TPTP Problem File: SCT170^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SCT170^1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 204, 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_l204 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 297 ( 46 unt; 80 typ; 0 def)
% Number of atoms : 762 ( 86 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1975 ( 84 ~; 2 |; 13 &;1549 @)
% ( 44 <=>; 283 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 1580 (1580 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 76 usr; 6 con; 0-4 aty)
% Number of variables : 686 ( 49 ^; 627 !; 10 ?; 686 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:07:19
%------------------------------------------------------------------------------
%----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__List__Olist_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_J,type,
list_A1528105233le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc__Arrow__,type,
produc1832616231le_alt: $tType ).
%----Explicit typings (76)
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_Obelow,type,
arrow_1760938802_below: ( 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_Ex,type,
ex: ( produc1832616231le_alt > $o ) > $o ).
thf(sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_000t,type,
in_rel895475842le_alt: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > arrow_1346734812le_alt > $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_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
equal_2044961839le_alt: list_A1528105233le_alt > list_A1528105233le_alt > $o ).
thf(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
distin1107700095le_alt: list_A1528105233le_alt > $o ).
thf(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
insert844458914le_alt: arrow_1346734812le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
cons_A1100118844le_alt: arrow_1346734812le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
nil_Ar10086284le_alt: list_A1528105233le_alt ).
thf(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
null_A244857236le_alt: list_A1528105233le_alt > $o ).
thf(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
splice244790623le_alt: list_A1528105233le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
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_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
produc443407182_alt_o: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > arrow_1346734812le_alt > $o ).
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_P_H____,type,
p_1: arrow_1092341143e_indi > 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 ).
%----Relevant facts (216)
thf(fact_0__096P_A_058_AProf_096,axiom,
member1561882372_alt_o @ p @ arrow_1605628760e_Prof ).
thf(fact_1_assms_I3_J,axiom,
arrow_1724561858le_IIA @ f ).
thf(fact_2_u,axiom,
arrow_1889221221nimity @ f ).
thf(fact_3__096a_A_126_061_Ab_096,axiom,
a != b ).
thf(fact_4_dist,axiom,
distin1107700095le_alt @ ( cons_A1100118844le_alt @ a @ ( cons_A1100118844le_alt @ b @ ( cons_A1100118844le_alt @ c @ nil_Ar10086284le_alt ) ) ) ).
thf(fact_5_iff,axiom,
! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ a @ b ) @ ( p @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ b @ a ) @ ( p_1 @ I ) ) ) ).
thf(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_,axiom,
~ ! [C: arrow_1346734812le_alt] :
~ ( distin1107700095le_alt @ ( cons_A1100118844le_alt @ a @ ( cons_A1100118844le_alt @ b @ ( cons_A1100118844le_alt @ C @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096,axiom,
( member1561882372_alt_o
@ ^ [P_4: arrow_1092341143e_indi] : ( arrow_1760938802_below @ ( arrow_1760938802_below @ ( p @ P_4 ) @ c @ b ) @ b @ a )
@ arrow_1605628760e_Prof ) ).
thf(fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_,axiom,
( member1561882372_alt_o
@ ^ [P_4: arrow_1092341143e_indi] : ( arrow_1760938802_below @ ( arrow_1760938802_below @ ( arrow_1760938802_below @ ( p @ P_4 ) @ c @ b ) @ b @ a ) @ a @ c )
@ arrow_1605628760e_Prof ) ).
thf(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
( member1561882372_alt_o
@ ^ [P_4: arrow_1092341143e_indi] : ( arrow_1760938802_below @ ( p @ P_4 ) @ c @ b )
@ arrow_1605628760e_Prof ) ).
thf(fact_10_in__mkbot,axiom,
! [X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o,Z: arrow_1346734812le_alt] :
( ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ ( arrow_1717184938_mkbot @ L_1 @ Z ) )
<=> ( ( Y_5 != Z )
& ( ( X_14 = Z )
=> ( X_14 != Y_5 ) )
& ( ( X_14 != Z )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ L_1 ) ) ) ) ).
thf(fact_11_in__mktop,axiom,
! [X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o,Z: arrow_1346734812le_alt] :
( ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ ( arrow_1865892024_mktop @ L_1 @ Z ) )
<=> ( ( X_14 != Z )
& ( ( Y_5 = Z )
=> ( X_14 != Y_5 ) )
& ( ( Y_5 != Z )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ L_1 ) ) ) ) ).
thf(fact_12_in__below,axiom,
! [X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o,A_19: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt] :
( ( A_19 != B_12 )
=> ( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ ( arrow_1760938802_below @ L_1 @ A_19 @ B_12 ) )
<=> ( ( X_14 != Y_5 )
& ( ( Y_5 = A_19 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ B_12 ) @ L_1 ) )
& ( ( Y_5 != A_19 )
=> ( ( ( X_14 = A_19 )
=> ( ( Y_5 = B_12 )
| ( member545531028le_alt @ ( produc990411159le_alt @ B_12 @ Y_5 ) @ L_1 ) ) )
& ( ( X_14 != A_19 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ L_1 ) ) ) ) ) ) ) ) ).
