TPTP Problem File: SCT171^1.p
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%------------------------------------------------------------------------------
% File : SCT171^1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_100_thf_l309 [Bla11]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0
% Syntax : Number of formulae : 287 ( 28 unt; 85 typ; 0 def)
% Number of atoms : 800 ( 114 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 1837 ( 115 ~; 6 |; 14 &;1399 @)
% ( 50 <=>; 253 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 1176 (1176 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 81 usr; 9 con; 0-4 aty)
% Number of variables : 523 ( 37 ^; 485 !; 1 ?; 523 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:16:58
%------------------------------------------------------------------------------
%----Should-be-implicit typings (4)
thf(ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
arrow_1346734812le_alt: $tType ).
thf(ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
arrow_1092341143e_indi: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
nat: $tType ).
thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc__Arrow__,type,
produc1832616231le_alt: $tType ).
%----Explicit typings (81)
thf(sy_c_All,type,
all: ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OIIA,type,
arrow_1724561858le_IIA: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OLin,type,
arrow_1751445586le_Lin: ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OProf,type,
arrow_1605628760e_Prof: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Oabove,type,
arrow_452340254_above: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Odictator,type,
arrow_1098709355ctator: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Omkbot,type,
arrow_1717184938_mkbot: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Omktop,type,
arrow_1865892024_mktop: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Ounanimity,type,
arrow_1889221221nimity: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
finite1907699781e_indi: ( arrow_1092341143e_indi > $o ) > nat ).
thf(sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000tc_,type,
inj_on945046484di_nat: ( arrow_1092341143e_indi > nat ) > ( arrow_1092341143e_indi > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O,type,
pi_Arr1422400881lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O_001,type,
pi_Arr1941314005e_indi: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M,type,
pi_Arr1021537730_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_002,type,
pi_Arr1767527177lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_003,type,
pi_Arr170420797e_indi: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd,type,
pi_Pro410810898lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > $o > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd_004,type,
pi_Pro1340600692e_indi: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o ) > ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojn,type,
pi_o_A1302557673_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__,type,
pi_o_A71242893_alt_o: ( $o > $o ) > ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sd,type,
pi_o_P1538584260_alt_o: ( $o > $o ) > ( $o > ( produc1832616231le_alt > $o ) > $o ) > ( $o > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk,type,
pi_o_P988780107le_alt: ( $o > $o ) > ( $o > produc1832616231le_alt > $o ) > ( $o > produc1832616231le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062,type,
pi_Arr1140519125_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062_005,type,
pi_Arr651234977_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062_006,type,
pi_Arr418143960_alt_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000tc__,type,
pi_Arr1055270199le_alt: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oal,type,
pi_Pro539263375_alt_o: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o > $o ) > ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oal_007,type,
pi_Pro1535452471e_indi: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > arrow_1092341143e_indi > $o ) > ( produc1832616231le_alt > arrow_1092341143e_indi ) > $o ).
thf(sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____sdiojnqkdh,type,
hilber564731065di_nat: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > nat ) > nat > arrow_1092341143e_indi ).
thf(sy_c_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_M,type,
if_Pro399136856_alt_o: $o > ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_I_062_Itc__Arrow____Order____Mira,type,
ord_le939309728lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__Arrow____Order____Mirabelle_,type,
ord_le972845494lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__prod_Itc__Arrow____Order____,type,
ord_le898419007lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____sdi,type,
ord_le316791758indi_o: ( arrow_1092341143e_indi > $o ) > ( arrow_1092341143e_indi > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__prod_Itc__Arrow____Order____Mirabe,type,
ord_le1973646398_alt_o: ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_Eo,type,
ord_less_o: $o > $o > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
ord_less_nat: nat > nat > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_I_062_Itc__Arrow____Order____Mirab,type,
top_to1049332548lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__,type,
top_to790289938lt_o_o: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__prod_Itc__Arrow____Order____M,type,
top_to1830848411lt_o_o: ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_Eo_M_Eo_J,type,
top_top_o_o: $o > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____sdio,type,
top_to527331954indi_o: arrow_1092341143e_indi > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel,type,
top_to679332578_alt_o: produc1832616231le_alt > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_Eo,type,
top_top_o: $o ).
thf(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_,type,
produc990411159le_alt: arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt ).
thf(sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__,type,
collec2125720304_alt_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_,type,
collec1718651462_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk,type,
collec1079683069_alt_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
collec1832628290e_indi: ( arrow_1092341143e_indi > $o ) > arrow_1092341143e_indi > $o ).
thf(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa,type,
collec1201320914le_alt: ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__,type,
member903234717lt_o_o: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > ( ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh___008,type,
member986213183e_indi: ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_,type,
member733327538_alt_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi__009,type,
member1754345465lt_o_o: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi__010,type,
member1208133347e_indi: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk,type,
member1949484546lt_o_o: ( ( produc1832616231le_alt > $o ) > $o ) > ( ( ( produc1832616231le_alt > $o ) > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk_011,type,
member1255309082e_indi: ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > ( ( ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnq,type,
member1710515983_alt_o: ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O,type,
member537117565_alt_o: ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( $o > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdi,type,
member1099673524_alt_o: ( $o > produc1832616231le_alt > $o ) > ( ( $o > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd,type,
member1368218865le_alt: ( $o > produc1832616231le_alt ) > ( ( $o > produc1832616231le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062_,type,
member24189887_alt_o: ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062__012,type,
member1079651021_alt_o: ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062__013,type,
member1561882372_alt_o: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_Mtc__p,type,
member1621875105le_alt: ( arrow_1092341143e_indi > produc1832616231le_alt ) > ( ( arrow_1092341143e_indi > produc1832616231le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa,type,
member1362619835_alt_o: ( produc1832616231le_alt > $o ) > ( ( produc1832616231le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa_014,type,
member1486844321e_indi: ( produc1832616231le_alt > arrow_1092341143e_indi ) > ( ( produc1832616231le_alt > arrow_1092341143e_indi ) > $o ) > $o ).
thf(sy_c_member_000_Eo,type,
member_o: $o > ( $o > $o ) > $o ).
thf(sy_c_member_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi,type,
member1714766084e_indi: arrow_1092341143e_indi > ( arrow_1092341143e_indi > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc,type,
member545531028le_alt: produc1832616231le_alt > ( produc1832616231le_alt > $o ) > $o ).
thf(sy_v_F,type,
f: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(sy_v_Lab____,type,
lab: produc1832616231le_alt > $o ).
thf(sy_v_Lba____,type,
lba: produc1832616231le_alt > $o ).
thf(sy_v_P____,type,
p: arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(sy_v_a____,type,
a: arrow_1346734812le_alt ).
thf(sy_v_b____,type,
b: arrow_1346734812le_alt ).
thf(sy_v_c____,type,
c: arrow_1346734812le_alt ).
thf(sy_v_d____,type,
d: arrow_1346734812le_alt ).
thf(sy_v_e____,type,
e: arrow_1346734812le_alt ).
thf(sy_v_h____,type,
h: arrow_1092341143e_indi > nat ).
thf(sy_v_n____,type,
n: nat ).
