TPTP Problem File: SCT171+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT171+2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_500_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, 0.07 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.33 v5.4.0, 0.36 v5.3.0
% Syntax : Number of formulae : 885 ( 252 unt; 0 def)
% Number of atoms : 2217 ( 403 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1618 ( 286 ~; 39 |; 125 &)
% ( 179 <=>; 989 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 12 ( 11 usr; 0 prp; 1-2 aty)
% Number of functors : 440 ( 440 usr; 140 con; 0-3 aty)
% Number of variables : 1964 (1948 !; 16 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:33:32
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (127)
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OIIA,axiom,
is_fun292781289l_bool(arrow_885770895le_IIA) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin,axiom,
is_fun1420103068l_bool(arrow_912654623le_Lin) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OProf,axiom,
is_fun701126715l_bool(arrow_583275979e_Prof) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Obelow,axiom,
! [B_1_1,B_2_1,B_3_1] :
( ( is_fun20916972t_bool(B_1_1)
& is_Arr723427730le_alt(B_2_1)
& is_Arr723427730le_alt(B_3_1) )
=> is_fun20916972t_bool(arrow_207701375_below(B_1_1,B_2_1,B_3_1)) ) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Ounanimity,axiom,
is_fun292781289l_bool(arrow_1550141362nimity) ).
fof(gsy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsun,axiom,
is_fun1420103068l_bool(finite955821396le_alt) ).
fof(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000,axiom,
! [B_1_1,B_2_1,B_3_1] :
( ( is_fun20916972t_bool(B_1_1)
& is_Arr723427730le_alt(B_2_1)
& is_Arr723427730le_alt(B_3_1) )
=> is_bool(in_rel1361124802le_alt(B_1_1,B_2_1,B_3_1)) ) ).
fof(gsy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
! [B_1_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun1420103068l_bool(inj_on398823523t_bool(B_1_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_1_1)
=> is_fun701126715l_bool(pi_Arr1801471756t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_1_1)
=> is_fun292781289l_bool(pi_fun1555365306t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun1420103068l_bool(pi_Pro1873779901t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
is_Arr723427730le_alt(undefi1471133025le_alt(arrow_1486210539le_alt)) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
is_Arr859726945e_indi(undefi1052853330e_indi(arrow_132732488e_indi)) ).
fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
is_fun20916972t_bool(undefi541132219t_bool(fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool))) ).
fof(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_1_1)
=> is_fun1084921220e_indi(hilber951314860di_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_fun2015243113i_bool(top_to207207712i_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_fun701126715l_bool(top_to935749874l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,axiom,
is_fun292781289l_bool(top_to1849101472l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,axiom,
is_fun1420103068l_bool(top_to846262053l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,axiom,
is_fun20916972t_bool(top_to1773227171t_bool) ).
fof(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
! [B_1_1] :
( is_fun2015243113i_bool(B_1_1)
=> is_fun2015243113i_bool(collec279390863e_indi(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__Product____Type__Ounit,axiom,
! [B_1_1] :
( is_fun1568535512t_bool(B_1_1)
=> is_fun1568535512t_bool(collect_Product_unit(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi,axiom,
! [B_1_1] :
( is_fun701126715l_bool(B_1_1)
=> is_fun701126715l_bool(collec1567922785t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu,axiom,
! [B_1_1] :
( is_fun292781289l_bool(B_1_1)
=> is_fun292781289l_bool(collec1517527055t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1] :
( is_fun1420103068l_bool(B_1_1)
=> is_fun1420103068l_bool(collec612883262t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
! [B_1_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun20916972t_bool(collec1376511890le_alt(B_1_1)) ) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun1420103068l_bool(hAPP_A433435097l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_001,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun20916972t_bool(hAPP_A1014090479t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O,axiom,
! [B_1_1,B_2_1] :
( ( is_fun2015243113i_bool(B_1_1)
& is_Arr859726945e_indi(B_2_1) )
=> is_bool(hAPP_A416869060i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun701126715l_bool(hAPP_A701636433l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_002,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun292781289l_bool(hAPP_A955165183l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_003,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun1420103068l_bool(hAPP_A659996934l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun20916972t_bool(hAPP_A340536322t_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____wyls,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_b2116075462i_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_fun701126715l_bool(hAPP_b1461182872l_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_fun292781289l_bool(hAPP_b651754310l_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_fun1420103068l_bool(hAPP_b805997823l_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_fun20916972t_bool(hAPP_b763490121t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi,axiom,
! [B_1_1,B_2_1] :
( is_fun1084921220e_indi(B_1_1)
=> is_Arr859726945e_indi(hAPP_n619554777e_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____wylsu,axiom,
! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_n1600508401i_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__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_fun701126715l_bool(hAPP_P667392034l_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_fun292781289l_bool(hAPP_P1305865168l_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_fun1420103068l_bool(hAPP_P288224245l_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_fun20916972t_bool(hAPP_P401722323t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f212509069l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_2_1)
=> is_bool(hAPP_f160177134l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__005,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_f1282033109i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__006,axiom,
! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_f350403485e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__007,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_1_1)
=> is_bool(hAPP_f1378099862l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__008,axiom,
! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_f1570138413i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1009478556t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__010,axiom,
! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_f1895971544l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__011,hypothesis,
! [B_1_1,B_2_1] : is_fun20916972t_bool(hAPP_f1817389232t_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__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____wylsunqmtb__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f599997089l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_012,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1898839893l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_013,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2016919811l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_014,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_2_1)
=> is_bool(hAPP_f147218624l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_2_1)
=> is_fun701126715l_bool(hAPP_f189058133l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_016,axiom,
! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_f2043811403e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_017,axiom,
! [B_1_1,B_2_1] :
( is_fun292781289l_bool(B_1_1)
=> is_bool(hAPP_f446648900l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_018,axiom,
! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_f783549695i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_019,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1841347694t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_020,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1291635206l_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_f620747982l_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_f740740988l_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_f937100551l_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_f2053170815l_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_f1428735377l_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__Nat__Onat_J_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1426445843l_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_f866114756l_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_f1597773170l_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_f1965705105l_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_f1117143157l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f882250837l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_021,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1138659662l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_022,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1082951236l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_023,axiom,
! [B_1_1,B_2_1] :
( is_fun292781289l_bool(B_2_1)
=> is_bool(hAPP_f322109294l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_024,axiom,
! [B_1_1,B_2_1] :
( is_fun292781289l_bool(B_2_1)
=> is_fun292781289l_bool(hAPP_f1028172757l_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_f742658307l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f750478076l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_026,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f966397426l_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_f1021828400l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f560261801l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_028,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1384787615l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_029,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1363425282l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f817344902l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_030,axiom,
! [B_1_1,B_2_1] :
( is_fun1420103068l_bool(B_2_1)
=> is_bool(hAPP_f560517119l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031,axiom,
! [B_1_1,B_2_1] :
( is_fun1420103068l_bool(B_2_1)
=> is_fun1420103068l_bool(hAPP_f574392641l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_032,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f557371893l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_Arr859726945e_indi(hAPP_f1283454584e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033,hypothesis,
! [B_1_1,B_2_1] :
( ( is_fun1420103068l_bool(B_1_1)
& is_fun20916972t_bool(B_2_1) )
=> is_bool(hAPP_f1733357041l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___034,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_f431432850i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___035,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun1568535512t_bool(hAPP_f649586561t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun701126715l_bool(hAPP_f1332130404l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___037,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun1420103068l_bool(hAPP_f1344932147l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___038,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun20916972t_bool(hAPP_f137597973t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_,axiom,
! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_P1645359566e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_1_1)
=> is_bool(hAPP_P1813625415t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__040,axiom,
! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_P957402556i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041,axiom,
! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_P822772139t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042,hypothesis,
! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_P1151433609l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_Lab____,axiom,
is_fun20916972t_bool(lab) ).
fof(gsy_v_Lba____,axiom,
is_fun20916972t_bool(lba) ).
fof(gsy_v_a____,axiom,
is_Arr723427730le_alt(a) ).
fof(gsy_v_b____,axiom,
is_Arr723427730le_alt(b) ).
fof(gsy_v_c____,hypothesis,
is_Arr723427730le_alt(c) ).
fof(gsy_v_d____,hypothesis,
is_Arr723427730le_alt(d) ).
fof(gsy_v_e____,axiom,
is_Arr723427730le_alt(e) ).