thf(fact_13_split__paired__All,axiom,
! [P_7: produc1832616231le_alt > $o] :
( ( all @ P_7 )
<=> ! [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] : ( P_7 @ ( produc990411159le_alt @ A_7 @ B_4 ) ) ) ).
thf(fact_14_Pair__eq,axiom,
! [A_25: arrow_1346734812le_alt,B_18: arrow_1346734812le_alt,A_24: arrow_1346734812le_alt,B_17: arrow_1346734812le_alt] :
( ( ( produc990411159le_alt @ A_25 @ B_18 )
= ( produc990411159le_alt @ A_24 @ B_17 ) )
<=> ( ( A_25 = A_24 )
& ( B_18 = B_17 ) ) ) ).
thf(fact_15_Pair__inject,axiom,
! [A_23: arrow_1346734812le_alt,B_16: arrow_1346734812le_alt,A_22: arrow_1346734812le_alt,B_15: arrow_1346734812le_alt] :
( ( ( produc990411159le_alt @ A_23 @ B_16 )
= ( produc990411159le_alt @ A_22 @ B_15 ) )
=> ~ ( ( A_23 = A_22 )
=> ( B_16 != B_15 ) ) ) ).
thf(fact_16_in__rel__def,axiom,
! [R_1: produc1832616231le_alt > $o,X_17: arrow_1346734812le_alt,Y_6: arrow_1346734812le_alt] :
( ( in_rel895475842le_alt @ R_1 @ X_17 @ Y_6 )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ X_17 @ Y_6 ) @ R_1 ) ) ).
thf(fact_17_below__Lin,axiom,
! [L_1: produc1832616231le_alt > $o,X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt] :
( ( X_14 != Y_5 )
=> ( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_1760938802_below @ L_1 @ X_14 @ Y_5 ) @ arrow_1751445586le_Lin ) ) ) ).
thf(fact_18__096P_H_A_058_AProf_096,axiom,
member1561882372_alt_o @ p_1 @ arrow_1605628760e_Prof ).
thf(fact_19__C1_C,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_21: arrow_1346734812le_alt,B_14: arrow_1346734812le_alt,A_20: arrow_1346734812le_alt,B_13: arrow_1346734812le_alt] :
( ( A_20 != B_13 )
=> ( ( A_21 != B_14 )
=> ( ( A_20 != B_14 )
=> ( ( B_13 != A_21 )
=> ( ( 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_20 @ B_13 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_21 @ B_14 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_20 @ B_13 ) @ ( f @ P_5 ) )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_21 @ B_14 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_20__C2_C,axiom,
! [P_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,P_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_21: arrow_1346734812le_alt,B_14: arrow_1346734812le_alt,A_20: arrow_1346734812le_alt,B_13: arrow_1346734812le_alt] :
( ( A_20 != B_13 )
=> ( ( A_21 != B_14 )
=> ( ( A_20 != B_14 )
=> ( ( B_13 != A_21 )
=> ( ( 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_20 @ B_13 ) @ ( P_5 @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_21 @ B_14 ) @ ( P_6 @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_20 @ B_13 ) @ ( f @ P_5 ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_21 @ B_14 ) @ ( f @ P_6 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_21_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_22_const__Lin__Prof,axiom,
! [L_1: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( member1561882372_alt_o
@ ^ [P_4: arrow_1092341143e_indi] : L_1
@ arrow_1605628760e_Prof ) ) ).
thf(fact_23_mkbot__Lin,axiom,
! [X_14: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_1717184938_mkbot @ L_1 @ X_14 ) @ arrow_1751445586le_Lin ) ) ).
thf(fact_24_mktop__Lin,axiom,
! [X_14: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_1865892024_mktop @ L_1 @ X_14 ) @ arrow_1751445586le_Lin ) ) ).
thf(fact_25_Lin__irrefl,axiom,
! [A_19: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_19 @ B_12 ) @ L_1 )
=> ~ ( member545531028le_alt @ ( produc990411159le_alt @ B_12 @ A_19 ) @ L_1 ) ) ) ).
thf(fact_26_notin__Lin__iff,axiom,
! [X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( ( X_14 != Y_5 )
=> ( ~ ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ L_1 )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ Y_5 @ X_14 ) @ L_1 ) ) ) ) ).
thf(fact_27_third__alt,axiom,
! [A_19: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt] :
( ( A_19 != B_12 )
=> ? [C: arrow_1346734812le_alt] : ( distin1107700095le_alt @ ( cons_A1100118844le_alt @ A_19 @ ( cons_A1100118844le_alt @ B_12 @ ( cons_A1100118844le_alt @ C @ nil_Ar10086284le_alt ) ) ) ) ) ).