%----Relevant facts (198)
thf(fact_0_assms_I3_J,axiom,
arrow_1724561858le_IIA @ f ).
thf(fact_1_u,axiom,
arrow_1889221221nimity @ f ).
thf(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
thf(fact_3__096P_A_058_AProf_096,axiom,
member1561882372_alt_o @ p @ arrow_1605628760e_Prof ).
thf(fact_4_in__mkbot,axiom,
! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o,Z_2: arrow_1346734812le_alt] :
( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ ( arrow_1717184938_mkbot @ L @ Z_2 ) )
<=> ( ( Y != Z_2 )
& ( ( X = Z_2 )
=> ( X != Y ) )
& ( ( X != Z_2 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L ) ) ) ) ).
thf(fact_5_in__mktop,axiom,
! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o,Z_2: arrow_1346734812le_alt] :
( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ ( arrow_1865892024_mktop @ L @ Z_2 ) )
<=> ( ( X != Z_2 )
& ( ( Y = Z_2 )
=> ( X != Y ) )
& ( ( Y != Z_2 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L ) ) ) ) ).
thf(fact_6__C2_C,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_26: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
( ( A_25 != B_15 )
=> ( ( A_26 != B_16 )
=> ( ( A_25 != B_16 )
=> ( ( B_15 != A_26 )
=> ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
=> ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
=> ( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_7__C1_C,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_26: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
( ( A_25 != B_15 )
=> ( ( A_26 != B_16 )
=> ( ( A_25 != B_16 )
=> ( ( B_15 != A_26 )
=> ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
=> ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
=> ( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_8__C4_C,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,C_4: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
( ( A_25 != B_15 )
=> ( ( B_15 != C_4 )
=> ( ( A_25 != C_4 )
=> ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
=> ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
=> ( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ C_4 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ C_4 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ).
thf(fact_9_pairwise__neutrality,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_26: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
( ( A_25 != B_15 )
=> ( ( A_26 != B_16 )
=> ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
=> ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
=> ( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_26 @ B_16 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ).
thf(fact_10__C3_C,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_25: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
( ( A_25 != B_15 )
=> ( ( member1561882372_alt_o @ P_5 @ arrow_1605628760e_Prof )
=> ( ( member1561882372_alt_o @ P_6 @ arrow_1605628760e_Prof )
=> ( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ A_25 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_25 @ B_15 ) @ ( f @ P_5 ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ B_15 @ A_25 ) @ ( f @ P_6 ) ) ) ) ) ) ) ).
thf(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( p @ I ) )
<=> ( ( ( ord_less_nat @ ( h @ I ) @ n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ I ) @ n )
=> ( ( ( ( h @ I )
= n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( arrow_452340254_above @ ( p @ I ) @ c @ e ) ) )
& ( ( ( h @ I )
!= n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ) ) ).
thf(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( p @ ( hilber564731065di_nat @ top_to527331954indi_o @ h @ n ) ) ).
thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [I: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ I )
= n )
@ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ).
thf(fact_14_PW,axiom,
( ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [I: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ I )
= n )
@ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ) ).
thf(fact_15_split__paired__All,axiom,
! [P_4: produc1832616231le_alt > $o] :
( ( all @ P_4 )
<=> ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] : ( P_4 @ ( produc990411159le_alt @ A_5 @ B_4 ) ) ) ).
thf(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
( member1561882372_alt_o
@ ^ [I: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ I )
= n )
@ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) )
@ arrow_1605628760e_Prof ) ).
thf(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
( member545531028le_alt @ ( produc990411159le_alt @ c @ e )
@ ( f
@ ^ [I: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ I )
= n )
@ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ).
thf(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
( member545531028le_alt @ ( produc990411159le_alt @ e @ d )
@ ( f
@ ^ [I: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ I )
= n )
@ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) ).
thf(fact_19_n_I1_J,axiom,
ord_less_nat @ n @ ( finite1907699781e_indi @ top_to527331954indi_o ) ).
thf(fact_20_injh,axiom,
inj_on945046484di_nat @ h @ top_to527331954indi_o ).
thf(fact_21_Pair__inject,axiom,
! [A_24: arrow_1346734812le_alt,B_14: arrow_1346734812le_alt,A_23: arrow_1346734812le_alt,B_13: arrow_1346734812le_alt] :
( ( ( produc990411159le_alt @ A_24 @ B_14 )
= ( produc990411159le_alt @ A_23 @ B_13 ) )
=> ~ ( ( A_24 = A_23 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_22_Pair__eq,axiom,
! [A_22: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt,A_21: arrow_1346734812le_alt,B_11: arrow_1346734812le_alt] :
( ( ( produc990411159le_alt @ A_22 @ B_12 )
= ( produc990411159le_alt @ A_21 @ B_11 ) )
<=> ( ( A_22 = A_21 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_23_IIA__def,axiom,
! [F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( arrow_1724561858le_IIA @ F )
<=> ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
=> ! [Xa: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ Xa @ arrow_1605628760e_Prof )
=> ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( X_1 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( Xa @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ X_1 ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ Xa ) ) ) ) ) ) ) ).
thf(fact_24_unanimity__def,axiom,
! [F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( arrow_1889221221nimity @ F )
<=> ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
=> ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( ! [I: arrow_1092341143e_indi] : ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( X_1 @ I ) )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ X_1 ) ) ) ) ) ).
thf(fact_25_top1I,axiom,
! [X_34: produc1832616231le_alt > $o] : ( top_to1830848411lt_o_o @ X_34 ) ).
thf(fact_26_top1I,axiom,
! [X_34: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( top_to790289938lt_o_o @ X_34 ) ).
thf(fact_27_top1I,axiom,
! [X_34: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( top_to1049332548lt_o_o @ X_34 ) ).
thf(fact_28_top1I,axiom,
! [X_34: produc1832616231le_alt] : ( top_to679332578_alt_o @ X_34 ) ).
thf(fact_29_top1I,axiom,
! [X_34: arrow_1092341143e_indi] : ( top_to527331954indi_o @ X_34 ) ).
thf(fact_30_UNIV__I,axiom,
! [X_33: $o] : ( member_o @ X_33 @ top_top_o_o ) ).
thf(fact_31_UNIV__I,axiom,
! [X_33: arrow_1092341143e_indi] : ( member1714766084e_indi @ X_33 @ top_to527331954indi_o ) ).
thf(fact_32_UNIV__I,axiom,
! [X_33: produc1832616231le_alt] : ( member545531028le_alt @ X_33 @ top_to679332578_alt_o ) ).
thf(fact_33_UNIV__I,axiom,
! [X_33: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X_33 @ top_to790289938lt_o_o ) ).
thf(fact_34_UNIV__I,axiom,
! [X_33: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X_33 @ top_to1049332548lt_o_o ) ).
thf(fact_35_UNIV__I,axiom,
! [X_33: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X_33 @ top_to1830848411lt_o_o ) ).
thf(fact_36_iso__tuple__UNIV__I,axiom,
! [X_32: $o] : ( member_o @ X_32 @ top_top_o_o ) ).
thf(fact_37_iso__tuple__UNIV__I,axiom,
! [X_32: arrow_1092341143e_indi] : ( member1714766084e_indi @ X_32 @ top_to527331954indi_o ) ).
thf(fact_38_iso__tuple__UNIV__I,axiom,
! [X_32: produc1832616231le_alt] : ( member545531028le_alt @ X_32 @ top_to679332578_alt_o ) ).
thf(fact_39_iso__tuple__UNIV__I,axiom,
! [X_32: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X_32 @ top_to790289938lt_o_o ) ).
thf(fact_40_iso__tuple__UNIV__I,axiom,
! [X_32: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X_32 @ top_to1049332548lt_o_o ) ).
thf(fact_41_iso__tuple__UNIV__I,axiom,
! [X_32: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X_32 @ top_to1830848411lt_o_o ) ).
thf(fact_42_top__apply,axiom,
! [X_31: produc1832616231le_alt > $o] :
( ( top_to1830848411lt_o_o @ X_31 )
<=> top_top_o ) ).
thf(fact_43_top__apply,axiom,
! [X_31: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( top_to790289938lt_o_o @ X_31 )
<=> top_top_o ) ).
thf(fact_44_top__apply,axiom,
! [X_31: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( top_to1049332548lt_o_o @ X_31 )
<=> top_top_o ) ).
