,axiom,
! [K,N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),N_2)) ).
fof(fact_999_not__add__less1,axiom,
! [I_2,J_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),I_2)) ).
fof(fact_1000_not__add__less2,axiom,
! [J_1,I_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I_2)),I_2)) ).
fof(fact_1001_nat__add__left__cancel__less,axiom,
! [K,M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).
fof(fact_1002_trans__less__add1,axiom,
! [M_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ) ).
fof(fact_1003_trans__less__add2,axiom,
! [M_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ) ).
fof(fact_1004_add__less__mono1,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ) ).
fof(fact_1005_add__less__mono,axiom,
! [K_2,L_1,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1))) ) ) ).
fof(fact_1006_less__add__eq__less,axiom,
! [M_2,N,K_2,L_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ) ).
fof(fact_1007_add__lessD1,axiom,
! [I_2,J_1,K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) ) ).
fof(fact_1008_nat__less__le,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
& M_1 != Na ) ) ).
fof(fact_1009_le__eq__less__or__eq,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
| M_1 = Na ) ) ).
fof(fact_1010_less__imp__le__nat,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).
fof(fact_1011_le__neq__implies__less,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
=> ( M_2 != N
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ) ).
fof(fact_1012_less__or__eq__imp__le,axiom,
! [M_2,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
| M_2 = N )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).
fof(fact_1013_le__add2,axiom,
! [N,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N))) ).
fof(fact_1014_le__add1,axiom,
! [N,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2))) ).
fof(fact_1015_le__iff__add,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
<=> ? [K_1] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1) ) ).
fof(fact_1016_nat__add__left__cancel__le,axiom,
! [K,M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ).
fof(fact_1017_trans__le__add1,axiom,
! [M_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ) ).
fof(fact_1018_trans__le__add2,axiom,
! [M_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ) ).
fof(fact_1019_add__le__mono1,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ) ).
fof(fact_1020_add__le__mono,axiom,
! [K_2,L_1,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1))) ) ) ).
fof(fact_1021_add__leD2,axiom,
! [M_2,K_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ).
fof(fact_1022_add__leD1,axiom,
! [M_2,K_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).
fof(fact_1023_mono__nat__linear__lb,axiom,
! [M_1,K,F] :
( ! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N_1))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_1)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K)))) ) ).
fof(fact_1024_less__mono__imp__le__mono,axiom,
! [I,J,F] :
( ! [I_1,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J))) ) ) ).
fof(fact_1025_termination__basic__simps_I3_J,axiom,
! [Z,X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1026_termination__basic__simps_I4_J,axiom,
! [Y,X,Z] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1027_termination__basic__simps_I5_J,axiom,
! [X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ).
fof(fact_1028_termination__basic__simps_I2_J,axiom,
! [Y,X,Z] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1029_termination__basic__simps_I1_J,axiom,
! [Z,X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1030_linear__alt,axiom,
? [L_2] :
( is_fun961089132t_bool(L_2)
& hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) ) ).
fof(fact_1031_finite__indi,axiom,
hBOOL(hAPP_f1599966040l_bool(finite106199483e_indi,top_to1576102282i_bool)) ).
fof(fact_1032_finite__Collect__le__nat,axiom,
! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))) ).
fof(fact_1033_finite__Collect__less__nat,axiom,
! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))) ).
fof(fact_1034_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)) ).
fof(fact_1035_card__UNIV__unit,axiom,
hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat ).
fof(fact_1036_card__Collect__less__nat,axiom,
! [Na] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na ).
fof(fact_1037_finite__M__bounded__by__nat,axiom,
! [Pa,I] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I))))) ).
fof(fact_1038_finite__nat__set__iff__bounded__le,axiom,
! [N_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
<=> ? [M] :
! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)) ) ) ).
fof(fact_1039_finite__nat__set__iff__bounded,axiom,
! [N_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
<=> ? [M] :
! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M)) ) ) ).
fof(fact_1040_finite__less__ub,axiom,
! [U,F] :
( ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))) ) ).
fof(fact_1041_bounded__nat__set__is__finite,axiom,
! [Na,N_2] :
( ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ).