%----Relevant facts (700)
fof(fact_0_assms_I3_J,axiom,
hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,f)) ).
fof(fact_1_u,axiom,
hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,f)) ).
fof(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
fof(fact_3__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,p),arrow_583275979e_Prof)) ).
fof(fact_4_in__mkbot,axiom,
! [X_2,Y_2,L_3,Z_1] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Z_1) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),Z_1)))
<=> ( Y_2 != Z_1
& ( X_2 = Z_1
=> X_2 != Y_2 )
& ( X_2 != Z_1
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) ) ) ) ) ).
fof(fact_5_in__mktop,axiom,
! [X_2,Y_2,L_3,Z_1] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Z_1) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),Z_1)))
<=> ( X_2 != Z_1
& ( Y_2 = Z_1
=> X_2 != Y_2 )
& ( Y_2 != Z_1
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) ) ) ) ) ).
fof(fact_6__C2_C,axiom,
! [P_1,Pa,A_34,B_32,Aa,Ba] :
( ( is_Arr723427730le_alt(A_34)
& is_Arr723427730le_alt(B_32)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( A_34 != B_32
=> ( Aa != B_32
=> ( Ba != A_34
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ) ) ).
fof(fact_7__C1_C,axiom,
! [P_1,Pa,A_34,B_32,Aa,Ba] :
( ( is_Arr723427730le_alt(A_34)
& is_Arr723427730le_alt(B_32)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( A_34 != B_32
=> ( Aa != B_32
=> ( Ba != A_34
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ) ) ).
fof(fact_8__C4_C,axiom,
! [P_1,Pa,Ca,Aa,Ba] :
( ( is_Arr723427730le_alt(Ca)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( Ba != Ca
=> ( Aa != Ca
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_A340536322t_bool(P_1,I_2))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).
fof(fact_9_pairwise__neutrality,axiom,
! [P_1,Pa,A_34,B_32,Aa,Ba] :
( ( is_Arr723427730le_alt(A_34)
& is_Arr723427730le_alt(B_32)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( A_34 != B_32
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ).
fof(fact_10__C3_C,axiom,
! [P_1,Pa,Aa,Ba] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_A340536322t_bool(P_1,I_2))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ).
fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I_2] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,I_2)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> ( ( hAPP_A1895296483di_nat(h,I_2) = n
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e))) )
& ( hAPP_A1895296483di_nat(h,I_2) != n
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))) ) ) ) ) ) ).
fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_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_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ).
fof(fact_14_PW,axiom,
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ) ).
fof(fact_15_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1813625415t_bool(Pa,X1))
<=> ! [A_1,B_25] :
( ( is_Arr723427730le_alt(A_1)
& is_Arr723427730le_alt(B_25) )
=> hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),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_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))),arrow_583275979e_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_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_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_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ).
fof(fact_19_n_I1_J,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite354462354e_indi(top_to207207712i_bool))) ).
fof(fact_20_injh,axiom,
hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(h),top_to207207712i_bool)) ).
fof(fact_21_Pair__inject,axiom,
! [A_36,B_34,A_35,B_33] :
( ( is_Arr723427730le_alt(A_36)
& is_Arr723427730le_alt(B_34)
& is_Arr723427730le_alt(A_35)
& is_Arr723427730le_alt(B_33) )
=> ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_36),B_34) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_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_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba)
& is_Arr723427730le_alt(A_34)
& is_Arr723427730le_alt(B_32) )
=> ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)
<=> ( Aa = A_34
& Ba = B_32 ) ) ) ).
fof(fact_23_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa))
<=> ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
=> ! [Xa] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof))
=> ! [A_1,B_25] :
( ( is_Arr723427730le_alt(A_1)
& is_Arr723427730le_alt(B_25) )
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa))) ) ) ) ) ) ) ).
fof(fact_24_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa))
<=> ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
=> ! [A_1,B_25] :
( ( is_Arr723427730le_alt(A_1)
& is_Arr723427730le_alt(B_25) )
=> ( ! [I_2] :
( is_Arr859726945e_indi(I_2)
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2))) )
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) ) ) ) ) ).
fof(fact_25_top1I,axiom,
! [X_2] : hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2)) ).
fof(fact_26_top1I,axiom,
! [X_2] : hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2)) ).
fof(fact_27_top1I,axiom,
! [X_2] : hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2)) ).
fof(fact_28_top1I,axiom,
! [X_2] : hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2)) ).
fof(fact_29_top1I,axiom,
! [X_2] : hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2)) ).
fof(fact_30_top1I,axiom,
! [X_2] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)) ).
fof(fact_31_top1I,axiom,
! [X_2] : hBOOL(hAPP_nat_bool(top_top_fun_nat_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_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_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_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)) ).
fof(fact_36_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)) ).
fof(fact_37_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)) ).
fof(fact_38_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_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_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_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_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)) ).
fof(fact_44_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)) ).
fof(fact_45_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)) ).
fof(fact_46_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_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_f1733357041l_bool(top_to846262053l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_49_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_50_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_51_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_52_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_53_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_54_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_55_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,top_to846262053l_bool),Aa)) ).
fof(fact_56_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,top_to935749874l_bool),Aa)) ).
fof(fact_57_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,top_to1849101472l_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_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,top_to1773227171t_bool),Aa)) ).
fof(fact_60_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,top_to207207712i_bool),Aa)) ).
fof(fact_61_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)) ).
fof(fact_62_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa)) ).
fof(fact_63_less__top,axiom,
! [Aa] :
( is_fun1420103068l_bool(Aa)
=> ( Aa != top_to846262053l_bool
<=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,Aa),top_to846262053l_bool)) ) ) ).
fof(fact_64_less__top,axiom,
! [Aa] :
( is_fun701126715l_bool(Aa)
=> ( Aa != top_to935749874l_bool
<=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,Aa),top_to935749874l_bool)) ) ) ).
fof(fact_65_less__top,axiom,
! [Aa] :
( is_fun292781289l_bool(Aa)
=> ( Aa != top_to1849101472l_bool
<=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,Aa),top_to1849101472l_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_fun20916972t_bool(Aa)
=> ( Aa != top_to1773227171t_bool
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,Aa),top_to1773227171t_bool)) ) ) ).
fof(fact_68_less__top,axiom,
! [Aa] :
( is_fun2015243113i_bool(Aa)
=> ( Aa != top_to207207712i_bool
<=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),top_to207207712i_bool)) ) ) ).
fof(fact_69_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_70_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_71_assms_I1_J,axiom,
hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,f),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_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_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba)))) ) ).
fof(fact_73__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lab),arrow_912654623le_Lin)) ).
fof(fact_74__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lba),arrow_912654623le_Lin)) ).
fof(fact_75__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab)) ).
fof(fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)) ).
fof(fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba)) ).
fof(fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)) ).
fof(fact_80_PiProf,axiom,
! [Na] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_583275979e_Prof)) ).
fof(fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
~ ! [Lab] :
( is_fun20916972t_bool(Lab)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),Lab))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lab),arrow_912654623le_Lin)) ) ) ).
fof(fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
~ ! [Lba] :
( is_fun20916972t_bool(Lba)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),Lba))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lba),arrow_912654623le_Lin)) ) ) ).
fof(fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> ( ( hAPP_A1895296483di_nat(h,I_2) = n
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e))) )
& ( hAPP_A1895296483di_nat(h,I_2) != n
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)) ) ) ) ).
fof(fact_84_n_I2_J,axiom,
! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))) ) ).
fof(fact_85_notin__Lin__iff,axiom,
! [X_2,Y_2,L_3] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2) )
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> ( X_2 != Y_2
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_2)),L_3)) ) ) ) ) ).
fof(fact_86_Lin__irrefl,axiom,
! [Aa,Ba,L_3] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),L_3))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),L_3)) ) ) ).
fof(fact_87_mktop__Lin,axiom,
! [X_2,L_3] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),X_2)),arrow_912654623le_Lin)) ) ).
fof(fact_88_mkbot__Lin,axiom,
! [X_2,L_3] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),X_2)),arrow_912654623le_Lin)) ) ).
fof(fact_89_above__Lin,axiom,
! [L_3,X_2,Y_2] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2) )
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),X_2),Y_2)),arrow_912654623le_Lin)) ) ) ) ).
fof(fact_90_const__Lin__Prof,axiom,
! [L_3] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,L_3)),arrow_583275979e_Prof)) ) ).
fof(fact_91_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_92_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_93_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_94_order__less__asym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ) ).
fof(fact_95_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_96_xt1_I10_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ) ).
fof(fact_97_xt1_I10_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ) ).
fof(fact_98_xt1_I10_J,axiom,
! [Z_1,Y_2,X_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2)) ) ) ).
fof(fact_99_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_100_order__less__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ) ).