thf(fact_45_top__apply,axiom,
! [X_31: produc1832616231le_alt] :
( ( top_to679332578_alt_o @ X_31 )
<=> top_top_o ) ).
thf(fact_46_top__apply,axiom,
! [X_31: arrow_1092341143e_indi] :
( ( top_to527331954indi_o @ X_31 )
<=> top_top_o ) ).
thf(fact_47_not__top__less,axiom,
! [A_20: ( produc1832616231le_alt > $o ) > $o] :
~ ( ord_le898419007lt_o_o @ top_to1830848411lt_o_o @ A_20 ) ).
thf(fact_48_not__top__less,axiom,
! [A_20: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
~ ( ord_le972845494lt_o_o @ top_to790289938lt_o_o @ A_20 ) ).
thf(fact_49_not__top__less,axiom,
! [A_20: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
~ ( ord_le939309728lt_o_o @ top_to1049332548lt_o_o @ A_20 ) ).
thf(fact_50_not__top__less,axiom,
! [A_20: $o] :
~ ( ord_less_o @ top_top_o @ A_20 ) ).
thf(fact_51_not__top__less,axiom,
! [A_20: produc1832616231le_alt > $o] :
~ ( ord_le1973646398_alt_o @ top_to679332578_alt_o @ A_20 ) ).
thf(fact_52_not__top__less,axiom,
! [A_20: arrow_1092341143e_indi > $o] :
~ ( ord_le316791758indi_o @ top_to527331954indi_o @ A_20 ) ).
thf(fact_53_linorder__cases,axiom,
! [X_30: nat,Y_23: nat] :
( ~ ( ord_less_nat @ X_30 @ Y_23 )
=> ( ( X_30 != Y_23 )
=> ( ord_less_nat @ Y_23 @ X_30 ) ) ) ).
thf(fact_54_order__less__asym,axiom,
! [X_29: arrow_1092341143e_indi > $o,Y_22: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_29 @ Y_22 )
=> ~ ( ord_le316791758indi_o @ Y_22 @ X_29 ) ) ).
thf(fact_55_order__less__asym,axiom,
! [X_29: nat,Y_22: nat] :
( ( ord_less_nat @ X_29 @ Y_22 )
=> ~ ( ord_less_nat @ Y_22 @ X_29 ) ) ).
thf(fact_56_xt1_I10_J,axiom,
! [Z_1: arrow_1092341143e_indi > $o,Y_21: arrow_1092341143e_indi > $o,X_28: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ Y_21 @ X_28 )
=> ( ( ord_le316791758indi_o @ Z_1 @ Y_21 )
=> ( ord_le316791758indi_o @ Z_1 @ X_28 ) ) ) ).
thf(fact_57_xt1_I10_J,axiom,
! [Z_1: nat,Y_21: nat,X_28: nat] :
( ( ord_less_nat @ Y_21 @ X_28 )
=> ( ( ord_less_nat @ Z_1 @ Y_21 )
=> ( ord_less_nat @ Z_1 @ X_28 ) ) ) ).
thf(fact_58_order__less__trans,axiom,
! [Z: arrow_1092341143e_indi > $o,X_27: arrow_1092341143e_indi > $o,Y_20: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_27 @ Y_20 )
=> ( ( ord_le316791758indi_o @ Y_20 @ Z )
=> ( ord_le316791758indi_o @ X_27 @ Z ) ) ) ).
thf(fact_59_order__less__trans,axiom,
! [Z: nat,X_27: nat,Y_20: nat] :
( ( ord_less_nat @ X_27 @ Y_20 )
=> ( ( ord_less_nat @ Y_20 @ Z )
=> ( ord_less_nat @ X_27 @ Z ) ) ) ).
thf(fact_60_xt1_I2_J,axiom,
! [C_3: arrow_1092341143e_indi > $o,B_10: arrow_1092341143e_indi > $o,A_19: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ B_10 @ A_19 )
=> ( ( B_10 = C_3 )
=> ( ord_le316791758indi_o @ C_3 @ A_19 ) ) ) ).
thf(fact_61_xt1_I2_J,axiom,
! [C_3: nat,B_10: nat,A_19: nat] :
( ( ord_less_nat @ B_10 @ A_19 )
=> ( ( B_10 = C_3 )
=> ( ord_less_nat @ C_3 @ A_19 ) ) ) ).
thf(fact_62_ord__less__eq__trans,axiom,
! [C_2: arrow_1092341143e_indi > $o,A_18: arrow_1092341143e_indi > $o,B_9: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ A_18 @ B_9 )
=> ( ( B_9 = C_2 )
=> ( ord_le316791758indi_o @ A_18 @ C_2 ) ) ) ).
thf(fact_63_ord__less__eq__trans,axiom,
! [C_2: nat,A_18: nat,B_9: nat] :
( ( ord_less_nat @ A_18 @ B_9 )
=> ( ( B_9 = C_2 )
=> ( ord_less_nat @ A_18 @ C_2 ) ) ) ).
thf(fact_64_xt1_I1_J,axiom,
! [C_1: arrow_1092341143e_indi > $o,A_17: arrow_1092341143e_indi > $o,B_8: arrow_1092341143e_indi > $o] :
( ( A_17 = B_8 )
=> ( ( ord_le316791758indi_o @ C_1 @ B_8 )
=> ( ord_le316791758indi_o @ C_1 @ A_17 ) ) ) ).
thf(fact_65_xt1_I1_J,axiom,
! [C_1: nat,A_17: nat,B_8: nat] :
( ( A_17 = B_8 )
=> ( ( ord_less_nat @ C_1 @ B_8 )
=> ( ord_less_nat @ C_1 @ A_17 ) ) ) ).
thf(fact_66_ord__eq__less__trans,axiom,
! [C: arrow_1092341143e_indi > $o,A_16: arrow_1092341143e_indi > $o,B_7: arrow_1092341143e_indi > $o] :
( ( A_16 = B_7 )
=> ( ( ord_le316791758indi_o @ B_7 @ C )
=> ( ord_le316791758indi_o @ A_16 @ C ) ) ) ).
thf(fact_67_ord__eq__less__trans,axiom,
! [C: nat,A_16: nat,B_7: nat] :
( ( A_16 = B_7 )
=> ( ( ord_less_nat @ B_7 @ C )
=> ( ord_less_nat @ A_16 @ C ) ) ) ).
thf(fact_68_xt1_I9_J,axiom,
! [B_6: arrow_1092341143e_indi > $o,A_15: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ B_6 @ A_15 )
=> ~ ( ord_le316791758indi_o @ A_15 @ B_6 ) ) ).
thf(fact_69_xt1_I9_J,axiom,
! [B_6: nat,A_15: nat] :
( ( ord_less_nat @ B_6 @ A_15 )
=> ~ ( ord_less_nat @ A_15 @ B_6 ) ) ).
thf(fact_70_order__less__asym_H,axiom,
! [A_14: arrow_1092341143e_indi > $o,B_5: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ A_14 @ B_5 )
=> ~ ( ord_le316791758indi_o @ B_5 @ A_14 ) ) ).
thf(fact_71_order__less__asym_H,axiom,
! [A_14: nat,B_5: nat] :
( ( ord_less_nat @ A_14 @ B_5 )
=> ~ ( ord_less_nat @ B_5 @ A_14 ) ) ).
thf(fact_72_order__less__imp__triv,axiom,
! [P_3: $o,X_26: arrow_1092341143e_indi > $o,Y_19: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_26 @ Y_19 )
=> ( ( ord_le316791758indi_o @ Y_19 @ X_26 )
=> P_3 ) ) ).