fof(fact_1042_less__zeroE,axiom,
! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).
fof(fact_1043_le0,axiom,
! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ).
fof(fact_1044_not__less0,axiom,
! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).
fof(fact_1045_neq0__conv,axiom,
! [Na] :
( Na != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ).
fof(fact_1046_less__nat__zero__code,axiom,
! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).
fof(fact_1047_gr__implies__not0,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> N != zero_zero_nat ) ).
fof(fact_1048_gr0I,axiom,
! [N] :
( N != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ).
fof(fact_1049_plus__nat_Oadd__0,axiom,
! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N ).
fof(fact_1050_Nat_Oadd__0__right,axiom,
! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2 ).
fof(fact_1051_add__is__0,axiom,
! [M_1,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = zero_zero_nat
<=> ( M_1 = zero_zero_nat
& Na = zero_zero_nat ) ) ).
fof(fact_1052_add__eq__self__zero,axiom,
! [M_2,N] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = M_2
=> N = zero_zero_nat ) ).
fof(fact_1053_le__0__eq,axiom,
! [Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
<=> Na = zero_zero_nat ) ).
fof(fact_1054_less__eq__nat_Osimps_I1_J,axiom,
! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ).
fof(fact_1055_add__gr__0,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ) ).
fof(fact_1056_ex__least__nat__less,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(Pa,Na))
=> ? [K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),Na))
& ! [I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))
=> ~ hBOOL(hAPP_nat_bool(Pa,I_1)) )
& hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),one_one_nat))) ) ) ) ).
fof(fact_1057_ex__least__nat__le,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(Pa,Na))
=> ? [K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),Na))
& ! [I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
=> ~ hBOOL(hAPP_nat_bool(Pa,I_1)) )
& hBOOL(hAPP_nat_bool(Pa,K_1)) ) ) ) ).
fof(fact_1058_less__imp__add__positive,axiom,
! [I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> ? [K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_1) = J_1 ) ) ).
fof(fact_1059_lessI,axiom,
! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))) ).
fof(fact_1060_Suc__mono,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N))) ) ).
fof(fact_1061_zero__less__Suc,axiom,
! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))) ).
fof(fact_1062_Suc__inject,axiom,
! [X,Y] :
( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
=> X = Y ) ).
fof(fact_1063_nat_Oinject,axiom,
! [Nat_5,Nat_4] :
( hAPP_nat_nat(suc,Nat_5) = hAPP_nat_nat(suc,Nat_4)
<=> Nat_5 = Nat_4 ) ).
fof(fact_1064_Suc__n__not__n,axiom,
! [N] : hAPP_nat_nat(suc,N) != N ).
fof(fact_1065_n__not__Suc__n,axiom,
! [N] : N != hAPP_nat_nat(suc,N) ).
fof(fact_1066_Suc__neq__Zero,axiom,
! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).
fof(fact_1067_Zero__neq__Suc,axiom,
! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).
fof(fact_1068_nat_Osimps_I3_J,axiom,
! [Nat_3] : hAPP_nat_nat(suc,Nat_3) != zero_zero_nat ).
fof(fact_1069_Suc__not__Zero,axiom,
! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).
fof(fact_1070_nat_Osimps_I2_J,axiom,
! [Nat_2] : zero_zero_nat != hAPP_nat_nat(suc,Nat_2) ).
fof(fact_1071_Zero__not__Suc,axiom,
! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).
fof(fact_1072_Suc__less__SucD,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ).
fof(fact_1073_Suc__lessD,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ).
fof(fact_1074_less__SucE,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> M_2 = N ) ) ).
fof(fact_1075_less__trans__Suc,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2)) ) ) ).
fof(fact_1076_Suc__lessI,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> ( hAPP_nat_nat(suc,M_2) != N
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N)) ) ) ).
fof(fact_1077_less__SucI,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ) ).
fof(fact_1078_less__antisym,axiom,
! [N,M_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_2)))
=> M_2 = N ) ) ).
fof(fact_1079_not__less__less__Suc__eq,axiom,
! [Na,M_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
<=> Na = M_1 ) ) ).