thf(fact_28_IIA__def,axiom,
! [F_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( arrow_1724561858le_IIA @ F_8 )
<=> ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ arrow_1605628760e_Prof )
=> ! [Xa: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ Xa @ arrow_1605628760e_Prof )
=> ! [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( ! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( X @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( Xa @ I ) ) )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( F_8 @ X ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( F_8 @ Xa ) ) ) ) ) ) ) ).
thf(fact_29_unanimity__def,axiom,
! [F_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( arrow_1889221221nimity @ F_8 )
<=> ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ arrow_1605628760e_Prof )
=> ! [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( ! [I: arrow_1092341143e_indi] : ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( X @ I ) )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( F_8 @ X ) ) ) ) ) ).
thf(fact_30_complete__Lin,axiom,
! [A_19: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt] :
( ( A_19 != B_12 )
=> ? [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ arrow_1751445586le_Lin )
& ( member545531028le_alt @ ( produc990411159le_alt @ A_19 @ B_12 ) @ X ) ) ) ).
thf(fact_31_in__above,axiom,
! [X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt,L_1: produc1832616231le_alt > $o,A_19: arrow_1346734812le_alt,B_12: arrow_1346734812le_alt] :
( ( A_19 != B_12 )
=> ( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ ( arrow_452340254_above @ L_1 @ A_19 @ B_12 ) )
<=> ( ( X_14 != Y_5 )
& ( ( X_14 = B_12 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_19 @ Y_5 ) @ L_1 ) )
& ( ( X_14 != B_12 )
=> ( ( ( Y_5 = B_12 )
=> ( ( X_14 = A_19 )
| ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ A_19 ) @ L_1 ) ) )
& ( ( Y_5 != B_12 )
=> ( member545531028le_alt @ ( produc990411159le_alt @ X_14 @ Y_5 ) @ L_1 ) ) ) ) ) ) ) ) ).
thf(fact_32_distinct_Osimps_I1_J,axiom,
distin1107700095le_alt @ nil_Ar10086284le_alt ).
thf(fact_33_list_Osimps_I2_J,axiom,
! [A_18: arrow_1346734812le_alt,List_4: list_A1528105233le_alt] :
( nil_Ar10086284le_alt
!= ( cons_A1100118844le_alt @ A_18 @ List_4 ) ) ).
thf(fact_34_list_Oinject,axiom,
! [A_17: arrow_1346734812le_alt,List_3: list_A1528105233le_alt,A_16: arrow_1346734812le_alt,List_2: list_A1528105233le_alt] :
( ( ( cons_A1100118844le_alt @ A_17 @ List_3 )
= ( cons_A1100118844le_alt @ A_16 @ List_2 ) )
<=> ( ( A_17 = A_16 )
& ( List_3 = List_2 ) ) ) ).
thf(fact_35_not__Cons__self2,axiom,
! [X_16: arrow_1346734812le_alt,Xs_11: list_A1528105233le_alt] :
( ( cons_A1100118844le_alt @ X_16 @ Xs_11 )
!= Xs_11 ) ).
thf(fact_36_not__Cons__self,axiom,
! [Xs_10: list_A1528105233le_alt,X_15: arrow_1346734812le_alt] :
( Xs_10
!= ( cons_A1100118844le_alt @ X_15 @ Xs_10 ) ) ).
thf(fact_37_above__Lin,axiom,
! [L_1: produc1832616231le_alt > $o,X_14: arrow_1346734812le_alt,Y_5: arrow_1346734812le_alt] :
( ( X_14 != Y_5 )
=> ( ( member1362619835_alt_o @ L_1 @ arrow_1751445586le_Lin )
=> ( member1362619835_alt_o @ ( arrow_452340254_above @ L_1 @ X_14 @ Y_5 ) @ arrow_1751445586le_Lin ) ) ) ).
thf(fact_38_list_Osimps_I3_J,axiom,
! [A_15: arrow_1346734812le_alt,List_1: list_A1528105233le_alt] :
( ( cons_A1100118844le_alt @ A_15 @ List_1 )
!= nil_Ar10086284le_alt ) ).
thf(fact_39_dictatorI,axiom,
! [I_1: arrow_1092341143e_indi,F_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ F_8
@ ( pi_Arr1021537730_alt_o @ arrow_1605628760e_Prof
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : arrow_1751445586le_Lin ) )
=> ( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ arrow_1605628760e_Prof )
=> ! [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( ( A_7 != B_4 )
=> ( ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( X @ I_1 ) )
=> ( member545531028le_alt @ ( produc990411159le_alt @ A_7 @ B_4 ) @ ( F_8 @ X ) ) ) ) )
=> ( arrow_1098709355ctator @ F_8 @ I_1 ) ) ) ).