thf(fact_73_order__less__imp__triv,axiom,
! [P_3: $o,X_26: nat,Y_19: nat] :
( ( ord_less_nat @ X_26 @ Y_19 )
=> ( ( ord_less_nat @ Y_19 @ X_26 )
=> P_3 ) ) ).
thf(fact_74_order__less__imp__not__eq2,axiom,
! [X_25: arrow_1092341143e_indi > $o,Y_18: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_25 @ Y_18 )
=> ( Y_18 != X_25 ) ) ).
thf(fact_75_order__less__imp__not__eq2,axiom,
! [X_25: nat,Y_18: nat] :
( ( ord_less_nat @ X_25 @ Y_18 )
=> ( Y_18 != X_25 ) ) ).
thf(fact_76_order__less__imp__not__eq,axiom,
! [X_24: arrow_1092341143e_indi > $o,Y_17: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_24 @ Y_17 )
=> ( X_24 != Y_17 ) ) ).
thf(fact_77_order__less__imp__not__eq,axiom,
! [X_24: nat,Y_17: nat] :
( ( ord_less_nat @ X_24 @ Y_17 )
=> ( X_24 != Y_17 ) ) ).
thf(fact_78_order__less__imp__not__less,axiom,
! [X_23: arrow_1092341143e_indi > $o,Y_16: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_23 @ Y_16 )
=> ~ ( ord_le316791758indi_o @ Y_16 @ X_23 ) ) ).
thf(fact_79_order__less__imp__not__less,axiom,
! [X_23: nat,Y_16: nat] :
( ( ord_less_nat @ X_23 @ Y_16 )
=> ~ ( ord_less_nat @ Y_16 @ X_23 ) ) ).
thf(fact_80_order__less__not__sym,axiom,
! [X_22: arrow_1092341143e_indi > $o,Y_15: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_22 @ Y_15 )
=> ~ ( ord_le316791758indi_o @ Y_15 @ X_22 ) ) ).
thf(fact_81_order__less__not__sym,axiom,
! [X_22: nat,Y_15: nat] :
( ( ord_less_nat @ X_22 @ Y_15 )
=> ~ ( ord_less_nat @ Y_15 @ X_22 ) ) ).
thf(fact_82_less__imp__neq,axiom,
! [X_21: arrow_1092341143e_indi > $o,Y_14: arrow_1092341143e_indi > $o] :
( ( ord_le316791758indi_o @ X_21 @ Y_14 )
=> ( X_21 != Y_14 ) ) ).
thf(fact_83_less__imp__neq,axiom,
! [X_21: nat,Y_14: nat] :
( ( ord_less_nat @ X_21 @ Y_14 )
=> ( X_21 != Y_14 ) ) ).
thf(fact_84_linorder__neqE,axiom,
! [X_20: nat,Y_13: nat] :
( ( X_20 != Y_13 )
=> ( ~ ( ord_less_nat @ X_20 @ Y_13 )
=> ( ord_less_nat @ Y_13 @ X_20 ) ) ) ).
thf(fact_85_linorder__antisym__conv3,axiom,
! [Y_12: nat,X_19: nat] :
( ~ ( ord_less_nat @ Y_12 @ X_19 )
=> ( ~ ( ord_less_nat @ X_19 @ Y_12 )
<=> ( X_19 = Y_12 ) ) ) ).
thf(fact_86_linorder__less__linear,axiom,
! [X_18: nat,Y_11: nat] :
( ( ord_less_nat @ X_18 @ Y_11 )
| ( X_18 = Y_11 )
| ( ord_less_nat @ Y_11 @ X_18 ) ) ).
thf(fact_87_not__less__iff__gr__or__eq,axiom,
! [X_17: nat,Y_10: nat] :
( ~ ( ord_less_nat @ X_17 @ Y_10 )
<=> ( ( ord_less_nat @ Y_10 @ X_17 )
| ( X_17 = Y_10 ) ) ) ).
thf(fact_88_linorder__neq__iff,axiom,
! [X_16: nat,Y_9: nat] :
( ( X_16 != Y_9 )
<=> ( ( ord_less_nat @ X_16 @ Y_9 )
| ( ord_less_nat @ Y_9 @ X_16 ) ) ) ).
thf(fact_89_order__less__irrefl,axiom,
! [X_15: arrow_1092341143e_indi > $o] :
~ ( ord_le316791758indi_o @ X_15 @ X_15 ) ).
thf(fact_90_order__less__irrefl,axiom,
! [X_15: nat] :
~ ( ord_less_nat @ X_15 @ X_15 ) ).
thf(fact_91_UNIV__def,axiom,
( top_to1830848411lt_o_o
= ( collec1079683069_alt_o
@ ^ [X_1: produc1832616231le_alt > $o] : $true ) ) ).
thf(fact_92_UNIV__def,axiom,
( top_to790289938lt_o_o
= ( collec1718651462_alt_o
@ ^ [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] : $true ) ) ).
thf(fact_93_UNIV__def,axiom,
( top_to1049332548lt_o_o
= ( collec2125720304_alt_o
@ ^ [X_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : $true ) ) ).
thf(fact_94_UNIV__def,axiom,
( top_to679332578_alt_o
= ( collec1201320914le_alt
@ ^ [X_1: produc1832616231le_alt] : $true ) ) ).
thf(fact_95_UNIV__def,axiom,
( top_to527331954indi_o
= ( collec1832628290e_indi
@ ^ [X_1: arrow_1092341143e_indi] : $true ) ) ).
thf(fact_96_pred__equals__eq2,axiom,
! [S: produc1832616231le_alt > $o,R: produc1832616231le_alt > $o] :
( ! [X_1: arrow_1346734812le_alt,Xa: arrow_1346734812le_alt] :
( ( member545531028le_alt @ ( produc990411159le_alt @ X_1 @ Xa ) @ R )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ X_1 @ Xa ) @ S ) )
<=> ( R = S ) ) ).
thf(fact_97_less__top,axiom,
! [A_13: ( produc1832616231le_alt > $o ) > $o] :
( ( A_13 != top_to1830848411lt_o_o )
<=> ( ord_le898419007lt_o_o @ A_13 @ top_to1830848411lt_o_o ) ) ).
thf(fact_98_less__top,axiom,
! [A_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( A_13 != top_to790289938lt_o_o )
<=> ( ord_le972845494lt_o_o @ A_13 @ top_to790289938lt_o_o ) ) ).
thf(fact_99_less__top,axiom,
! [A_13: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( A_13 != top_to1049332548lt_o_o )
<=> ( ord_le939309728lt_o_o @ A_13 @ top_to1049332548lt_o_o ) ) ).
thf(fact_100_less__top,axiom,
! [A_13: $o] :
( ~ ( A_13
<=> top_top_o )
<=> ( ord_less_o @ A_13 @ top_top_o ) ) ).
thf(fact_101_less__top,axiom,
! [A_13: produc1832616231le_alt > $o] :
( ( A_13 != top_to679332578_alt_o )
<=> ( ord_le1973646398_alt_o @ A_13 @ top_to679332578_alt_o ) ) ).
thf(fact_102_less__top,axiom,
! [A_13: arrow_1092341143e_indi > $o] :
( ( A_13 != top_to527331954indi_o )
<=> ( ord_le316791758indi_o @ A_13 @ top_to527331954indi_o ) ) ).
thf(fact_103_inv__f__eq,axiom,
! [X_14: arrow_1092341143e_indi,Y_8: nat,F_15: arrow_1092341143e_indi > nat] :
( ( inj_on945046484di_nat @ F_15 @ top_to527331954indi_o )
=> ( ( ( F_15 @ X_14 )
= Y_8 )
=> ( ( hilber564731065di_nat @ top_to527331954indi_o @ F_15 @ Y_8 )
= X_14 ) ) ) ).