fof(fact_101_order__less__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ) ).
fof(fact_102_order__less__trans,axiom,
! [Z_1,X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1)) ) ) ).
fof(fact_103_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_104_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_105_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_106_xt1_I2_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa)) ) ) ).
fof(fact_107_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_108_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_109_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_110_ord__less__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca)) ) ) ).
fof(fact_111_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_112_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_113_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_114_xt1_I1_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Ba))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa)) ) ) ).
fof(fact_115_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_116_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_117_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_118_ord__eq__less__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Ca))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca)) ) ) ).
fof(fact_119_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_120_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_121_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_122_xt1_I9_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ) ).
fof(fact_123_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_124_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_125_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_126_order__less__asym_H,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ) ).
fof(fact_127_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_128_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_129_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_130_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_131_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_132_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_133_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_134_order__less__imp__not__eq2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> Y_2 != X_2 ) ).
fof(fact_135_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_136_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_137_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_138_order__less__imp__not__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_139_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_140_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_141_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_142_order__less__imp__not__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ) ).
fof(fact_143_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_144_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_145_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_146_order__less__not__sym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ) ).
fof(fact_147_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_148_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_149_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_150_less__imp__neq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_151_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_152_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_153_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_154_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_155_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_156_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_157_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)) ).
fof(fact_158_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)) ).
fof(fact_159_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),X_2)) ).
fof(fact_160_order__less__irrefl,axiom,
! [X_21] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)) ).
fof(fact_161_UNIV__def,axiom,
top_to846262053l_bool = collec612883262t_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,fTrue)) ).
fof(fact_162_UNIV__def,axiom,
top_to935749874l_bool = collec1567922785t_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,fTrue)) ).
fof(fact_163_UNIV__def,axiom,
top_to1849101472l_bool = collec1517527055t_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,fTrue)) ).
fof(fact_164_UNIV__def,axiom,
top_to1773227171t_bool = collec1376511890le_alt(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,fTrue)) ).
fof(fact_165_UNIV__def,axiom,
top_to207207712i_bool = collec279390863e_indi(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,fTrue)) ).
fof(fact_166_UNIV__def,axiom,
top_to1257323279t_bool = collect_Product_unit(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)) ).
fof(fact_167_UNIV__def,axiom,
top_top_fun_nat_bool = collect_nat(hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)) ).
fof(fact_168_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
<=> hBOOL(hAPP_A416869060i_bool(A,X_2)) ) ).
fof(fact_169_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_170_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_171_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
<=> hBOOL(hAPP_P1813625415t_bool(A,X_2)) ) ).
fof(fact_172_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
<=> hBOOL(hAPP_f1378099862l_bool(A,X_2)) ) ).
fof(fact_173_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
<=> hBOOL(hAPP_f446648900l_bool(A,X_2)) ) ).
fof(fact_174_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
<=> hBOOL(hAPP_f1733357041l_bool(A,X_2)) ) ).
fof(fact_175_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_176_Collect__def,axiom,
! [Pa] :
( is_fun1568535512t_bool(Pa)
=> collect_Product_unit(Pa) = Pa ) ).
fof(fact_177_Collect__def,axiom,
! [Pa] :
( is_fun2015243113i_bool(Pa)
=> collec279390863e_indi(Pa) = Pa ) ).
fof(fact_178_Collect__def,axiom,
! [Pa] : collect_nat(Pa) = Pa ).
fof(fact_179_in__above,axiom,
! [X_2,Y_2,L_3,Aa,Ba] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),Aa),Ba)))
<=> ( X_2 != Y_2
& ( X_2 = Ba
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_3)) )
& ( X_2 != Ba
=> ( ( Y_2 = Ba
=> ( X_2 = Aa
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Aa)),L_3)) ) )
& ( Y_2 != Ba
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ) ).
fof(fact_180_pred__equals__eq2,axiom,
! [S_1,R_1] :
( ( is_fun20916972t_bool(S_1)
& is_fun20916972t_bool(R_1) )
=> ( ! [X_1,Xa] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Xa) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1)) ) )
<=> R_1 = S_1 ) ) ).
fof(fact_181_n_I3_J,axiom,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ).
fof(fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ) ).
fof(fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
! [I_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
=> ( ( hAPP_A1895296483di_nat(h,I_2) = n
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e))) )
& ( hAPP_A1895296483di_nat(h,I_2) != n
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba)) ) ) ) ).
fof(fact_184_inv__f__eq,axiom,
! [X_2,Y_2,F] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
=> ( hAPP_A1895296483di_nat(F,X_2) = Y_2
=> hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),Y_2) = X_2 ) ) ) ).
fof(fact_185_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_186_inv__f__f,axiom,
! [X_2,F] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
=> hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),hAPP_A1895296483di_nat(F,X_2)) = X_2 ) ) ).
fof(fact_187_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_188_dictatorI,axiom,
! [I_1,Fa] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Fa),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin))))
=> ( ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
=> ! [A_1,B_25] :
( ( is_Arr723427730le_alt(A_1)
& is_Arr723427730le_alt(B_25) )
=> ( A_1 != B_25
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_1)))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) ) ) ) )
=> hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1)) ) ) ).
fof(fact_189_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ) ).
fof(fact_190_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ) ).
fof(fact_191_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_192_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1117143157l_bool(hAPP_f2011903565l_bool(member485283698le_alt,F),pi_Pro1208494515le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P1931143485le_alt(F,X_2)),hAPP_P401722323t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_193_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ) ).
fof(fact_194_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_195_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f866114756l_bool(hAPP_f813426957l_bool(member1044213697t_bool,F),pi_Pro1114473858t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1245388556t_bool(F,X_2)),hAPP_P667392034l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_196_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ) ).
fof(fact_197_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_198_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1597773170l_bool(hAPP_f627309453l_bool(member1775405935t_bool,F),pi_Pro831923248t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P1157363642t_bool(F,X_2)),hAPP_P1305865168l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_199_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).
fof(fact_200_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1965705105l_bool(hAPP_f177302985l_bool(member928589940t_bool,F),pi_Pro1925515229t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P401722323t_bool(F,X_2)),hAPP_P288224245l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).
fof(fact_201_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,B)))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1895296483di_nat(F,X_2)),hAPP_A1948275303t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ) ).
fof(fact_202_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_203_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_204_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ) ).
fof(fact_205_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f557371893l_bool(hAPP_f785487437l_bool(member1226631410t_unit,F),pi_Pro269694131t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P992343101t_unit(F,X_2)),hAPP_P822772139t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ) ).
fof(fact_206_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ) ).
fof(fact_207_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ) ).
fof(fact_208_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1082951236l_bool(hAPP_f1160956173l_bool(member982489409t_unit,F),pi_fun623621634t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f754536332t_unit(F,X_2)),hAPP_f1009478556t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ) ).
fof(fact_209_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ) ).
fof(fact_210_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ) ).
fof(fact_211_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f966397426l_bool(hAPP_f1957108621l_bool(member1941767151t_unit,F),pi_fun1390764464t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1716204858t_unit(F,X_2)),hAPP_f1841347694t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ) ).
fof(fact_212_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ) ).
fof(fact_213_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ) ).
fof(fact_214_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1384787615l_bool(hAPP_f715600357l_bool(member416763266t_unit,F),pi_fun1012573681t_unit(A,B)))
=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1636264423t_unit(F,X_2)),hAPP_f649586561t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ) ).
fof(fact_215_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1428735377l_bool(hAPP_f544923081l_bool(member1801639028e_indi,F),pi_nat1476290531e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_n619554777e_indi(F,X_2)),hAPP_n1600508401i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).
fof(fact_216_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_217_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_218_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ) ).
fof(fact_219_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ) ).
fof(fact_220_complete__Lin,axiom,
! [Aa,Ba] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ? [X_1] :
( is_fun20916972t_bool(X_1)
& hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),arrow_912654623le_Lin))
& hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),X_1)) ) ) ) ).
fof(fact_221_Pi__UNIV,axiom,
! [A] : pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool ).
fof(fact_222_Pi__UNIV,axiom,
! [A] : pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool ).
fof(fact_223_Pi__UNIV,axiom,
! [A] : pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool ).
fof(fact_224_order__refl,axiom,
! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)) ).
fof(fact_225_order__refl,axiom,
! [X_20] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)) ).
fof(fact_226_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)) ).
fof(fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
? [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool)))
& ! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
& hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba)))) ) ).
fof(fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
~ ! [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool)))
=> ( ! [M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba)))) ) ) ).
fof(fact_229_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_230_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_231_xt1_I6_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_2)) ) ) ).