thf(fact_40_PiE,axiom,
! [X_13: produc1832616231le_alt,F_11: produc1832616231le_alt > $o,A_14: produc1832616231le_alt > $o,B_11: produc1832616231le_alt > $o > $o] :
( ( member1362619835_alt_o @ F_11 @ ( pi_Pro539263375_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member545531028le_alt @ X_13 @ A_14 ) ) ) ).
thf(fact_41_PiE,axiom,
! [X_13: arrow_1092341143e_indi,F_11: arrow_1092341143e_indi > produc1832616231le_alt,A_14: arrow_1092341143e_indi > $o,B_11: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1621875105le_alt @ F_11 @ ( pi_Arr1055270199le_alt @ A_14 @ B_11 ) )
=> ( ~ ( member545531028le_alt @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1714766084e_indi @ X_13 @ A_14 ) ) ) ).
thf(fact_42_PiE,axiom,
! [X_13: $o,F_11: $o > produc1832616231le_alt,A_14: $o > $o,B_11: $o > produc1832616231le_alt > $o] :
( ( member1368218865le_alt @ F_11 @ ( pi_o_P988780107le_alt @ A_14 @ B_11 ) )
=> ( ~ ( member545531028le_alt @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member_o @ X_13 @ A_14 ) ) ) ).
thf(fact_43_PiE,axiom,
! [X_13: arrow_1092341143e_indi,F_11: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_14: arrow_1092341143e_indi > $o,B_11: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1079651021_alt_o @ F_11 @ ( pi_Arr651234977_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member1561882372_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1714766084e_indi @ X_13 @ A_14 ) ) ) ).
thf(fact_44_PiE,axiom,
! [X_13: $o,F_11: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_14: $o > $o,B_11: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member537117565_alt_o @ F_11 @ ( pi_o_A71242893_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member1561882372_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member_o @ X_13 @ A_14 ) ) ) ).
thf(fact_45_PiE,axiom,
! [X_13: $o,F_11: $o > produc1832616231le_alt > $o,A_14: $o > $o,B_11: $o > ( produc1832616231le_alt > $o ) > $o] :
( ( member1099673524_alt_o @ F_11 @ ( pi_o_P1538584260_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member1362619835_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member_o @ X_13 @ A_14 ) ) ) ).
thf(fact_46_PiE,axiom,
! [X_13: arrow_1092341143e_indi,F_11: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_14: arrow_1092341143e_indi > $o,B_11: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member24189887_alt_o @ F_11 @ ( pi_Arr1140519125_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member733327538_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1714766084e_indi @ X_13 @ A_14 ) ) ) ).
thf(fact_47_PiE,axiom,
! [X_13: $o,F_11: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_14: $o > $o,B_11: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member1710515983_alt_o @ F_11 @ ( pi_o_A1302557673_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member733327538_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member_o @ X_13 @ A_14 ) ) ) ).
thf(fact_48_PiE,axiom,
! [X_13: produc1832616231le_alt,F_11: produc1832616231le_alt > arrow_1092341143e_indi,A_14: produc1832616231le_alt > $o,B_11: produc1832616231le_alt > arrow_1092341143e_indi > $o] :
( ( member1486844321e_indi @ F_11 @ ( pi_Pro1535452471e_indi @ A_14 @ B_11 ) )
=> ( ~ ( member1714766084e_indi @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member545531028le_alt @ X_13 @ A_14 ) ) ) ).
thf(fact_49_PiE,axiom,
! [X_13: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_14: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1208133347e_indi @ F_11 @ ( pi_Arr170420797e_indi @ A_14 @ B_11 ) )
=> ( ~ ( member1714766084e_indi @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1561882372_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_50_PiE,axiom,
! [X_13: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_14: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o] :
( ( member1754345465lt_o_o @ F_11 @ ( pi_Arr1767527177lt_o_o @ A_14 @ B_11 ) )
=> ( ~ ( member_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1561882372_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_51_PiE,axiom,
! [X_13: produc1832616231le_alt > $o,F_11: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_14: ( produc1832616231le_alt > $o ) > $o,B_11: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1255309082e_indi @ F_11 @ ( pi_Pro1340600692e_indi @ A_14 @ B_11 ) )
=> ( ~ ( member1714766084e_indi @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1362619835_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_52_PiE,axiom,
! [X_13: produc1832616231le_alt > $o,F_11: ( produc1832616231le_alt > $o ) > $o,A_14: ( produc1832616231le_alt > $o ) > $o,B_11: ( produc1832616231le_alt > $o ) > $o > $o] :
( ( member1949484546lt_o_o @ F_11 @ ( pi_Pro410810898lt_o_o @ A_14 @ B_11 ) )
=> ( ~ ( member_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1362619835_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_53_PiE,axiom,
! [X_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_14: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member986213183e_indi @ F_11 @ ( pi_Arr1941314005e_indi @ A_14 @ B_11 ) )
=> ( ~ ( member1714766084e_indi @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member733327538_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_54_PiE,axiom,
! [X_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_14: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o] :
( ( member903234717lt_o_o @ F_11 @ ( pi_Arr1422400881lt_o_o @ A_14 @ B_11 ) )
=> ( ~ ( member_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member733327538_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_55_PiE,axiom,
! [X_13: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_14: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ F_11 @ ( pi_Arr1021537730_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member1362619835_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1561882372_alt_o @ X_13 @ A_14 ) ) ) ).