thf(fact_104_inv__f__f,axiom,
! [X_13: arrow_1092341143e_indi,F_14: arrow_1092341143e_indi > nat] :
( ( inj_on945046484di_nat @ F_14 @ top_to527331954indi_o )
=> ( ( hilber564731065di_nat @ top_to527331954indi_o @ F_14 @ ( F_14 @ X_13 ) )
= X_13 ) ) ).
thf(fact_105_inv__into__f__f,axiom,
! [X_12: arrow_1092341143e_indi,F_13: arrow_1092341143e_indi > nat,A_12: arrow_1092341143e_indi > $o] :
( ( inj_on945046484di_nat @ F_13 @ A_12 )
=> ( ( member1714766084e_indi @ X_12 @ A_12 )
=> ( ( hilber564731065di_nat @ A_12 @ F_13 @ ( F_13 @ X_12 ) )
= X_12 ) ) ) ).
thf(fact_106_inv__into__f__eq,axiom,
! [Y_7: nat,X_11: arrow_1092341143e_indi,F_12: arrow_1092341143e_indi > nat,A_11: arrow_1092341143e_indi > $o] :
( ( inj_on945046484di_nat @ F_12 @ A_11 )
=> ( ( member1714766084e_indi @ X_11 @ A_11 )
=> ( ( ( F_12 @ X_11 )
= Y_7 )
=> ( ( hilber564731065di_nat @ A_11 @ F_12 @ Y_7 )
= X_11 ) ) ) ) ).
thf(fact_107_inj__eq,axiom,
! [X_10: arrow_1092341143e_indi,Y_6: arrow_1092341143e_indi,F_11: arrow_1092341143e_indi > nat] :
( ( inj_on945046484di_nat @ F_11 @ top_to527331954indi_o )
=> ( ( ( F_11 @ X_10 )
= ( F_11 @ Y_6 ) )
<=> ( X_10 = Y_6 ) ) ) ).
thf(fact_108_inj__on__def,axiom,
! [F_10: arrow_1092341143e_indi > nat,A_10: arrow_1092341143e_indi > $o] :
( ( inj_on945046484di_nat @ F_10 @ A_10 )
<=> ! [X_1: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X_1 @ A_10 )
=> ! [Xa: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ Xa @ A_10 )
=> ( ( ( F_10 @ X_1 )
= ( F_10 @ Xa ) )
=> ( X_1 = Xa ) ) ) ) ) ).
thf(fact_109_inj__on__contraD,axiom,
! [X_9: arrow_1092341143e_indi,Y_5: arrow_1092341143e_indi,F_9: arrow_1092341143e_indi > nat,A_9: arrow_1092341143e_indi > $o] :
( ( inj_on945046484di_nat @ F_9 @ A_9 )
=> ( ( X_9 != Y_5 )
=> ( ( member1714766084e_indi @ X_9 @ A_9 )
=> ( ( member1714766084e_indi @ Y_5 @ A_9 )
=> ( ( F_9 @ X_9 )
!= ( F_9 @ Y_5 ) ) ) ) ) ) ).
thf(fact_110_inj__on__iff,axiom,
! [Y_4: arrow_1092341143e_indi,X_8: arrow_1092341143e_indi,F_8: arrow_1092341143e_indi > nat,A_8: arrow_1092341143e_indi > $o] :
( ( inj_on945046484di_nat @ F_8 @ A_8 )
=> ( ( member1714766084e_indi @ X_8 @ A_8 )
=> ( ( member1714766084e_indi @ Y_4 @ A_8 )
=> ( ( ( F_8 @ X_8 )
= ( F_8 @ Y_4 ) )
<=> ( X_8 = Y_4 ) ) ) ) ) ).
thf(fact_111_inj__onD,axiom,
! [X_7: arrow_1092341143e_indi,Y_3: arrow_1092341143e_indi,F_7: arrow_1092341143e_indi > nat,A_7: arrow_1092341143e_indi > $o] :
( ( inj_on945046484di_nat @ F_7 @ A_7 )
=> ( ( ( F_7 @ X_7 )
= ( F_7 @ Y_3 ) )
=> ( ( member1714766084e_indi @ X_7 @ A_7 )
=> ( ( member1714766084e_indi @ Y_3 @ A_7 )
=> ( X_7 = Y_3 ) ) ) ) ) ).
thf(fact_112_injD,axiom,
! [X_6: arrow_1092341143e_indi,Y_2: arrow_1092341143e_indi,F_6: arrow_1092341143e_indi > nat] :
( ( inj_on945046484di_nat @ F_6 @ top_to527331954indi_o )
=> ( ( ( F_6 @ X_6 )
= ( F_6 @ Y_2 ) )
=> ( X_6 = Y_2 ) ) ) ).
thf(fact_113_inj__imp__inv__eq,axiom,
! [G: nat > arrow_1092341143e_indi,F_5: arrow_1092341143e_indi > nat] :
( ( inj_on945046484di_nat @ F_5 @ top_to527331954indi_o )
=> ( ! [X_1: nat] :
( ( F_5 @ ( G @ X_1 ) )
= X_1 )
=> ( ( hilber564731065di_nat @ top_to527331954indi_o @ F_5 )
= G ) ) ) ).
thf(fact_114_injI,axiom,
! [F_4: arrow_1092341143e_indi > nat] :
( ! [X_1: arrow_1092341143e_indi,Y_1: arrow_1092341143e_indi] :
( ( ( F_4 @ X_1 )
= ( F_4 @ Y_1 ) )
=> ( X_1 = Y_1 ) )
=> ( inj_on945046484di_nat @ F_4 @ top_to527331954indi_o ) ) ).
thf(fact_115_assms_I1_J,axiom,
( member733327538_alt_o @ f
@ ( pi_Arr1021537730_alt_o @ arrow_1605628760e_Prof
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : arrow_1751445586le_Lin ) ) ).
thf(fact_116__096Lba_A_058_ALin_096,axiom,
member1362619835_alt_o @ lba @ arrow_1751445586le_Lin ).
thf(fact_117__096Lab_A_058_ALin_096,axiom,
member1362619835_alt_o @ lab @ arrow_1751445586le_Lin ).
thf(fact_118_Lin__irrefl,axiom,
! [A_3: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_3 @ B_2 ) @ L )
=> ~ ( member545531028le_alt @ ( produc990411159le_alt @ B_2 @ A_3 ) @ L ) ) ) ).
thf(fact_119_notin__Lin__iff,axiom,
! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( ( X != Y )
=> ( ~ ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ Y @ X ) @ L ) ) ) ) ).
thf(fact_120_mem__def,axiom,
! [X_5: arrow_1092341143e_indi,A_6: arrow_1092341143e_indi > $o] :
( ( member1714766084e_indi @ X_5 @ A_6 )
<=> ( A_6 @ X_5 ) ) ).
thf(fact_121_mem__def,axiom,
! [X_5: $o,A_6: $o > $o] :
( ( member_o @ X_5 @ A_6 )
<=> ( A_6 @ X_5 ) ) ).
thf(fact_122_mem__def,axiom,
! [X_5: produc1832616231le_alt,A_6: produc1832616231le_alt > $o] :
( ( member545531028le_alt @ X_5 @ A_6 )
<=> ( A_6 @ X_5 ) ) ).
thf(fact_123_mem__def,axiom,
! [X_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ X_5 @ A_6 )
<=> ( A_6 @ X_5 ) ) ).
thf(fact_124_mem__def,axiom,
! [X_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_6: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ X_5 @ A_6 )
<=> ( A_6 @ X_5 ) ) ).