fof(fact_232_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_233_xt1_I6_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_2)) ) ) ).
fof(fact_234_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_235_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_236_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_237_order__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_1)) ) ) ).
fof(fact_238_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_239_order__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_1)) ) ) ).
fof(fact_240_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_241_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_242_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_243_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_244_xt1_I4_J,axiom,
! [C_20,B_24,A_27] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_27))
=> ( B_24 = C_20
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_27)) ) ) ).
fof(fact_245_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_246_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_247_ord__le__eq__trans,axiom,
! [C_19,A_26,B_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_23))
=> ( B_23 = C_19
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),C_19)) ) ) ).
fof(fact_248_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_249_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_250_xt1_I3_J,axiom,
! [C_18,A_25,B_22] :
( A_25 = 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_25)) ) ) ).
fof(fact_251_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_252_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_253_ord__eq__le__trans,axiom,
! [C_17,A_24,B_21] :
( A_24 = 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_24),C_17)) ) ) ).
fof(fact_254_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_255_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_256_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_257_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_258_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_259_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_260_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_261_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_262_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_263_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_264_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_265_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_266_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_267_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_268_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_269_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_270_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_271_order__less__le,axiom,
! [X_2,Y_2] :
( ( is_fun2015243113i_bool(X_2)
& is_fun2015243113i_bool(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ) ).
fof(fact_272_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_273_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_274_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_275_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_276_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2)) ) ) ).
fof(fact_277_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_278_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_279_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_280_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_281_order__le__less,axiom,
! [X_2,Y_2] :
( ( is_fun2015243113i_bool(X_2)
& is_fun2015243113i_bool(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_282_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_283_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_284_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_285_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_286_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_287_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_288_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_289_order__neq__le__trans,axiom,
! [Aa,Ba] :
( ( is_fun2015243113i_bool(Aa)
& is_fun2015243113i_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ) ) ) ).
fof(fact_290_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_291_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_292_order__neq__le__trans,axiom,
! [A_23,B_20] :
( A_23 != B_20
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),B_20))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_20)) ) ) ).
fof(fact_293_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_294_xt1_I12_J,axiom,
! [Aa,Ba] :
( ( is_fun2015243113i_bool(Aa)
& is_fun2015243113i_bool(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ) ) ) ).
fof(fact_295_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_296_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_297_xt1_I12_J,axiom,
! [A_22,B_19] :
( A_22 != B_19
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_22)) ) ) ).
fof(fact_298_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_299_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_300_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) ) ).
fof(fact_301_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_302_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_303_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_304_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_305_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_306_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( ( is_fun2015243113i_bool(X_2)
& is_fun2015243113i_bool(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
| X_2 = Y_2 ) ) ) ).
fof(fact_307_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_308_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_309_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_310_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_311_order__le__neq__trans,axiom,
! [Aa,Ba] :
( ( is_fun2015243113i_bool(Aa)
& is_fun2015243113i_bool(Ba) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba))
=> ( Aa != Ba
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ) ) ) ).
fof(fact_312_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_313_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_314_order__le__neq__trans,axiom,
! [A_21,B_18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_18))
=> ( A_21 != B_18
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_18)) ) ) ).
fof(fact_315_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_316_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_317_xt1_I11_J,axiom,
! [Ba,Aa] :
( ( is_fun2015243113i_bool(Ba)
& is_fun2015243113i_bool(Aa) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa))
=> ( Aa != Ba
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ) ) ) ).
fof(fact_318_xt1_I11_J,axiom,
! [B_17,A_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_20))
=> ( A_20 != B_17
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_20)) ) ) ).
fof(fact_319_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_320_order__less__le__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ) ).
fof(fact_321_order__less__le__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ) ).
fof(fact_322_order__less__le__trans,axiom,
! [Z_1,X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),Z_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1)) ) ) ).
fof(fact_323_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_324_order__less__le__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1)) ) ) ).
fof(fact_325_xt1_I7_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ) ).
fof(fact_326_xt1_I7_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ) ).
fof(fact_327_xt1_I7_J,axiom,
! [Z_1,Y_2,X_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Z_1),Y_2))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2)) ) ) ).
fof(fact_328_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_329_xt1_I7_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2)) ) ) ).
fof(fact_330_order__le__less__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ) ).
fof(fact_331_order__le__less__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ) ).
fof(fact_332_order__le__less__trans,axiom,
! [Z_1,X_2,Y_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1)) ) ) ).
fof(fact_333_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_334_order__le__less__trans,axiom,
! [Z_1,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_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1)) ) ) ).
fof(fact_335_xt1_I8_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ) ).
fof(fact_336_xt1_I8_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ) ).
fof(fact_337_xt1_I8_J,axiom,
! [Z_1,Y_2,X_2] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2)) ) ) ).
fof(fact_338_xt1_I8_J,axiom,
! [Z_2,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_2),Y_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3)) ) ) ).
fof(fact_339_xt1_I8_J,axiom,
! [Z_1,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_1),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2)) ) ) ).
fof(fact_340_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)) ).
fof(fact_341_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,Aa),top_to846262053l_bool)) ).
fof(fact_342_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,Aa),top_to1849101472l_bool)) ).
fof(fact_343_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,Aa),top_to935749874l_bool)) ).
fof(fact_344_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,Aa),top_to1773227171t_bool)) ).
fof(fact_345_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)) ).
fof(fact_346_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)) ).
fof(fact_347_top__greatest,axiom,
! [Aa] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),top_to207207712i_bool)) ).
fof(fact_348_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_349_top__unique,axiom,
! [Aa] :
( is_fun1420103068l_bool(Aa)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa))
<=> Aa = top_to846262053l_bool ) ) ).
fof(fact_350_top__unique,axiom,
! [Aa] :
( is_fun292781289l_bool(Aa)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa))
<=> Aa = top_to1849101472l_bool ) ) ).
fof(fact_351_top__unique,axiom,
! [Aa] :
( is_fun701126715l_bool(Aa)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa))
<=> Aa = top_to935749874l_bool ) ) ).
fof(fact_352_top__unique,axiom,
! [Aa] :
( is_fun20916972t_bool(Aa)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa))
<=> Aa = top_to1773227171t_bool ) ) ).
fof(fact_353_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_354_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_355_top__unique,axiom,
! [Aa] :
( is_fun2015243113i_bool(Aa)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa))
<=> Aa = top_to207207712i_bool ) ) ).
fof(fact_356_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_357_top__le,axiom,
! [Aa] :
( is_fun1420103068l_bool(Aa)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa))
=> Aa = top_to846262053l_bool ) ) ).
fof(fact_358_top__le,axiom,
! [Aa] :
( is_fun292781289l_bool(Aa)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa))
=> Aa = top_to1849101472l_bool ) ) ).
fof(fact_359_top__le,axiom,
! [Aa] :
( is_fun701126715l_bool(Aa)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa))
=> Aa = top_to935749874l_bool ) ) ).
fof(fact_360_top__le,axiom,
! [Aa] :
( is_fun20916972t_bool(Aa)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa))
=> Aa = top_to1773227171t_bool ) ) ).
fof(fact_361_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_362_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_363_top__le,axiom,
! [Aa] :
( is_fun2015243113i_bool(Aa)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa))
=> Aa = top_to207207712i_bool ) ) ).
fof(fact_364_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_365_inj__on__def,axiom,
! [F,A] :
( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
<=> ! [X_1] :
( is_Arr859726945e_indi(X_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> ! [Xa] :
( is_Arr859726945e_indi(Xa)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Xa),A))
=> ( hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Xa)
=> X_1 = Xa ) ) ) ) ) ) ).
fof(fact_366_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_367_inj__on__contraD,axiom,
! [X_2,Y_2,F,A] :
( ( is_Arr859726945e_indi(X_2)
& is_Arr859726945e_indi(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
=> hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2) ) ) ) ) ) ).
fof(fact_368_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_369_inj__on__iff,axiom,
! [Y_2,X_2,F,A] :
( ( is_Arr859726945e_indi(Y_2)
& is_Arr859726945e_indi(X_2) )
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
=> ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
<=> X_2 = Y_2 ) ) ) ) ) ).
fof(fact_370_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_371_inj__onD,axiom,
! [X_2,Y_2,F,A] :
( ( is_Arr859726945e_indi(X_2)
& is_Arr859726945e_indi(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
=> ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
=> X_2 = Y_2 ) ) ) ) ) ).
fof(fact_372_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2))) ) ) ).
fof(fact_373_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2))) ) ) ).
fof(fact_374_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2))) ) ) ).