fof(fact_1080_Suc__less__eq,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).
fof(fact_1081_less__Suc__eq,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
| M_1 = Na ) ) ).
fof(fact_1082_not__less__eq,axiom,
! [M_1,Na] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ) ).
fof(fact_1083_add__Suc__shift,axiom,
! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)) ).
fof(fact_1084_add__Suc,axiom,
! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) ).
fof(fact_1085_add__Suc__right,axiom,
! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) ).
fof(fact_1086_Suc__leD,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).
fof(fact_1087_le__SucE,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
=> M_2 = hAPP_nat_nat(suc,N) ) ) ).
fof(fact_1088_le__SucI,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N))) ) ).
fof(fact_1089_Suc__le__mono,axiom,
! [Na,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) ) ).
fof(fact_1090_le__Suc__eq,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
| M_1 = hAPP_nat_nat(suc,Na) ) ) ).
fof(fact_1091_not__less__eq__eq,axiom,
! [M_1,Na] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ) ).
fof(fact_1092_Suc__n__not__le__n,axiom,
! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)) ).
fof(fact_1093_inj__Suc,axiom,
! [N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)) ).
fof(fact_1094_gr0__conv__Suc,axiom,
! [Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
<=> ? [M] : Na = hAPP_nat_nat(suc,M) ) ).
fof(fact_1095_less__Suc0,axiom,
! [Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
<=> Na = zero_zero_nat ) ).
fof(fact_1096_less__Suc__eq__0__disj,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
<=> ( M_1 = zero_zero_nat
| ? [J_2] :
( M_1 = hAPP_nat_nat(suc,J_2)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na)) ) ) ) ).
fof(fact_1097_add__is__1,axiom,
! [M_1,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat)
& Na = zero_zero_nat )
| ( M_1 = zero_zero_nat
& Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_1098_one__is__add,axiom,
! [M_1,Na] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na)
<=> ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat)
& Na = zero_zero_nat )
| ( M_1 = zero_zero_nat
& Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_1099_less__add__Suc1,axiom,
! [I_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),M_2)))) ).
fof(fact_1100_less__add__Suc2,axiom,
! [I_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I_2)))) ).
fof(fact_1101_less__iff__Suc__add,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
<=> ? [K_1] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)) ) ).
fof(fact_1102_less__eq__Suc__le,axiom,
! [Na,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ) ).
fof(fact_1103_less__Suc__eq__le,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ).
fof(fact_1104_Suc__le__eq,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).
fof(fact_1105_le__imp__less__Suc,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ) ).
fof(fact_1106_Suc__leI,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N)) ) ).
fof(fact_1107_le__less__Suc__eq,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
<=> Na = M_1 ) ) ).
fof(fact_1108_Suc__le__lessD,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ).
fof(fact_1109_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).
fof(fact_1110_less__eq__Suc__le__raw,axiom,
! [X_1] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)) ).
fof(fact_1111_card__Collect__le__nat,axiom,
! [Na] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na) ).
fof(fact_1112_card__less__Suc,axiom,
! [I,M_4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
=> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) ) ).
fof(fact_1113_card__less,axiom,
! [I,M_4] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) != zero_zero_nat ) ).
fof(fact_1114_card__less__Suc2,axiom,
! [I,M_4] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) ) ).
fof(fact_1115_inc__induct,axiom,
! [Pa,I,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
=> ( hBOOL(hAPP_nat_bool(Pa,J))
=> ( ! [I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_1)))
=> hBOOL(hAPP_nat_bool(Pa,I_1)) ) )
=> hBOOL(hAPP_nat_bool(Pa,I)) ) ) ) ).
fof(fact_1116_less__imp__Suc__add,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
=> ? [K_1] : N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)) ) ).
fof(fact_1117_gr0__implies__Suc,axiom,
! [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
=> ? [M] : N = hAPP_nat_nat(suc,M) ) ).
fof(fact_1118_Suc__eq__plus1,axiom,
! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ).
fof(fact_1119_Suc__eq__plus1__left,axiom,
! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N) ).