thf(fact_56_PiE,axiom,
! [X_13: arrow_1092341143e_indi,F_11: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_14: arrow_1092341143e_indi > $o,B_11: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ F_11 @ ( pi_Arr418143960_alt_o @ A_14 @ B_11 ) )
=> ( ~ ( member1362619835_alt_o @ ( F_11 @ X_13 ) @ ( B_11 @ X_13 ) )
=> ~ ( member1714766084e_indi @ X_13 @ A_14 ) ) ) ).
thf(fact_57_list_Oexhaust,axiom,
! [Y_4: list_A1528105233le_alt] :
( ( Y_4 != nil_Ar10086284le_alt )
=> ~ ! [A_7: arrow_1346734812le_alt,List: list_A1528105233le_alt] :
( Y_4
!= ( cons_A1100118844le_alt @ A_7 @ List ) ) ) ).
thf(fact_58_neq__Nil__conv,axiom,
! [Xs_9: list_A1528105233le_alt] :
( ( Xs_9 != nil_Ar10086284le_alt )
<=> ? [Y_1: arrow_1346734812le_alt,Ys_2: list_A1528105233le_alt] :
( Xs_9
= ( cons_A1100118844le_alt @ Y_1 @ Ys_2 ) ) ) ).
thf(fact_59_alt3,axiom,
? [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt,C: arrow_1346734812le_alt] : ( distin1107700095le_alt @ ( cons_A1100118844le_alt @ A_7 @ ( cons_A1100118844le_alt @ B_4 @ ( cons_A1100118844le_alt @ C @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_60_Pi__mem,axiom,
! [X_12: produc1832616231le_alt,F_10: produc1832616231le_alt > $o,A_13: produc1832616231le_alt > $o,B_10: produc1832616231le_alt > $o > $o] :
( ( member1362619835_alt_o @ F_10 @ ( pi_Pro539263375_alt_o @ A_13 @ B_10 ) )
=> ( ( member545531028le_alt @ X_12 @ A_13 )
=> ( member_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_61_Pi__mem,axiom,
! [X_12: produc1832616231le_alt,F_10: produc1832616231le_alt > arrow_1092341143e_indi,A_13: produc1832616231le_alt > $o,B_10: produc1832616231le_alt > arrow_1092341143e_indi > $o] :
( ( member1486844321e_indi @ F_10 @ ( pi_Pro1535452471e_indi @ A_13 @ B_10 ) )
=> ( ( member545531028le_alt @ X_12 @ A_13 )
=> ( member1714766084e_indi @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_62_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1208133347e_indi @ F_10 @ ( pi_Arr170420797e_indi @ A_13 @ B_10 ) )
=> ( ( member1561882372_alt_o @ X_12 @ A_13 )
=> ( member1714766084e_indi @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_63_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o] :
( ( member1754345465lt_o_o @ F_10 @ ( pi_Arr1767527177lt_o_o @ A_13 @ B_10 ) )
=> ( ( member1561882372_alt_o @ X_12 @ A_13 )
=> ( member_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_64_Pi__mem,axiom,
! [X_12: produc1832616231le_alt > $o,F_10: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_13: ( produc1832616231le_alt > $o ) > $o,B_10: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member1255309082e_indi @ F_10 @ ( pi_Pro1340600692e_indi @ A_13 @ B_10 ) )
=> ( ( member1362619835_alt_o @ X_12 @ A_13 )
=> ( member1714766084e_indi @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_65_Pi__mem,axiom,
! [X_12: produc1832616231le_alt > $o,F_10: ( produc1832616231le_alt > $o ) > $o,A_13: ( produc1832616231le_alt > $o ) > $o,B_10: ( produc1832616231le_alt > $o ) > $o > $o] :
( ( member1949484546lt_o_o @ F_10 @ ( pi_Pro410810898lt_o_o @ A_13 @ B_10 ) )
=> ( ( member1362619835_alt_o @ X_12 @ A_13 )
=> ( member_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_66_Pi__mem,axiom,
! [X_12: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_10: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_13: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_10: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o] :
( ( member986213183e_indi @ F_10 @ ( pi_Arr1941314005e_indi @ A_13 @ B_10 ) )
=> ( ( member733327538_alt_o @ X_12 @ A_13 )
=> ( member1714766084e_indi @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_67_Pi__mem,axiom,
! [X_12: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_10: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_13: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_10: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o] :
( ( member903234717lt_o_o @ F_10 @ ( pi_Arr1422400881lt_o_o @ A_13 @ B_10 ) )
=> ( ( member733327538_alt_o @ X_12 @ A_13 )
=> ( member_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_68_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi,F_10: arrow_1092341143e_indi > produc1832616231le_alt,A_13: arrow_1092341143e_indi > $o,B_10: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1621875105le_alt @ F_10 @ ( pi_Arr1055270199le_alt @ A_13 @ B_10 ) )
=> ( ( member1714766084e_indi @ X_12 @ A_13 )
=> ( member545531028le_alt @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_69_Pi__mem,axiom,
! [X_12: $o,F_10: $o > produc1832616231le_alt,A_13: $o > $o,B_10: $o > produc1832616231le_alt > $o] :
( ( member1368218865le_alt @ F_10 @ ( pi_o_P988780107le_alt @ A_13 @ B_10 ) )