fof(fact_375_Prof__def,axiom,
arrow_583275979e_Prof = pi_Arr1801471756t_bool(top_to207207712i_bool,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,arrow_912654623le_Lin)) ).
fof(fact_376_inj__on__id2,axiom,
! [A] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)) ).
fof(fact_377_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),B)) ) ) ).
fof(fact_378_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),B)) ) ) ).
fof(fact_379_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),B)) ) ) ).
fof(fact_380_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1))
<=> ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
=> hAPP_f1817389232t_bool(Fa,X_1) = hAPP_A340536322t_bool(X_1,I_1) ) ) ).
fof(fact_381_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_382_inj__eq,axiom,
! [X_2,Y_2,F] :
( ( is_Arr859726945e_indi(X_2)
& is_Arr859726945e_indi(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
=> ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
<=> X_2 = Y_2 ) ) ) ).
fof(fact_383_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_384_injD,axiom,
! [X_2,Y_2,F] :
( ( is_Arr859726945e_indi(X_2)
& is_Arr859726945e_indi(Y_2) )
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
=> ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
=> X_2 = Y_2 ) ) ) ).
fof(fact_385_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_386_inv__into__f__f,axiom,
! [X_2,F,A] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> hAPP_n619554777e_indi(hilber951314860di_nat(A,F),hAPP_A1895296483di_nat(F,X_2)) = X_2 ) ) ) ).
fof(fact_387_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_388_inv__into__f__eq,axiom,
! [Y_2,X_2,F,A] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> ( hAPP_A1895296483di_nat(F,X_2) = Y_2
=> hAPP_n619554777e_indi(hilber951314860di_nat(A,F),Y_2) = X_2 ) ) ) ) ).
fof(fact_389_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1))) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ) ).
fof(fact_390_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr859726945e_indi(X_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ) ).
fof(fact_391_Pi__I,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1))) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ) ).
fof(fact_392_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_393_inj__imp__inv__eq,axiom,
! [G,F] :
( is_fun1084921220e_indi(G)
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
=> ( ! [X_1] : hAPP_A1895296483di_nat(F,hAPP_n619554777e_indi(G,X_1)) = X_1
=> hilber951314860di_nat(top_to207207712i_bool,F) = G ) ) ) ).
fof(fact_394_less__add__one,axiom,
! [A_19] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),one_one_nat))) ).
fof(fact_395_add__less__le__mono,axiom,
! [C_16,D_3,A_18,B_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),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_18),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3))) ) ) ).
fof(fact_396_add__le__less__mono,axiom,
! [C_15,D_2,A_17,B_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),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_17),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2))) ) ) ).
fof(fact_397_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_398_injI,axiom,
! [F] :
( ! [X_1,Y_1] :
( ( is_Arr859726945e_indi(X_1)
& is_Arr859726945e_indi(Y_1) )
=> ( hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1)
=> X_1 = Y_1 ) )
=> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) ) ).
fof(fact_399_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_400_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_401_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,F),G))
<=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,F),G))
& ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,G),F)) ) ) ).
fof(fact_402_Pi__anti__mono,axiom,
! [B,A_16,A] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A_16),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A_16,B))) ) ).
fof(fact_403_Pi__anti__mono,axiom,
! [B,A_16,A] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A_16),A))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A_16,B))) ) ).
fof(fact_404_Pi__anti__mono,axiom,
! [B,A_16,A] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A_16),A))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A_16,B))) ) ).
fof(fact_405_pred__subset__eq2,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),R_1)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),S_1)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)) ) ).
fof(fact_406_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),top_to846262053l_bool)) ).
fof(fact_407_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),top_to1849101472l_bool)) ).
fof(fact_408_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),top_to935749874l_bool)) ).
fof(fact_409_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),top_to1773227171t_bool)) ).
fof(fact_410_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)) ).
fof(fact_411_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)) ).
fof(fact_412_subset__UNIV,axiom,
! [A] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),top_to207207712i_bool)) ).
fof(fact_413_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_414_subset__inj__on,axiom,
! [A,F,B] :
( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
=> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) ) ) ).
fof(fact_415_add__right__imp__eq,axiom,
! [B_14,A_15,C_14] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_15)
=> B_14 = C_14 ) ).
fof(fact_416_add__imp__eq,axiom,
! [A_14,B_13,C_13] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_13)
=> B_13 = C_13 ) ).
fof(fact_417_add__left__imp__eq,axiom,
! [A_13,B_12,C_12] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_12)
=> B_12 = C_12 ) ).
fof(fact_418_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_419_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_420_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_12,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_12),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)) ).
fof(fact_421_one__reorient,axiom,
! [X_2] :
( one_one_nat = X_2
<=> X_2 = one_one_nat ) ).
fof(fact_422_add__le__imp__le__left,axiom,
! [C_10,A_11,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_11)),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_11),B_10)) ) ).
fof(fact_423_add__le__imp__le__right,axiom,
! [A_10,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_10),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_10),B_9)) ) ).
fof(fact_424_add__mono,axiom,
! [C_8,D_1,A_9,B_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),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_9),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1))) ) ) ).
fof(fact_425_add__left__mono,axiom,
! [C_7,A_8,B_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),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_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))) ) ).
fof(fact_426_add__right__mono,axiom,
! [C_6,A_7,B_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),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_7),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))) ) ).
fof(fact_427_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_428_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_429_add__less__imp__less__left,axiom,
! [C_5,A_6,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_6)),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_6),B_5)) ) ).
fof(fact_430_add__less__imp__less__right,axiom,
! [A_5,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_5),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_5),B_4)) ) ).
fof(fact_431_add__strict__mono,axiom,
! [C_3,D,A_4,B_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),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_4),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D))) ) ) ).
fof(fact_432_add__strict__left__mono,axiom,
! [C_2,A_3,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),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_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))) ) ).
fof(fact_433_add__strict__right__mono,axiom,
! [C_1,A_2,B_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))) ) ).
fof(fact_434_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_435_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_436_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_437_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_438_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_439_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_440_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B)) ) ) ).
fof(fact_441_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_442_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B)) ) ) ).
fof(fact_443_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B)) ) ) ).
fof(fact_444_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B)) ) ) ).
fof(fact_445_subsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B)) ) ) ).
fof(fact_446_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_447_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_448_psubset__eq,axiom,
! [A,B] :
( ( is_fun2015243113i_bool(A)
& is_fun2015243113i_bool(B) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
<=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
& A != B ) ) ) ).
fof(fact_449_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_450_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_451_subset__iff__psubset__eq,axiom,
! [A,B] :
( ( is_fun2015243113i_bool(A)
& is_fun2015243113i_bool(B) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
<=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
| A = B ) ) ) ).
fof(fact_452_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_453_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_454_psubset__imp__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ) ).
fof(fact_455_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_456_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_457_psubset__subset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,B),C))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C)) ) ) ).
fof(fact_458_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_459_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).
fof(fact_460_subset__psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C)) ) ) ).
fof(fact_461_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_462_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_463_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ) ).
fof(fact_464_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ) ).
fof(fact_465_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B)) ) ) ).
fof(fact_466_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_467_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B)) ) ) ).
fof(fact_468_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B)) ) ) ).
fof(fact_469_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B)) ) ) ).
fof(fact_470_set__mp,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B)) ) ) ).
fof(fact_471_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ) ).
fof(fact_472_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ) ).
fof(fact_473_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B)) ) ) ).
fof(fact_474_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_475_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B)) ) ) ).
fof(fact_476_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B)) ) ) ).
fof(fact_477_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B)) ) ) ).
fof(fact_478_set__rev__mp,axiom,
! [B,X_2,A] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B)) ) ) ).
fof(fact_479_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_480_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ) ).
fof(fact_481_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ) ).
fof(fact_482_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B)) ) ) ).
fof(fact_483_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_484_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B)) ) ) ).
fof(fact_485_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B)) ) ) ).
fof(fact_486_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B)) ) ) ).
fof(fact_487_in__mono,axiom,
! [X_2,A,B] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B)) ) ) ).
fof(fact_488_equalityD2,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ).
fof(fact_489_equalityD1,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).
fof(fact_490_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_491_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_492_subset__refl,axiom,
! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)) ).
fof(fact_493_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1)))
<=> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)) ) ).
fof(fact_494_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),R_1)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),S_1)))
<=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,R_1),S_1)) ) ).
fof(fact_495_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),R_1)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),S_1)))
<=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,R_1),S_1)) ) ).
fof(fact_496_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_497_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),R_1)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),S_1)))
<=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,R_1),S_1)) ) ).
fof(fact_498_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),R_1)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),S_1)))
<=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,R_1),S_1)) ) ).