fof(fact_1120_Suc__le__D,axiom,
! [N,M_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3))
=> ? [M] : M_3 = hAPP_nat_nat(suc,M) ) ).
fof(fact_1121_lessE,axiom,
! [I_2,K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
=> ( K_2 != hAPP_nat_nat(suc,I_2)
=> ~ ! [J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2))
=> K_2 != hAPP_nat_nat(suc,J_2) ) ) ) ).
fof(fact_1122_Suc__lessE,axiom,
! [I_2,K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2))
=> ~ ! [J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2))
=> K_2 != hAPP_nat_nat(suc,J_2) ) ) ).
fof(fact_1123_not0__implies__Suc,axiom,
! [N] :
( N != zero_zero_nat
=> ? [M] : N = hAPP_nat_nat(suc,M) ) ).
fof(fact_1124_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero_nat
=> ~ ! [Nat_1] : Y != hAPP_nat_nat(suc,Nat_1) ) ).
fof(fact_1125_zero__induct,axiom,
! [Pa,K] :
( hBOOL(hAPP_nat_bool(Pa,K))
=> ( ! [N_1] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
=> hBOOL(hAPP_nat_bool(Pa,N_1)) )
=> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).
fof(fact_1126_nat__induct,axiom,
! [Na,Pa] :
( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( ! [N_1] :
( hBOOL(hAPP_nat_bool(Pa,N_1))
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
=> hBOOL(hAPP_nat_bool(Pa,Na)) ) ) ).
fof(fact_1127_surjh,axiom,
hAPP_f2026336507t_bool(image_579431497di_nat(h),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)) ).
fof(fact_1128_finite__atLeastLessThan,axiom,
! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))) ).
fof(fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12,axiom,
~ ! [H] :
( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(H),top_to1576102282i_bool))
=> hAPP_f2026336507t_bool(image_579431497di_nat(H),top_to1576102282i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)) ) ).
fof(fact_1130_subset__card__intvl__is__intvl,axiom,
! [A,K] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),hAPP_f22106695ol_nat(finite_card_nat,A)))))
=> A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ).
fof(fact_1131_image__Suc__atLeastLessThan,axiom,
! [I,J] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)) ).
fof(fact_1132_image__add__atLeastLessThan,axiom,
! [K,I,J] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) ).
fof(fact_1133_all__nat__less__eq,axiom,
! [Pa,Na] :
( ! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
=> hBOOL(hAPP_nat_bool(Pa,M)) )
<=> ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na)))
=> hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).
fof(fact_1134_ex__nat__less__eq,axiom,
! [Pa,Na] :
( ? [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
& hBOOL(hAPP_nat_bool(Pa,M)) )
<=> ? [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na)))
& hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).
fof(fact_1135_greaterThan__0,axiom,
hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool) ).
fof(fact_1136_less__eq__nat_Osimps_I2_J,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) ) ).
fof(fact_1137_finite__greaterThanAtMost,axiom,
! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U))) ).
fof(fact_1138_finite__greaterThanLessThan,axiom,
! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U))) ).
fof(fact_1139_atLeastSucLessThan__greaterThanLessThan,axiom,
! [L,U] : hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U) ).
fof(fact_1140_le__square,axiom,
! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),M_2))) ).
fof(fact_1141_le__cube,axiom,
! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(M_2),M_2)))) ).
fof(fact_1142_mult__le__mono1,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2))) ) ).
fof(fact_1143_mult__le__mono2,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1))) ) ).
fof(fact_1144_mult__le__mono,axiom,
! [K_2,L_1,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),L_1))) ) ) ).
fof(fact_1145_nat__mult__eq__1__iff,axiom,
! [M_1,Na] :
( hAPP_nat_nat(times_times_nat(M_1),Na) = one_one_nat
<=> ( M_1 = one_one_nat
& Na = one_one_nat ) ) ).
fof(fact_1146_nat__mult__1__right,axiom,
! [N] : hAPP_nat_nat(times_times_nat(N),one_one_nat) = N ).
fof(fact_1147_nat__1__eq__mult__iff,axiom,
! [M_1,Na] :
( one_one_nat = hAPP_nat_nat(times_times_nat(M_1),Na)
<=> ( M_1 = one_one_nat
& Na = one_one_nat ) ) ).