=> ( ( member_o @ X_12 @ A_13 )
=> ( member545531028le_alt @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_70_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi,F_10: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_13: arrow_1092341143e_indi > $o,B_10: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1079651021_alt_o @ F_10 @ ( pi_Arr651234977_alt_o @ A_13 @ B_10 ) )
=> ( ( member1714766084e_indi @ X_12 @ A_13 )
=> ( member1561882372_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_71_Pi__mem,axiom,
! [X_12: $o,F_10: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_13: $o > $o,B_10: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member537117565_alt_o @ F_10 @ ( pi_o_A71242893_alt_o @ A_13 @ B_10 ) )
=> ( ( member_o @ X_12 @ A_13 )
=> ( member1561882372_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_72_Pi__mem,axiom,
! [X_12: $o,F_10: $o > produc1832616231le_alt > $o,A_13: $o > $o,B_10: $o > ( produc1832616231le_alt > $o ) > $o] :
( ( member1099673524_alt_o @ F_10 @ ( pi_o_P1538584260_alt_o @ A_13 @ B_10 ) )
=> ( ( member_o @ X_12 @ A_13 )
=> ( member1362619835_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_73_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi,F_10: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_13: arrow_1092341143e_indi > $o,B_10: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member24189887_alt_o @ F_10 @ ( pi_Arr1140519125_alt_o @ A_13 @ B_10 ) )
=> ( ( member1714766084e_indi @ X_12 @ A_13 )
=> ( member733327538_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_74_Pi__mem,axiom,
! [X_12: $o,F_10: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_13: $o > $o,B_10: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member1710515983_alt_o @ F_10 @ ( pi_o_A1302557673_alt_o @ A_13 @ B_10 ) )
=> ( ( member_o @ X_12 @ A_13 )
=> ( member733327538_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_75_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_13: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ F_10 @ ( pi_Arr1021537730_alt_o @ A_13 @ B_10 ) )
=> ( ( member1561882372_alt_o @ X_12 @ A_13 )
=> ( member1362619835_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_76_Pi__mem,axiom,
! [X_12: arrow_1092341143e_indi,F_10: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_13: arrow_1092341143e_indi > $o,B_10: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ F_10 @ ( pi_Arr418143960_alt_o @ A_13 @ B_10 ) )
=> ( ( member1714766084e_indi @ X_12 @ A_13 )
=> ( member1362619835_alt_o @ ( F_10 @ X_12 ) @ ( B_10 @ X_12 ) ) ) ) ).
thf(fact_77_funcset__mem,axiom,
! [X_11: produc1832616231le_alt,F_9: produc1832616231le_alt > $o,A_12: produc1832616231le_alt > $o,B_9: $o > $o] :
( ( member1362619835_alt_o @ F_9
@ ( pi_Pro539263375_alt_o @ A_12
@ ^ [Uu: produc1832616231le_alt] : B_9 ) )
=> ( ( member545531028le_alt @ X_11 @ A_12 )
=> ( member_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_78_funcset__mem,axiom,
! [X_11: produc1832616231le_alt,F_9: produc1832616231le_alt > arrow_1092341143e_indi,A_12: produc1832616231le_alt > $o,B_9: arrow_1092341143e_indi > $o] :
( ( member1486844321e_indi @ F_9
@ ( pi_Pro1535452471e_indi @ A_12
@ ^ [Uu: produc1832616231le_alt] : B_9 ) )
=> ( ( member545531028le_alt @ X_11 @ A_12 )
=> ( member1714766084e_indi @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_79_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_12: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_9: arrow_1092341143e_indi > $o] :
( ( member1208133347e_indi @ F_9
@ ( pi_Arr170420797e_indi @ A_12
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member1561882372_alt_o @ X_11 @ A_12 )
=> ( member1714766084e_indi @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_80_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_12: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_9: $o > $o] :
( ( member1754345465lt_o_o @ F_9
@ ( pi_Arr1767527177lt_o_o @ A_12
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member1561882372_alt_o @ X_11 @ A_12 )
=> ( member_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_81_funcset__mem,axiom,
! [X_11: produc1832616231le_alt > $o,F_9: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_12: ( produc1832616231le_alt > $o ) > $o,B_9: arrow_1092341143e_indi > $o] :
( ( member1255309082e_indi @ F_9
@ ( pi_Pro1340600692e_indi @ A_12
@ ^ [Uu: produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member1362619835_alt_o @ X_11 @ A_12 )
=> ( member1714766084e_indi @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_82_funcset__mem,axiom,
! [X_11: produc1832616231le_alt > $o,F_9: ( produc1832616231le_alt > $o ) > $o,A_12: ( produc1832616231le_alt > $o ) > $o,B_9: $o > $o] :