fof(fact_499_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),R_1)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),S_1)))
<=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,R_1),S_1)) ) ).
fof(fact_500_pred__subset__eq,axiom,
! [R_1,S_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),R_1)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),S_1)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)) ) ).
fof(fact_501_Pi__mono,axiom,
! [B,C,A] :
( ! [X_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(B,X_1)),hAPP_P1122857141l_bool(C,X_1))) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A,C))) ) ).
fof(fact_502_Pi__mono,axiom,
! [B,C,A] :
( ! [X_1] :
( is_Arr859726945e_indi(X_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(B,X_1)),hAPP_A659996934l_bool(C,X_1))) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A,C))) ) ).
fof(fact_503_Pi__mono,axiom,
! [B,C,A] :
( ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(B,X_1)),hAPP_f1895971544l_bool(C,X_1))) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A,C))) ) ).
fof(fact_504_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( is_bool(X_1)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),B)) ) )
=> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) ) ).
fof(fact_505_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),B)) )
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) ).
fof(fact_506_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( is_Arr859726945e_indi(X_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),B)) ) )
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ) ).
fof(fact_507_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).
fof(fact_508_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( is_fun20916972t_bool(X_1)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),B)) ) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) ) ).
fof(fact_509_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),B)) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) ) ).
fof(fact_510_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),B)) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) ) ).
fof(fact_511_subsetI,axiom,
! [B,A] :
( ! [X_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),B)) )
=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) ) ).
fof(fact_512_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_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_513_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_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_514_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B)) ) ) ).
fof(fact_515_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_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_516_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,A),B))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B)) ) ) ).
fof(fact_517_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,A),B))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B)) ) ) ).
fof(fact_518_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,A),B))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B)) ) ) ).
fof(fact_519_psubsetD,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,A),B))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B)) ) ) ).
fof(fact_520_psubset__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_le382113706t_bool,B),C))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).
fof(fact_521_psubset__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_le1976645739t_bool,B),C))
=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).
fof(fact_522_psubset__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C))
=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C)) ) ) ).
fof(fact_523_in__below,axiom,
! [X_2,Y_2,L_3,Aa,Ba] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),arrow_207701375_below(L_3,Aa,Ba)))
<=> ( X_2 != Y_2
& ( Y_2 = Aa
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Ba)),L_3)) )
& ( Y_2 != Aa
=> ( ( X_2 = Aa
=> ( Y_2 = Ba
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_3)) ) )
& ( X_2 != Aa
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ) ).
fof(fact_524_add__leE,axiom,
! [M_2,K_1,N_1] :
( 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_1)),N_1))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ) ).
fof(fact_525_add__leD1,axiom,
! [M_2,K_1,N_1] :
( 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_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
fof(fact_526_add__leD2,axiom,
! [M_2,K_1,N_1] :
( 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_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ).
fof(fact_527_less__not__refl,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).
fof(fact_528_nat__neq__iff,axiom,
! [M_4,Na] :
( M_4 != Na
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) ) ) ).
fof(fact_529_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_530_less__irrefl__nat,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).
fof(fact_531_less__not__refl2,axiom,
! [N_1,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2))
=> M_2 != N_1 ) ).
fof(fact_532_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ) ).
fof(fact_533_nat__less__cases,axiom,
! [Pa,M_4,Na] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
=> ( ( M_4 = Na
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) ) ) ) ).
fof(fact_534_nat__add__commute,axiom,
! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2) ).
fof(fact_535_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_536_nat__add__assoc,axiom,
! [M_2,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),K_1) = 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_1),K_1)) ).
fof(fact_537_nat__add__left__cancel,axiom,
! [K,M_4,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
<=> M_4 = Na ) ).
fof(fact_538_nat__add__right__cancel,axiom,
! [M_4,K,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
<=> M_4 = Na ) ).
fof(fact_539_le__refl,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)) ).
fof(fact_540_nat__le__linear,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) ) ).
fof(fact_541_eq__imp__le,axiom,
! [M_2,N_1] :
( M_2 = N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
fof(fact_542_le__trans,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_1)) ) ) ).
fof(fact_543_le__antisym,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
=> M_2 = N_1 ) ) ).
fof(fact_544_below__Lin,axiom,
! [L_3,X_2,Y_2] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_2) )
=> ( X_2 != Y_2
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,arrow_207701375_below(L_3,X_2,Y_2)),arrow_912654623le_Lin)) ) ) ) ).
fof(fact_545_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_546_not__add__less1,axiom,
! [I,J_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),I)) ).
fof(fact_547_not__add__less2,axiom,
! [J_2,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),I)) ).
fof(fact_548_nat__add__left__cancel__less,axiom,
! [K,M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ).
fof(fact_549_trans__less__add1,axiom,
! [M_2,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))) ) ).
fof(fact_550_trans__less__add2,axiom,
! [M_2,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))) ) ).
fof(fact_551_add__less__mono1,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))) ) ).
fof(fact_552_add__less__mono,axiom,
! [K_1,L_2,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2))) ) ) ).
fof(fact_553_less__add__eq__less,axiom,
! [M_2,N_1,K_1,L_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ) ).
fof(fact_554_add__lessD1,axiom,
! [I,J_2,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)) ) ).
fof(fact_555_nat__less__le,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
& M_4 != Na ) ) ).
fof(fact_556_le__eq__less__or__eq,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
| M_4 = Na ) ) ).
fof(fact_557_less__imp__le__nat,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
fof(fact_558_le__neq__implies__less,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
=> ( M_2 != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ) ).
fof(fact_559_less__or__eq__imp__le,axiom,
! [M_2,N_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
| M_2 = N_1 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
fof(fact_560_le__add2,axiom,
! [N_1,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1))) ).
fof(fact_561_le__add1,axiom,
! [N_1,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2))) ).
fof(fact_562_le__iff__add,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
<=> ? [K_2] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2) ) ).
fof(fact_563_nat__add__left__cancel__le,axiom,
! [K,M_4,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_4)),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_4),Na)) ) ).
fof(fact_564_trans__le__add1,axiom,
! [M_2,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))) ) ).
fof(fact_565_trans__le__add2,axiom,
! [M_2,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))) ) ).
fof(fact_566_add__le__mono1,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))) ) ).
fof(fact_567_add__le__mono,axiom,
! [K_1,L_2,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2))) ) ) ).
fof(fact_568_mono__nat__linear__lb,axiom,
! [M_4,K,F] :
( ! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N))) )
=> 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_4)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K)))) ) ).
fof(fact_569_less__mono__imp__le__mono,axiom,
! [I_1,J_1,F] :
( ! [I_2,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1))) ) ) ).
fof(fact_570_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_571_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_572_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_573_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_574_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_575_in__rel__def,axiom,
! [R_1,X_2,Y_2] :
( hBOOL(in_rel1361124802le_alt(R_1,X_2,Y_2))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1)) ) ).
fof(fact_576_funcsetI,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),B)) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) ) ).
fof(fact_577_funcsetI,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr859726945e_indi(X_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),B)) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) ) ).
fof(fact_578_funcsetI,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),B)) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) ) ).
fof(fact_579_linear__alt,axiom,
? [L_1] :
( is_fun20916972t_bool(L_1)
& hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) ) ).
fof(fact_580_Pi__cong,axiom,
! [B,G,F,A] :
( ! [W] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,W),A))
=> ( hBOOL(hAPP_P1813625415t_bool(F,W))
<=> hBOOL(hAPP_P1813625415t_bool(G,W)) ) )
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
<=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A,B))) ) ) ).
fof(fact_581_Pi__cong,axiom,
! [B,F,G,A] :
( ! [W] :
( is_Arr859726945e_indi(W)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,W),A))
=> hAPP_A340536322t_bool(F,W) = hAPP_A340536322t_bool(G,W) ) )
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
<=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A,B))) ) ) ).
fof(fact_582_Pi__cong,axiom,
! [B,F,G,A] :
( ! [W] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,W),A))
=> hAPP_f1817389232t_bool(F,W) = hAPP_f1817389232t_bool(G,W) )
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
<=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A,B))) ) ) ).
fof(fact_583_Pi__I_H,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1))) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ) ).
fof(fact_584_Pi__I_H,axiom,
! [F,B,A] :
( ! [X_1] :
( is_Arr859726945e_indi(X_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1))) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ) ).
fof(fact_585_Pi__I_H,axiom,
! [F,B,A] :
( ! [X_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1))) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ) ).
fof(fact_586_card__inj,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,F),pi_nat_nat(A,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,B))))
=> ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(A)),finite_card_nat(B))) ) ) ) ).