thf(fact_125_mem__def,axiom,
! [X_5: produc1832616231le_alt > $o,A_6: ( produc1832616231le_alt > $o ) > $o] :
( ( member1362619835_alt_o @ X_5 @ A_6 )
<=> ( A_6 @ X_5 ) ) ).
thf(fact_126_Collect__def,axiom,
! [P_2: arrow_1092341143e_indi > $o] :
( ( collec1832628290e_indi @ P_2 )
= P_2 ) ).
thf(fact_127_mktop__Lin,axiom,
! [X: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_1865892024_mktop @ L @ X ) @ arrow_1751445586le_Lin ) ) ).
thf(fact_128_mkbot__Lin,axiom,
! [X: arrow_1346734812le_alt,L: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_1717184938_mkbot @ L @ X ) @ arrow_1751445586le_Lin ) ) ).
thf(fact_129_above__Lin,axiom,
! [L: produc1832616231le_alt > $o,X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt] :
( ( X != Y )
=> ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_452340254_above @ L @ X @ Y ) @ arrow_1751445586le_Lin ) ) ) ).
thf(fact_130_const__Lin__Prof,axiom,
! [L: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( member1561882372_alt_o
@ ^ [P_1: arrow_1092341143e_indi] : L
@ arrow_1605628760e_Prof ) ) ).
thf(fact_131_in__above,axiom,
! [X: arrow_1346734812le_alt,Y: arrow_1346734812le_alt,L: produc1832616231le_alt > $o,A_3: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt] :
( ( A_3 != B_2 )
=> ( ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ ( arrow_452340254_above @ L @ A_3 @ B_2 ) )
<=> ( ( X != Y )
& ( ( X = B_2 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_3 @ Y ) @ L ) )
& ( ( X != B_2 )
=> ( ( ( Y = B_2 )
=> ( ( X = A_3 )
| ( member545531028le_alt @ ( produc990411159le_alt @ X @ A_3 ) @ L ) ) )
& ( ( Y != B_2 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X @ Y ) @ L ) ) ) ) ) ) ) ) ).
thf(fact_132_dictatorI,axiom,
! [I_1: arrow_1092341143e_indi,F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ F
@ ( pi_Arr1021537730_alt_o @ arrow_1605628760e_Prof
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : arrow_1751445586le_Lin ) )
=> ( ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
=> ! [A_5: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( ( A_5 != B_4 )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( X_1 @ I_1 ) )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_5 @ B_4 ) @ ( F @ X_1 ) ) ) ) )
=> ( arrow_1098709355ctator @ F @ I_1 ) ) ) ).
thf(fact_133_PiE,axiom,
! [X_4: produc1832616231le_alt,F_3: produc1832616231le_alt > $o,A_4: produc1832616231le_alt > $o,B_3: produc1832616231le_alt > $o > $o] :
( ( member1362619835_alt_o @ F_3 @ ( pi_Pro539263375_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member545531028le_alt @ X_4 @ A_4 ) ) ) ).
thf(fact_134_PiE,axiom,
! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > produc1832616231le_alt,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1621875105le_alt @ F_3 @ ( pi_Arr1055270199le_alt @ A_4 @ B_3 ) )
=> ( ~ ( member545531028le_alt @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
thf(fact_135_PiE,axiom,
! [X_4: $o,F_3: $o > produc1832616231le_alt,A_4: $o > $o,B_3: $o > produc1832616231le_alt > $o] :
( ( member1368218865le_alt @ F_3 @ ( pi_o_P988780107le_alt @ A_4 @ B_3 ) )
=> ( ~ ( member545531028le_alt @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member_o @ X_4 @ A_4 ) ) ) ).
thf(fact_136_PiE,axiom,
! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1079651021_alt_o @ F_3 @ ( pi_Arr651234977_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member1561882372_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
thf(fact_137_PiE,axiom,
! [X_4: $o,F_3: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_4: $o > $o,B_3: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member537117565_alt_o @ F_3 @ ( pi_o_A71242893_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member1561882372_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member_o @ X_4 @ A_4 ) ) ) ).
thf(fact_138_PiE,axiom,
! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member24189887_alt_o @ F_3 @ ( pi_Arr1140519125_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member733327538_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
thf(fact_139_PiE,axiom,
! [X_4: $o,F_3: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_4: $o > $o,B_3: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member1710515983_alt_o @ F_3 @ ( pi_o_A1302557673_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member733327538_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member_o @ X_4 @ A_4 ) ) ) ).
thf(fact_140_PiE,axiom,
! [X_4: $o,F_3: $o > produc1832616231le_alt > $o,A_4: $o > $o,B_3: $o > ( produc1832616231le_alt > $o ) > $o] :
( ( member1099673524_alt_o @ F_3 @ ( pi_o_P1538584260_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member1362619835_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member_o @ X_4 @ A_4 ) ) ) ).
thf(fact_141_PiE,axiom,
! [X_4: produc1832616231le_alt,F_3: produc1832616231le_alt > arrow_1092341143e_indi,A_4: produc1832616231le_alt > $o,B_3: produc1832616231le_alt > arrow_1092341143e_indi > $o] :
( ( member1486844321e_indi @ F_3 @ ( pi_Pro1535452471e_indi @ A_4 @ B_3 ) )
=> ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member545531028le_alt @ X_4 @ A_4 ) ) ) ).
thf(fact_142_PiE,axiom,
! [X_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1208133347e_indi @ F_3 @ ( pi_Arr170420797e_indi @ A_4 @ B_3 ) )
=> ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1561882372_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_143_PiE,axiom,
! [X_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o] :
( ( member1754345465lt_o_o @ F_3 @ ( pi_Arr1767527177lt_o_o @ A_4 @ B_3 ) )
=> ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1561882372_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_144_PiE,axiom,
! [X_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_4: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member986213183e_indi @ F_3 @ ( pi_Arr1941314005e_indi @ A_4 @ B_3 ) )
=> ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member733327538_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_145_PiE,axiom,
! [X_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_4: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_3: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o] :
( ( member903234717lt_o_o @ F_3 @ ( pi_Arr1422400881lt_o_o @ A_4 @ B_3 ) )
=> ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member733327538_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_146_PiE,axiom,
! [X_4: produc1832616231le_alt > $o,F_3: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_4: ( produc1832616231le_alt > $o ) > $o,B_3: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1255309082e_indi @ F_3 @ ( pi_Pro1340600692e_indi @ A_4 @ B_3 ) )
=> ( ~ ( member1714766084e_indi @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1362619835_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_147_PiE,axiom,
! [X_4: produc1832616231le_alt > $o,F_3: ( produc1832616231le_alt > $o ) > $o,A_4: ( produc1832616231le_alt > $o ) > $o,B_3: ( produc1832616231le_alt > $o ) > $o > $o] :
( ( member1949484546lt_o_o @ F_3 @ ( pi_Pro410810898lt_o_o @ A_4 @ B_3 ) )
=> ( ~ ( member_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1362619835_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_148_PiE,axiom,
! [X_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ F_3 @ ( pi_Arr1021537730_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member1362619835_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1561882372_alt_o @ X_4 @ A_4 ) ) ) ).
thf(fact_149_PiE,axiom,
! [X_4: arrow_1092341143e_indi,F_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_4: arrow_1092341143e_indi > $o,B_3: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ F_3 @ ( pi_Arr418143960_alt_o @ A_4 @ B_3 ) )
=> ( ~ ( member1362619835_alt_o @ ( F_3 @ X_4 ) @ ( B_3 @ X_4 ) )
=> ~ ( member1714766084e_indi @ X_4 @ A_4 ) ) ) ).
thf(fact_150_complete__Lin,axiom,
! [A_3: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt] :
( ( A_3 != B_2 )
=> ? [X_1: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X_1 @ arrow_1751445586le_Lin )
& ( member545531028le_alt @ ( produc990411159le_alt @ A_3 @ B_2 ) @ X_1 ) ) ) ).