( ( member1949484546lt_o_o @ F_9
@ ( pi_Pro410810898lt_o_o @ A_12
@ ^ [Uu: produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member1362619835_alt_o @ X_11 @ A_12 )
=> ( member_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_83_funcset__mem,axiom,
! [X_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_9: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,A_12: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_9: arrow_1092341143e_indi > $o] :
( ( member986213183e_indi @ F_9
@ ( pi_Arr1941314005e_indi @ A_12
@ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member733327538_alt_o @ X_11 @ A_12 )
=> ( member1714766084e_indi @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_84_funcset__mem,axiom,
! [X_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,F_9: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_12: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_9: $o > $o] :
( ( member903234717lt_o_o @ F_9
@ ( pi_Arr1422400881lt_o_o @ A_12
@ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member733327538_alt_o @ X_11 @ A_12 )
=> ( member_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_85_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi,F_9: arrow_1092341143e_indi > produc1832616231le_alt,A_12: arrow_1092341143e_indi > $o,B_9: produc1832616231le_alt > $o] :
( ( member1621875105le_alt @ F_9
@ ( pi_Arr1055270199le_alt @ A_12
@ ^ [Uu: arrow_1092341143e_indi] : B_9 ) )
=> ( ( member1714766084e_indi @ X_11 @ A_12 )
=> ( member545531028le_alt @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_86_funcset__mem,axiom,
! [X_11: $o,F_9: $o > produc1832616231le_alt,A_12: $o > $o,B_9: produc1832616231le_alt > $o] :
( ( member1368218865le_alt @ F_9
@ ( pi_o_P988780107le_alt @ A_12
@ ^ [Uu: $o] : B_9 ) )
=> ( ( member_o @ X_11 @ A_12 )
=> ( member545531028le_alt @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_87_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi,F_9: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_12: arrow_1092341143e_indi > $o,B_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1079651021_alt_o @ F_9
@ ( pi_Arr651234977_alt_o @ A_12
@ ^ [Uu: arrow_1092341143e_indi] : B_9 ) )
=> ( ( member1714766084e_indi @ X_11 @ A_12 )
=> ( member1561882372_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_88_funcset__mem,axiom,
! [X_11: $o,F_9: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,A_12: $o > $o,B_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member537117565_alt_o @ F_9
@ ( pi_o_A71242893_alt_o @ A_12
@ ^ [Uu: $o] : B_9 ) )
=> ( ( member_o @ X_11 @ A_12 )
=> ( member1561882372_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_89_funcset__mem,axiom,
! [X_11: $o,F_9: $o > produc1832616231le_alt > $o,A_12: $o > $o,B_9: ( produc1832616231le_alt > $o ) > $o] :
( ( member1099673524_alt_o @ F_9
@ ( pi_o_P1538584260_alt_o @ A_12
@ ^ [Uu: $o] : B_9 ) )
=> ( ( member_o @ X_11 @ A_12 )
=> ( member1362619835_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_90_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi,F_9: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_12: arrow_1092341143e_indi > $o,B_9: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member24189887_alt_o @ F_9
@ ( pi_Arr1140519125_alt_o @ A_12
@ ^ [Uu: arrow_1092341143e_indi] : B_9 ) )
=> ( ( member1714766084e_indi @ X_11 @ A_12 )
=> ( member733327538_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_91_funcset__mem,axiom,
! [X_11: $o,F_9: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_12: $o > $o,B_9: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ( member1710515983_alt_o @ F_9
@ ( pi_o_A1302557673_alt_o @ A_12
@ ^ [Uu: $o] : B_9 ) )
=> ( ( member_o @ X_11 @ A_12 )
=> ( member733327538_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_92_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi > produc1832616231le_alt > $o,F_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_12: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_9: ( produc1832616231le_alt > $o ) > $o] :
( ( member733327538_alt_o @ F_9
@ ( pi_Arr1021537730_alt_o @ A_12
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B_9 ) )
=> ( ( member1561882372_alt_o @ X_11 @ A_12 )
=> ( member1362619835_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_93_funcset__mem,axiom,
! [X_11: arrow_1092341143e_indi,F_9: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_12: arrow_1092341143e_indi > $o,B_9: ( produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ F_9
@ ( pi_Arr418143960_alt_o @ A_12
@ ^ [Uu: arrow_1092341143e_indi] : B_9 ) )
=> ( ( member1714766084e_indi @ X_11 @ A_12 )
=> ( member1362619835_alt_o @ ( F_9 @ X_11 ) @ B_9 ) ) ) ).