fof(fact_1148_nat__mult__1,axiom,
! [N] : hAPP_nat_nat(times_times_nat(one_one_nat),N) = N ).
fof(fact_1149_add__mult__distrib,axiom,
! [M_2,N,K_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(M_2),K_2)),hAPP_nat_nat(times_times_nat(N),K_2)) ).
fof(fact_1150_add__mult__distrib2,axiom,
! [K_2,M_2,N] : hAPP_nat_nat(times_times_nat(K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(K_2),M_2)),hAPP_nat_nat(times_times_nat(K_2),N)) ).
fof(fact_1151_Suc__mult__cancel1,axiom,
! [K,M_1,Na] :
( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)
<=> M_1 = Na ) ).
fof(fact_1152_mult__cancel2,axiom,
! [M_1,K,Na] :
( hAPP_nat_nat(times_times_nat(M_1),K) = hAPP_nat_nat(times_times_nat(Na),K)
<=> ( M_1 = Na
| K = zero_zero_nat ) ) ).
fof(fact_1153_mult__cancel1,axiom,
! [K,M_1,Na] :
( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
<=> ( M_1 = Na
| K = zero_zero_nat ) ) ).
fof(fact_1154_mult__is__0,axiom,
! [M_1,Na] :
( hAPP_nat_nat(times_times_nat(M_1),Na) = zero_zero_nat
<=> ( M_1 = zero_zero_nat
| Na = zero_zero_nat ) ) ).
fof(fact_1155_mult__0__right,axiom,
! [M_2] : hAPP_nat_nat(times_times_nat(M_2),zero_zero_nat) = zero_zero_nat ).
fof(fact_1156_mult__0,axiom,
! [N] : hAPP_nat_nat(times_times_nat(zero_zero_nat),N) = zero_zero_nat ).
fof(fact_1157_mult__eq__1__iff,axiom,
! [M_1,Na] :
( hAPP_nat_nat(times_times_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( M_1 = hAPP_nat_nat(suc,zero_zero_nat)
& Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ).
fof(fact_1158_mult__less__mono2,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1))) ) ) ).
fof(fact_1159_mult__less__mono1,axiom,
! [K_2,I_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2))) ) ) ).
fof(fact_1160_mult__less__cancel2,axiom,
! [M_1,K,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ).
fof(fact_1161_mult__less__cancel1,axiom,
! [K,M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ).
fof(fact_1162_nat__0__less__mult__iff,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(M_1),Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ) ).
fof(fact_1163_Suc__mult__less__cancel1,axiom,
! [K,M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).
fof(fact_1164_mult__Suc__right,axiom,
! [M_2,N] : hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),N)) ).
fof(fact_1165_mult__Suc,axiom,
! [M_2,N] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(times_times_nat(M_2),N)) ).
fof(fact_1166_Suc__mult__le__cancel1,axiom,
! [K,M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ).
fof(fact_1167_mult__eq__self__implies__10,axiom,
! [M_2,N] :
( M_2 = hAPP_nat_nat(times_times_nat(M_2),N)
=> ( N = one_one_nat
| M_2 = zero_zero_nat ) ) ).
fof(fact_1168_n__less__m__mult__n,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(M_2),N))) ) ) ).
fof(fact_1169_n__less__n__mult__m,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(N),M_2))) ) ) ).
fof(fact_1170_one__less__mult,axiom,
! [M_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_2),N))) ) ) ).
fof(fact_1171_one__le__mult__iff,axiom,
! [M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_1),Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na)) ) ) ).
fof(fact_1172_mult__le__cancel2,axiom,
! [M_1,K,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ).
fof(fact_1173_mult__le__cancel1,axiom,
! [K,M_1,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ).
fof(fact_1174_nat__mult__commute,axiom,
! [M_2,N] : hAPP_nat_nat(times_times_nat(M_2),N) = hAPP_nat_nat(times_times_nat(N),M_2) ).
fof(fact_1175_nat__mult__assoc,axiom,
! [M_2,N,K_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M_2),N)),K_2) = hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(N),K_2)) ).