thf(fact_151_PiProf,axiom,
! [N: nat] :
( member1561882372_alt_o
@ ^ [I: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ N ) @ lab @ lba )
@ arrow_1605628760e_Prof ) ).
thf(fact_152_Pi__mem,axiom,
! [X_3: produc1832616231le_alt,F_2: produc1832616231le_alt > $o,A_2: produc1832616231le_alt > $o,B_1: produc1832616231le_alt > $o > $o] :
( ( member1362619835_alt_o @ F_2 @ ( pi_Pro539263375_alt_o @ A_2 @ B_1 ) )
=> ( ( member545531028le_alt @ X_3 @ A_2 )
=> ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_153_Pi__mem,axiom,
! [X_3: produc1832616231le_alt,F_2: produc1832616231le_alt > arrow_1092341143e_indi,A_2: produc1832616231le_alt > $o,B_1: produc1832616231le_alt > arrow_1092341143e_indi > $o] :
( ( member1486844321e_indi @ F_2 @ ( pi_Pro1535452471e_indi @ A_2 @ B_1 ) )
=> ( ( member545531028le_alt @ X_3 @ A_2 )
=> ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_154_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1208133347e_indi @ F_2 @ ( pi_Arr170420797e_indi @ A_2 @ B_1 ) )
=> ( ( member1561882372_alt_o @ X_3 @ A_2 )
=> ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_155_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o] :
( ( member1754345465lt_o_o @ F_2 @ ( pi_Arr1767527177lt_o_o @ A_2 @ B_1 ) )
=> ( ( member1561882372_alt_o @ X_3 @ A_2 )
=> ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_156_Pi__mem,axiom,
! [X_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member986213183e_indi @ F_2 @ ( pi_Arr1941314005e_indi @ A_2 @ B_1 ) )
=> ( ( member733327538_alt_o @ X_3 @ A_2 )
=> ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_157_Pi__mem,axiom,
! [X_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_2: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o] :
( ( member903234717lt_o_o @ F_2 @ ( pi_Arr1422400881lt_o_o @ A_2 @ B_1 ) )
=> ( ( member733327538_alt_o @ X_3 @ A_2 )
=> ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_158_Pi__mem,axiom,
! [X_3: produc1832616231le_alt > $o,F_2: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_2: ( produc1832616231le_alt > $o ) > $o,B_1: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1255309082e_indi @ F_2 @ ( pi_Pro1340600692e_indi @ A_2 @ B_1 ) )
=> ( ( member1362619835_alt_o @ X_3 @ A_2 )
=> ( member1714766084e_indi @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_159_Pi__mem,axiom,
! [X_3: produc1832616231le_alt > $o,F_2: ( produc1832616231le_alt > $o ) > $o,A_2: ( produc1832616231le_alt > $o ) > $o,B_1: ( produc1832616231le_alt > $o ) > $o > $o] :
( ( member1949484546lt_o_o @ F_2 @ ( pi_Pro410810898lt_o_o @ A_2 @ B_1 ) )
=> ( ( member1362619835_alt_o @ X_3 @ A_2 )
=> ( member_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_160_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > produc1832616231le_alt,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1621875105le_alt @ F_2 @ ( pi_Arr1055270199le_alt @ A_2 @ B_1 ) )
=> ( ( member1714766084e_indi @ X_3 @ A_2 )
=> ( member545531028le_alt @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_161_Pi__mem,axiom,
! [X_3: $o,F_2: $o > produc1832616231le_alt,A_2: $o > $o,B_1: $o > produc1832616231le_alt > $o] :
( ( member1368218865le_alt @ F_2 @ ( pi_o_P988780107le_alt @ A_2 @ B_1 ) )
=> ( ( member_o @ X_3 @ A_2 )
=> ( member545531028le_alt @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_162_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1079651021_alt_o @ F_2 @ ( pi_Arr651234977_alt_o @ A_2 @ B_1 ) )
=> ( ( member1714766084e_indi @ X_3 @ A_2 )
=> ( member1561882372_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_163_Pi__mem,axiom,
! [X_3: $o,F_2: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_2: $o > $o,B_1: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member537117565_alt_o @ F_2 @ ( pi_o_A71242893_alt_o @ A_2 @ B_1 ) )
=> ( ( member_o @ X_3 @ A_2 )
=> ( member1561882372_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_164_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member24189887_alt_o @ F_2 @ ( pi_Arr1140519125_alt_o @ A_2 @ B_1 ) )
=> ( ( member1714766084e_indi @ X_3 @ A_2 )
=> ( member733327538_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_165_Pi__mem,axiom,
! [X_3: $o,F_2: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_2: $o > $o,B_1: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member1710515983_alt_o @ F_2 @ ( pi_o_A1302557673_alt_o @ A_2 @ B_1 ) )
=> ( ( member_o @ X_3 @ A_2 )
=> ( member733327538_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_166_Pi__mem,axiom,
! [X_3: $o,F_2: $o > produc1832616231le_alt > $o,A_2: $o > $o,B_1: $o > ( produc1832616231le_alt > $o ) > $o] :
( ( member1099673524_alt_o @ F_2 @ ( pi_o_P1538584260_alt_o @ A_2 @ B_1 ) )
=> ( ( member_o @ X_3 @ A_2 )
=> ( member1362619835_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_167_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ F_2 @ ( pi_Arr1021537730_alt_o @ A_2 @ B_1 ) )
=> ( ( member1561882372_alt_o @ X_3 @ A_2 )
=> ( member1362619835_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_168_Pi__mem,axiom,
! [X_3: arrow_1092341143e_indi,F_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_2: arrow_1092341143e_indi > $o,B_1: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ F_2 @ ( pi_Arr418143960_alt_o @ A_2 @ B_1 ) )
=> ( ( member1714766084e_indi @ X_3 @ A_2 )
=> ( member1362619835_alt_o @ ( F_2 @ X_3 ) @ ( B_1 @ X_3 ) ) ) ) ).
thf(fact_169_Prof__def,axiom,
( arrow_1605628760e_Prof
= ( pi_Arr418143960_alt_o @ top_to527331954indi_o
@ ^ [Uu: arrow_1092341143e_indi] : arrow_1751445586le_Lin ) ) ).