fof(fact_587_card__inj,axiom,
! [F,A,B] :
( hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,B))))
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite_card_nat(B))) ) ) ) ).
fof(fact_588_card__inj,axiom,
! [F,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
=> ( hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A))
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1044330389le_alt(A)),finite_card_bool(B))) ) ) ) ).
fof(fact_589_card__inj,axiom,
! [F,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A))
=> ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite945540987t_bool(B))) ) ) ) ).
fof(fact_590_card__inj,axiom,
! [F,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
=> ( hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A))
=> ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1524925796t_bool(A)),finite945540987t_bool(B))) ) ) ) ).
fof(fact_591_inj__onI,axiom,
! [F,A] :
( ! [X_1,Y_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A))
=> ( 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),A)) ) ).
fof(fact_592_inj__onI,axiom,
! [F,A] :
( ! [X_1,Y_1] :
( ( is_Arr859726945e_indi(X_1)
& is_Arr859726945e_indi(Y_1) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_1),A))
=> ( hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1)
=> X_1 = Y_1 ) ) ) )
=> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) ) ).
fof(fact_593_inj__on__cong,axiom,
! [F,G,A] :
( ! [A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
=> hAPP_nat_nat(F,A_1) = hAPP_nat_nat(G,A_1) )
=> ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
<=> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(G),A)) ) ) ).
fof(fact_594_inj__on__cong,axiom,
! [F,G,A] :
( ! [A_1] :
( is_Arr859726945e_indi(A_1)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,A_1),A))
=> hAPP_A1895296483di_nat(F,A_1) = hAPP_A1895296483di_nat(G,A_1) ) )
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
<=> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(G),A)) ) ) ).
fof(fact_595_finite__indi,axiom,
hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,top_to207207712i_bool)) ).
fof(fact_596_card__bij,axiom,
! [G,F,A,B] :
( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B))))
=> ( hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(F),A))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(B,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,A))))
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(G),B))
=> ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A))
=> ( hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,B))
=> finite945540987t_bool(A) = finite354462354e_indi(B) ) ) ) ) ) ) ).
fof(fact_597_card__bij,axiom,
! [G,F,A,B] :
( hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,F),pi_fun328162388t_bool(A,hAPP_f23348649l_bool(cOMBK_761999167t_bool,B))))
=> ( hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(F),A))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(B,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,A))))
=> ( hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(G),B))
=> ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A))
=> ( hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,B))
=> finite945540987t_bool(A) = finite1524925796t_bool(B) ) ) ) ) ) ) ).
fof(fact_598_card__bij,axiom,
! [G,F,A,B] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
=> ( hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A))
=> ( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,G),pi_boo1542163389le_alt(B,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,A))))
=> ( hBOOL(hAPP_f387058535l_bool(inj_on67207011le_alt(G),B))
=> ( hBOOL(hAPP_f1733357041l_bool(finite955821396le_alt,A))
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
=> finite1044330389le_alt(A) = finite_card_bool(B) ) ) ) ) ) ) ).
fof(fact_599_card__bij,axiom,
! [G,F,A,B] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
=> ( hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A))
=> ( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,G),pi_fun596906370e_indi(B,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,A))))
=> ( hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(G),B))
=> ( hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,A))
=> ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
=> finite354462354e_indi(A) = finite945540987t_bool(B) ) ) ) ) ) ) ).
fof(fact_600_card__bij,axiom,
! [G,F,A,B] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
=> ( hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A))
=> ( hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,G),pi_fun328162388t_bool(B,hAPP_f23348649l_bool(cOMBK_761999167t_bool,A))))
=> ( hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(G),B))
=> ( hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,A))
=> ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
=> finite1524925796t_bool(A) = finite945540987t_bool(B) ) ) ) ) ) ) ).
fof(fact_601_finite__Collect__less__nat,axiom,
! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))) ).
fof(fact_602_finite__Collect__le__nat,axiom,
! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))) ).
fof(fact_603_card__UNIV__unit,axiom,
finite1949902593t_unit(top_to1257323279t_bool) = one_one_nat ).
fof(fact_604_card__Collect__less__nat,axiom,
! [Na] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na ).
fof(fact_605_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)) ).
fof(fact_606_finite__M__bounded__by__nat,axiom,
! [Pa,I_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(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_1))))) ).
fof(fact_607_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_608_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_609_finite__less__ub,axiom,
! [U,F] :
( ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,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_610_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_611_less__zeroE,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).
fof(fact_612_le0,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)) ).
fof(fact_613_gr0I,axiom,
! [N_1] :
( N_1 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ).
fof(fact_614_gr__implies__not0,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> N_1 != zero_zero_nat ) ).
fof(fact_615_less__nat__zero__code,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).
fof(fact_616_neq0__conv,axiom,
! [Na] :
( Na != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ).
fof(fact_617_not__less0,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).
fof(fact_618_plus__nat_Oadd__0,axiom,
! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1 ).
fof(fact_619_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_620_add__is__0,axiom,
! [M_4,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = zero_zero_nat
<=> ( M_4 = zero_zero_nat
& Na = zero_zero_nat ) ) ).
fof(fact_621_add__eq__self__zero,axiom,
! [M_2,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = M_2
=> N_1 = zero_zero_nat ) ).
fof(fact_622_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_623_less__eq__nat_Osimps_I1_J,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)) ).
fof(fact_624_add__gr__0,axiom,
! [M_4,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_4),Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ) ).
fof(fact_625_ex__least__nat__less,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(Pa,Na))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na))
& ! [I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2))
=> ~ hBOOL(hAPP_nat_bool(Pa,I_2)) )
& hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat))) ) ) ) ).
fof(fact_626_ex__least__nat__le,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(Pa,Na))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
& ! [I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
=> ~ hBOOL(hAPP_nat_bool(Pa,I_2)) )
& hBOOL(hAPP_nat_bool(Pa,K_2)) ) ) ) ).
fof(fact_627_less__imp__add__positive,axiom,
! [I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2) = J_2 ) ) ).
fof(fact_628_lessI,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1))) ).
fof(fact_629_Suc__mono,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_630_zero__less__Suc,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1))) ).
fof(fact_631_Suc__n__not__le__n,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)) ).
fof(fact_632_not__less__eq__eq,axiom,
! [M_4,Na] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) ) ).
fof(fact_633_le__Suc__eq,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),hAPP_nat_nat(suc,Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
| M_4 = hAPP_nat_nat(suc,Na) ) ) ).
fof(fact_634_Suc__le__mono,axiom,
! [Na,M_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_4)) ) ).
fof(fact_635_le__SucI,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_636_le__SucE,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
=> M_2 = hAPP_nat_nat(suc,N_1) ) ) ).
fof(fact_637_Suc__leD,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
fof(fact_638_Suc__inject,axiom,
! [X,Y] :
( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
=> X = Y ) ).
fof(fact_639_nat_Oinject,axiom,
! [Nat_4,Nat_3] :
( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3)
<=> Nat_4 = Nat_3 ) ).
fof(fact_640_Suc__n__not__n,axiom,
! [N_1] : hAPP_nat_nat(suc,N_1) != N_1 ).
fof(fact_641_n__not__Suc__n,axiom,
! [N_1] : N_1 != hAPP_nat_nat(suc,N_1) ).
fof(fact_642_add__Suc__shift,axiom,
! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) ).
fof(fact_643_add__Suc,axiom,
! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)) ).
fof(fact_644_add__Suc__right,axiom,
! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)) ).
fof(fact_645_not__less__eq,axiom,
! [M_4,Na] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) ) ).
fof(fact_646_less__Suc__eq,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
| M_4 = Na ) ) ).
fof(fact_647_Suc__less__eq,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_4)),hAPP_nat_nat(suc,Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ).
fof(fact_648_not__less__less__Suc__eq,axiom,
! [Na,M_4] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
<=> Na = M_4 ) ) ).
fof(fact_649_less__antisym,axiom,
! [N_1,M_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_2)))
=> M_2 = N_1 ) ) ).
fof(fact_650_less__SucI,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_651_Suc__lessI,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> ( hAPP_nat_nat(suc,M_2) != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1)) ) ) ).
fof(fact_652_less__trans__Suc,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1)) ) ) ).
fof(fact_653_less__SucE,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> M_2 = N_1 ) ) ).
fof(fact_654_Suc__lessD,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ).
fof(fact_655_Suc__less__SucD,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ).
fof(fact_656_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).
fof(fact_657_Suc__le__lessD,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ).
fof(fact_658_le__less__Suc__eq,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
<=> Na = M_4 ) ) ).
fof(fact_659_Suc__leI,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) ) ).