fof(fact_1176_nat__mult__le__cancel1,axiom,
! [M_1,Na,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ).
fof(fact_1177_nat__mult__less__cancel1,axiom,
! [M_1,Na,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ).
fof(fact_1178_nat__mult__eq__cancel1,axiom,
! [M_1,Na,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
<=> M_1 = Na ) ) ).
fof(fact_1179_nat__mult__eq__cancel__disj,axiom,
! [K,M_1,Na] :
( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
<=> ( K = zero_zero_nat
| M_1 = Na ) ) ).
fof(fact_1180_left__add__mult__distrib,axiom,
! [I_2,U_1,J_1,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(I_2),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(J_1),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),U_1)),K_2) ).
fof(fact_1181_nat_Osize_I2_J,axiom,
! [Nat] : hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1182_nat_Osize_I1_J,axiom,
hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat ).
fof(fact_1183_nat_Osize_I4_J,axiom,
! [Nat] : hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1184_nat__size,axiom,
! [N] : hAPP_nat_nat(size_size_nat,N) = N ).
fof(fact_1185_nat_Osize_I3_J,axiom,
hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat ).
fof(fact_1186_weak__decr__stable,axiom,
! [F] :
( ! [I_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I_1))),hAPP_nat_nat(F,I_1)))
=> ? [I_1] :
! [K_1] : hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)) = hAPP_nat_nat(F,I_1) ) ).
fof(fact_1187_bool_Osize_I1_J,axiom,
hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat ).
fof(fact_1188_bool_Osize_I2_J,axiom,
hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat ).
fof(fact_1189_finite__atLeastAtMost,axiom,
! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U))) ).
fof(fact_1190_atLeastLessThanSuc__atLeastAtMost,axiom,
! [L,U] : hAPP_n1699378549t_bool(ord_at4362885an_nat(L),hAPP_nat_nat(suc,U)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U) ).
fof(fact_1191_ex__nat__less,axiom,
! [Pa,Na] :
( ? [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
& hBOOL(hAPP_nat_bool(Pa,M)) )
<=> ? [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na)))
& hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).
fof(fact_1192_all__nat__less,axiom,
! [Pa,Na] :
( ! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
=> hBOOL(hAPP_nat_bool(Pa,M)) )
<=> ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na)))
=> hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).
fof(fact_1193_image__Suc__atLeastAtMost,axiom,
! [I,J] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)) ).
fof(fact_1194_atLeastSucAtMost__greaterThanAtMost,axiom,
! [L,U] : hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U) ).
fof(fact_1195_image__add__atLeastAtMost,axiom,
! [K,I,J] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) ).
fof(fact_1196_atLeastLessThan__add__Un,axiom,
! [K,I,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
=> hAPP_n1699378549t_bool(ord_at4362885an_nat(I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)),hAPP_n1699378549t_bool(ord_at4362885an_nat(J),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))) ) ).
fof(fact_1197_atLeast__0,axiom,
hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool ).
fof(fact_1198_atLeast__Suc__greaterThan,axiom,
! [K] : hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,K)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,K) ).
fof(fact_1199_setsum__shift__lb__Suc0__0,axiom,
! [K,F] :
( hAPP_nat_nat(F,zero_zero_nat) = zero_zero_nat
=> hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),K)) = hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),K)) ) ).
%----Helper facts (78)
fof(help_fTrue_1_1_U,axiom,
hBOOL(fTrue) ).
fof(help_fTrue_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(P) ) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(Q) ) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse) ).
fof(help_fFalse_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
! [P] : hAPP_nat_nat(cOMBI_nat,P) = P ).
fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
! [P,Q,R] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On,axiom,
! [P,Q] : hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [P,Q] : hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_,axiom,
! [P,Q] : hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00,axiom,
! [P,Q] :
( is_fun1568535512t_bool(P)
=> hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000,axiom,
! [P,Q,R] : hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A2046586321t_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
! [P,Q] :
( is_fun1236654035i_bool(P)
=> hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
! [P,Q] : hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_indi,P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
! [P,Q,R] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049,axiom,
! [P,Q,R] : hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1637648121di_nat(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,P),Q) = P ) ).