thf(fact_170_funcset__mem,axiom,
! [X_2: produc1832616231le_alt,F_1: produc1832616231le_alt > $o,A_1: produc1832616231le_alt > $o,B: $o > $o] :
( ( member1362619835_alt_o @ F_1
@ ( pi_Pro539263375_alt_o @ A_1
@ ^ [Uu: produc1832616231le_alt] : B ) )
=> ( ( member545531028le_alt @ X_2 @ A_1 )
=> ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_171_funcset__mem,axiom,
! [X_2: produc1832616231le_alt,F_1: produc1832616231le_alt > arrow_1092341143e_indi,A_1: produc1832616231le_alt > $o,B: arrow_1092341143e_indi > $o] :
( ( member1486844321e_indi @ F_1
@ ( pi_Pro1535452471e_indi @ A_1
@ ^ [Uu: produc1832616231le_alt] : B ) )
=> ( ( member545531028le_alt @ X_2 @ A_1 )
=> ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_172_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B: arrow_1092341143e_indi > $o] :
( ( member1208133347e_indi @ F_1
@ ( pi_Arr170420797e_indi @ A_1
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B ) )
=> ( ( member1561882372_alt_o @ X_2 @ A_1 )
=> ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_173_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B: $o > $o] :
( ( member1754345465lt_o_o @ F_1
@ ( pi_Arr1767527177lt_o_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B ) )
=> ( ( member1561882372_alt_o @ X_2 @ A_1 )
=> ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_174_funcset__mem,axiom,
! [X_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B: arrow_1092341143e_indi > $o] :
( ( member986213183e_indi @ F_1
@ ( pi_Arr1941314005e_indi @ A_1
@ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B ) )
=> ( ( member733327538_alt_o @ X_2 @ A_1 )
=> ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_175_funcset__mem,axiom,
! [X_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_1: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B: $o > $o] :
( ( member903234717lt_o_o @ F_1
@ ( pi_Arr1422400881lt_o_o @ A_1
@ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B ) )
=> ( ( member733327538_alt_o @ X_2 @ A_1 )
=> ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_176_funcset__mem,axiom,
! [X_2: produc1832616231le_alt > $o,F_1: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_1: ( produc1832616231le_alt > $o ) > $o,B: arrow_1092341143e_indi > $o] :
( ( member1255309082e_indi @ F_1
@ ( pi_Pro1340600692e_indi @ A_1
@ ^ [Uu: produc1832616231le_alt > $o] : B ) )
=> ( ( member1362619835_alt_o @ X_2 @ A_1 )
=> ( member1714766084e_indi @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_177_funcset__mem,axiom,
! [X_2: produc1832616231le_alt > $o,F_1: ( produc1832616231le_alt > $o ) > $o,A_1: ( produc1832616231le_alt > $o ) > $o,B: $o > $o] :
( ( member1949484546lt_o_o @ F_1
@ ( pi_Pro410810898lt_o_o @ A_1
@ ^ [Uu: produc1832616231le_alt > $o] : B ) )
=> ( ( member1362619835_alt_o @ X_2 @ A_1 )
=> ( member_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_178_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > produc1832616231le_alt,A_1: arrow_1092341143e_indi > $o,B: produc1832616231le_alt > $o] :
( ( member1621875105le_alt @ F_1
@ ( pi_Arr1055270199le_alt @ A_1
@ ^ [Uu: arrow_1092341143e_indi] : B ) )
=> ( ( member1714766084e_indi @ X_2 @ A_1 )
=> ( member545531028le_alt @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_179_funcset__mem,axiom,
! [X_2: $o,F_1: $o > produc1832616231le_alt,A_1: $o > $o,B: produc1832616231le_alt > $o] :
( ( member1368218865le_alt @ F_1
@ ( pi_o_P988780107le_alt @ A_1
@ ^ [Uu: $o] : B ) )
=> ( ( member_o @ X_2 @ A_1 )
=> ( member545531028le_alt @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_180_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_1: arrow_1092341143e_indi > $o,B: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1079651021_alt_o @ F_1
@ ( pi_Arr651234977_alt_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi] : B ) )
=> ( ( member1714766084e_indi @ X_2 @ A_1 )
=> ( member1561882372_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_181_funcset__mem,axiom,
! [X_2: $o,F_1: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_1: $o > $o,B: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member537117565_alt_o @ F_1
@ ( pi_o_A71242893_alt_o @ A_1
@ ^ [Uu: $o] : B ) )
=> ( ( member_o @ X_2 @ A_1 )
=> ( member1561882372_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_182_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_1: arrow_1092341143e_indi > $o,B: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member24189887_alt_o @ F_1
@ ( pi_Arr1140519125_alt_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi] : B ) )
=> ( ( member1714766084e_indi @ X_2 @ A_1 )
=> ( member733327538_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_183_funcset__mem,axiom,
! [X_2: $o,F_1: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_1: $o > $o,B: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member1710515983_alt_o @ F_1
@ ( pi_o_A1302557673_alt_o @ A_1
@ ^ [Uu: $o] : B ) )
=> ( ( member_o @ X_2 @ A_1 )
=> ( member733327538_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_184_funcset__mem,axiom,
! [X_2: $o,F_1: $o > produc1832616231le_alt > $o,A_1: $o > $o,B: ( produc1832616231le_alt > $o ) > $o] :
( ( member1099673524_alt_o @ F_1
@ ( pi_o_P1538584260_alt_o @ A_1
@ ^ [Uu: $o] : B ) )
=> ( ( member_o @ X_2 @ A_1 )
=> ( member1362619835_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_185_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B: ( produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ F_1
@ ( pi_Arr1021537730_alt_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B ) )
=> ( ( member1561882372_alt_o @ X_2 @ A_1 )
=> ( member1362619835_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_186_funcset__mem,axiom,
! [X_2: arrow_1092341143e_indi,F_1: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_1: arrow_1092341143e_indi > $o,B: ( produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ F_1
@ ( pi_Arr418143960_alt_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi] : B ) )
=> ( ( member1714766084e_indi @ X_2 @ A_1 )
=> ( member1362619835_alt_o @ ( F_1 @ X_2 ) @ B ) ) ) ).
thf(fact_187_dictator__def,axiom,
! [F: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,I_1: arrow_1092341143e_indi] :
( ( arrow_1098709355ctator @ F @ I_1 )
<=> ! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X_1 @ arrow_1605628760e_Prof )
=> ( ( F @ X_1 )
= ( X_1 @ I_1 ) ) ) ) ).
thf(fact_188_Pi__UNIV,axiom,
! [A: produc1832616231le_alt > $o] :
( ( pi_Pro539263375_alt_o @ A
@ ^ [Uu: produc1832616231le_alt] : top_top_o_o )
= top_to1830848411lt_o_o ) ).
thf(fact_189_Pi__UNIV,axiom,
! [A: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( pi_Arr1021537730_alt_o @ A
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : top_to1830848411lt_o_o )
= top_to1049332548lt_o_o ) ).
thf(fact_190_Pi__UNIV,axiom,
! [A: arrow_1092341143e_indi > $o] :
( ( pi_Arr418143960_alt_o @ A
@ ^ [Uu: arrow_1092341143e_indi] : top_to1830848411lt_o_o )
= top_to790289938lt_o_o ) ).
thf(fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( ( member545531028le_alt @ ( produc990411159le_alt @ e @ d )
@ ( f
@ ^ [I: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ I )
= n )
@ ( arrow_452340254_above @ ( p @ I ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ b @ a )
@ ( f
@ ^ [I: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ I ) @ n ) @ lab @ lba ) ) ) ) ).
thf(fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
! [I: arrow_1092341143e_indi] :
( ( ( ( ord_less_nat @ ( h @ I ) @ n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ e @ d ) @ ( arrow_1865892024_mktop @ ( p @ I ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ I ) @ n )
=> ( ( ( ( h @ I )
= n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ e @ d ) @ ( arrow_452340254_above @ ( p @ I ) @ c @ e ) ) )
& ( ( ( h @ I )
!= n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ e @ d ) @ ( arrow_1717184938_mkbot @ ( p @ I ) @ e ) ) ) ) ) )
<=> ( ( ( ord_less_nat @ ( h @ I ) @ n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ I ) @ n )
=> ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lba ) ) ) ) ).
thf(fact_193__096a_A_126_061_Ab_096,axiom,
a != b ).
thf(fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lba ).
thf(fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
member545531028le_alt @ ( produc990411159le_alt @ a @ b ) @ lab ).
thf(fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ ( member545531028le_alt @ ( produc990411159le_alt @ a @ b ) @ lba ) ).
thf(fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ lab ) ).
%----Helper facts (3)
thf(help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_,axiom,
! [X: produc1832616231le_alt > $o,Y: produc1832616231le_alt > $o] :
( ( if_Pro399136856_alt_o @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_,axiom,
! [X: produc1832616231le_alt > $o,Y: produc1832616231le_alt > $o] :
( ( if_Pro399136856_alt_o @ $false @ X @ Y )
= Y ) ).
thf(help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) ).
%------------------------------------------------------------------------------