fof(fact_660_le__imp__less__Suc,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).
fof(fact_661_Suc__le__eq,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_4)),Na))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ).
fof(fact_662_less__Suc__eq__le,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ).
fof(fact_663_less__eq__Suc__le,axiom,
! [Na,M_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) ) ).
fof(fact_664_less__iff__Suc__add,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
<=> ? [K_2] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2)) ) ).
fof(fact_665_less__add__Suc2,axiom,
! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I)))) ).
fof(fact_666_less__add__Suc1,axiom,
! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2)))) ).
fof(fact_667_one__is__add,axiom,
! [M_4,Na] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na)
<=> ( ( M_4 = hAPP_nat_nat(suc,zero_zero_nat)
& Na = zero_zero_nat )
| ( M_4 = zero_zero_nat
& Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_668_add__is__1,axiom,
! [M_4,Na] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( M_4 = hAPP_nat_nat(suc,zero_zero_nat)
& Na = zero_zero_nat )
| ( M_4 = zero_zero_nat
& Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_669_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_670_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_671_less__Suc__eq__0__disj,axiom,
! [M_4,Na] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
<=> ( M_4 = zero_zero_nat
| ? [J] :
( M_4 = hAPP_nat_nat(suc,J)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Na)) ) ) ) ).
fof(fact_672_inj__Suc,axiom,
! [N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)) ).
fof(fact_673_Suc__neq__Zero,axiom,
! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).
fof(fact_674_Zero__neq__Suc,axiom,
! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).
fof(fact_675_nat_Osimps_I3_J,axiom,
! [Nat_2] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat ).
fof(fact_676_Suc__not__Zero,axiom,
! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).
fof(fact_677_nat_Osimps_I2_J,axiom,
! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1) ).
fof(fact_678_Zero__not__Suc,axiom,
! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).
fof(fact_679_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_680_card__Collect__le__nat,axiom,
! [Na] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na) ).
fof(fact_681_card__less__Suc,axiom,
! [I_1,M_3] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
=> hAPP_nat_nat(suc,finite_card_nat(collect_nat(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_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) ) ).
fof(fact_682_card__less,axiom,
! [I_1,M_3] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
=> finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) != zero_zero_nat ) ).
fof(fact_683_card__less__Suc2,axiom,
! [I_1,M_3] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
=> finite_card_nat(collect_nat(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_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) ) ).
fof(fact_684_inc__induct,axiom,
! [Pa,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(Pa,J_1))
=> ( ! [I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
=> ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2)))
=> hBOOL(hAPP_nat_bool(Pa,I_2)) ) )
=> hBOOL(hAPP_nat_bool(Pa,I_1)) ) ) ) ).
fof(fact_685_less__imp__Suc__add,axiom,
! [M_2,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
=> ? [K_2] : N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)) ) ).
fof(fact_686_gr0__implies__Suc,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ? [M] : N_1 = hAPP_nat_nat(suc,M) ) ).
fof(fact_687_Suc__eq__plus1__left,axiom,
! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1) ).
fof(fact_688_Suc__eq__plus1,axiom,
! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat) ).
fof(fact_689_Suc__le__D,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1))
=> ? [M] : M_1 = hAPP_nat_nat(suc,M) ) ).
fof(fact_690_lessE,axiom,
! [I,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1))
=> ( K_1 != hAPP_nat_nat(suc,I)
=> ~ ! [J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
=> K_1 != hAPP_nat_nat(suc,J) ) ) ) ).
fof(fact_691_Suc__lessE,axiom,
! [I,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1))
=> ~ ! [J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
=> K_1 != hAPP_nat_nat(suc,J) ) ) ).
fof(fact_692_not0__implies__Suc,axiom,
! [N_1] :
( N_1 != zero_zero_nat
=> ? [M] : N_1 = hAPP_nat_nat(suc,M) ) ).
fof(fact_693_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero_nat
=> ~ ! [Nat] : Y != hAPP_nat_nat(suc,Nat) ) ).
fof(fact_694_zero__induct,axiom,
! [Pa,K] :
( hBOOL(hAPP_nat_bool(Pa,K))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N)))
=> hBOOL(hAPP_nat_bool(Pa,N)) )
=> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).
fof(fact_695_nat__induct,axiom,
! [Na,Pa] :
( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,N))
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) )
=> hBOOL(hAPP_nat_bool(Pa,Na)) ) ) ).
fof(fact_696_surjh,axiom,
image_837079859di_nat(h,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)) ).
fof(fact_697_finite__atLeastLessThan,axiom,
! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))) ).
fof(fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123,axiom,
~ ! [H] :
( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(H),top_to207207712i_bool))
=> image_837079859di_nat(H,top_to207207712i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)) ) ).
fof(fact_699_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),finite_card_nat(A)))))
=> A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A))) ) ).
%----Helper facts (57)
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_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(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__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,axiom,
! [P,Q] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,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__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000,axiom,
! [P,Q,R] : hAPP_A416869060i_bool(hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A1948275303t_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
! [P,Q] : hAPP_A1948275303t_bool(hAPP_f1393414918t_bool(cOMBK_1662914336e_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_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty,axiom,
! [P,Q,R] : hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,P),Q),R) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043,axiom,
! [P,Q,R] : hAPP_A1948275303t_bool(hAPP_f1882280879t_bool(cOMBB_552200224e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1895296483di_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_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,P),Q) = P ) ).
fof(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
! [X,Y] :
( is_fun20916972t_bool(X)
=> hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),X),Y) = X ) ).
fof(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
! [X,Y] :
( is_fun20916972t_bool(Y)
=> hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fFalse),X),Y) = Y ) ).
fof(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_044,axiom,
! [P,Q,R] : hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,P),Q),R) = hAPP_f160177134l_bool(hAPP_A45661955l_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_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_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [P,Q] :
( is_fun20916972t_bool(P)
=> hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_045,axiom,
! [P,Q] :
( is_fun20916972t_bool(P)
=> hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t,axiom,
! [P,Q,R] : hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_A433435097l_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_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [P,Q] :
( is_fun2015243113i_bool(P)
=> hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_046,axiom,
! [P,Q,R] : hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,P),Q),R) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_047,axiom,
! [P,Q,R] : hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,P),Q),R) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
! [P,Q,R] : hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_048,axiom,
! [P,Q,R] : hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,P),Q),R) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [P,Q,R] : hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,P),Q),R) = hAPP_f560517119l_bool(hAPP_f1332197581l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
! [P,Q,R] : hAPP_A433435097l_bool(hAPP_f1656652505l_bool(cOMBB_711698847le_alt(P),Q),R) = hAPP_P1151433609l_bool(P,hAPP_A1561816353le_alt(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049,axiom,
! [P,Q,R] : hAPP_A340536322t_bool(hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,P),Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000,axiom,
! [P,Q,R] : hAPP_A340536322t_bool(cOMBS_178315313t_bool(P,Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),hAPP_A340536322t_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_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [P,Q] :
( is_fun701126715l_bool(P)
=> hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_050,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [P,Q,R] : hAPP_A85603248t_bool(hAPP_f2027600413t_bool(cOMBB_640263118e_indi(P),Q),R) = hAPP_f102394819t_bool(P,hAPP_A340536322t_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [P,Q,R] : hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,P),Q),R) = hAPP_f147218624l_bool(hAPP_f621397159l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [P,Q,R] : hAPP_A643475905l_bool(hAPP_f1747206697l_bool(cOMBB_885534287le_alt(P),Q),R) = hAPP_f1656652505l_bool(P,hAPP_A1171966089le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_051,axiom,
! [P,Q,R] : hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(cOMBB_930893948e_indi(P),Q),R) = hAPP_f684072049t_bool(P,hAPP_A340536322t_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_052,axiom,
! [P,Q,R] : hAPP_A1906804694t_bool(hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,P),Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_053,axiom,
! [P,Q,R] : hAPP_A1906804694t_bool(cOMBS_995062533t_bool(P,Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),hAPP_A340536322t_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___054,axiom,
! [P,Q,R] : hAPP_A64811457t_bool(hAPP_f1092358369t_bool(cOMBB_333235735le_alt(P),Q),R) = hAPP_f372913425t_bool(P,hAPP_A643475905l_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_A725195434t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(P),Q),R) = hAPP_b910261233t_bool(P,hAPP_A416869060i_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [P,Q,R] : hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,P),Q),R) = hAPP_f322109294l_bool(hAPP_f881677315l_bool(P,R),Q) ).
%----Conjectures (1)
fof(conj_0,conjecture,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) ).
%------------------------------------------------------------------------------