fof(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
! [X,Y] :
( is_fun961089132t_bool(X)
=> hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),X),Y) = X ) ).
fof(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
! [X,Y] :
( is_fun961089132t_bool(Y)
=> hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),X),Y) = Y ) ).
fof(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
! [P,Q] : hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
! [P,Q] :
( is_fun961089132t_bool(P)
=> hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050,axiom,
! [P,Q] :
( is_fun1568535512t_bool(P)
=> hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051,axiom,
! [P,Q] :
( is_fun961089132t_bool(P)
=> hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
! [P,Q] : hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_fun279392540l_bool(P)
=> hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052,axiom,
! [P,Q] :
( is_fun1236654035i_bool(P)
=> hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053,axiom,
! [P,Q] :
( is_fun961089132t_bool(P)
=> hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054,axiom,
! [P,Q] :
( is_fun1568535512t_bool(P)
=> hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055,axiom,
! [P,Q] :
( is_fun279392540l_bool(P)
=> hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t,axiom,
! [P,Q,R] : hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___056,axiom,
! [P,Q] :
( is_fun1236654035i_bool(P)
=> hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057,axiom,
! [P,Q] :
( is_fun279392540l_bool(P)
=> hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058,axiom,
! [P,Q] : hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
! [P,Q] :
( is_fun288122577l_bool(P)
=> hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059,axiom,
! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,P),Q),R) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060,axiom,
! [P,Q] :
( is_fun1568535512t_bool(P)
=> hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061,axiom,
! [P,Q] :
( is_fun288122577l_bool(P)
=> hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062,axiom,
! [P,Q,R] : hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,P),Q),R) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_,axiom,
! [P,Q,R] : hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063,axiom,
! [P,Q] :
( is_fun1236654035i_bool(P)
=> hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064,axiom,
! [P,Q] :
( is_fun288122577l_bool(P)
=> hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065,axiom,
! [P,Q,R] : hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,P),Q),R) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
! [P,Q,R] : hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,P),Q),R) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_,axiom,
! [P,Q,R] : hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(P),Q),R) = hAPP_P229966473l_bool(P,hAPP_A702847159le_alt(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066,axiom,
! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,P),Q),R) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000,axiom,
! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(P),Q),R) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(P,R),hAPP_A1677245848t_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067,axiom,
! [P,Q] :
( is_fun279392540l_bool(P)
=> hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068,axiom,
! [P,Q] : hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q] :
( is_fun158382675l_bool(P)
=> hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
! [P,Q,R] : hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(P),Q),R) = hAPP_f393984045t_bool(P,hAPP_A1677245848t_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069,axiom,
! [P,Q] :
( is_fun1568535512t_bool(P)
=> hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070,axiom,
! [P,Q] :
( is_fun158382675l_bool(P)
=> hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071,axiom,
! [P,Q] :
( is_fun1236654035i_bool(P)
=> hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072,axiom,
! [P,Q] :
( is_fun158382675l_bool(P)
=> hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
! [P,Q,R] : hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,P),Q),R) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
! [P,Q,R] : hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(P),Q),R) = hAPP_f1539445765l_bool(P,hAPP_A1505516597le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073,axiom,
! [P,Q,R] : hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(P),Q),R) = hAPP_f344580165t_bool(P,hAPP_A1677245848t_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074,axiom,
! [P,Q,R] : hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,P),Q),R) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075,axiom,
! [P,Q,R] : hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(P),Q),R) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(P,R),hAPP_A1677245848t_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076,axiom,
! [P,Q,R] : hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(P),Q),R) = hAPP_f653880381t_bool(P,hAPP_A1553574765l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
! [P,Q,R] : hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(P),Q),R) = hAPP_b1588041841t_bool(P,hAPP_A1785763630i_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
! [P,Q,R] : hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,P),Q),R) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(P,R),Q) ).
%----Conjectures (1)
fof(conj_0,conjecture,
hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))) ).
%------------------------------------------------------------------------------