thf(fact_94_dictator__def,axiom,
! [F_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,I_1: arrow_1092341143e_indi] :
( ( arrow_1098709355ctator @ F_8 @ I_1 )
<=> ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ arrow_1605628760e_Prof )
=> ( ( F_8 @ X )
= ( X @ I_1 ) ) ) ) ).
thf(fact_95_Pi__I,axiom,
! [F_7: produc1832616231le_alt > arrow_1092341143e_indi,B_8: produc1832616231le_alt > arrow_1092341143e_indi > $o,A_11: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] :
( ( member545531028le_alt @ X @ A_11 )
=> ( member1714766084e_indi @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1486844321e_indi @ F_7 @ ( pi_Pro1535452471e_indi @ A_11 @ B_8 ) ) ) ).
thf(fact_96_Pi__I,axiom,
! [F_7: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o,A_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_11 )
=> ( member1714766084e_indi @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1208133347e_indi @ F_7 @ ( pi_Arr170420797e_indi @ A_11 @ B_8 ) ) ) ).
thf(fact_97_Pi__I,axiom,
! [F_7: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o,A_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_11 )
=> ( member_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1754345465lt_o_o @ F_7 @ ( pi_Arr1767527177lt_o_o @ A_11 @ B_8 ) ) ) ).
thf(fact_98_Pi__I,axiom,
! [F_7: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_8: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o,A_11: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ A_11 )
=> ( member1714766084e_indi @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1255309082e_indi @ F_7 @ ( pi_Pro1340600692e_indi @ A_11 @ B_8 ) ) ) ).
thf(fact_99_Pi__I,axiom,
! [F_7: ( produc1832616231le_alt > $o ) > $o,B_8: ( produc1832616231le_alt > $o ) > $o > $o,A_11: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ A_11 )
=> ( member_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1949484546lt_o_o @ F_7 @ ( pi_Pro410810898lt_o_o @ A_11 @ B_8 ) ) ) ).
thf(fact_100_Pi__I,axiom,
! [F_7: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_8: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o,A_11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ X @ A_11 )
=> ( member1714766084e_indi @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member986213183e_indi @ F_7 @ ( pi_Arr1941314005e_indi @ A_11 @ B_8 ) ) ) ).
thf(fact_101_Pi__I,axiom,
! [F_7: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_8: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o,A_11: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ X @ A_11 )
=> ( member_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member903234717lt_o_o @ F_7 @ ( pi_Arr1422400881lt_o_o @ A_11 @ B_8 ) ) ) ).
thf(fact_102_Pi__I,axiom,
! [F_7: arrow_1092341143e_indi > produc1832616231le_alt,B_8: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_11: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_11 )
=> ( member545531028le_alt @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1621875105le_alt @ F_7 @ ( pi_Arr1055270199le_alt @ A_11 @ B_8 ) ) ) ).
thf(fact_103_Pi__I,axiom,
! [F_7: $o > produc1832616231le_alt,B_8: $o > produc1832616231le_alt > $o,A_11: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_11 )
=> ( member545531028le_alt @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1368218865le_alt @ F_7 @ ( pi_o_P988780107le_alt @ A_11 @ B_8 ) ) ) ).
thf(fact_104_Pi__I,axiom,
! [F_7: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,B_8: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_11: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_11 )
=> ( member1561882372_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1079651021_alt_o @ F_7 @ ( pi_Arr651234977_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_105_Pi__I,axiom,
! [F_7: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,B_8: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_11: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_11 )
=> ( member1561882372_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member537117565_alt_o @ F_7 @ ( pi_o_A71242893_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_106_Pi__I,axiom,
! [F_7: $o > produc1832616231le_alt > $o,B_8: $o > ( produc1832616231le_alt > $o ) > $o,A_11: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_11 )
=> ( member1362619835_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1099673524_alt_o @ F_7 @ ( pi_o_P1538584260_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_107_Pi__I,axiom,
! [F_7: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_8: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_11: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_11 )
=> ( member733327538_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member24189887_alt_o @ F_7 @ ( pi_Arr1140519125_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_108_Pi__I,axiom,
! [F_7: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_8: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_11: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_11 )
=> ( member733327538_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1710515983_alt_o @ F_7 @ ( pi_o_A1302557673_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_109_Pi__I,axiom,
! [F_7: produc1832616231le_alt > $o,B_8: produc1832616231le_alt > $o > $o,A_11: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] :
( ( member545531028le_alt @ X @ A_11 )
=> ( member_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1362619835_alt_o @ F_7 @ ( pi_Pro539263375_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_110_Pi__I,axiom,
! [F_7: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o,A_11: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_11 )
=> ( member1362619835_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member733327538_alt_o @ F_7 @ ( pi_Arr1021537730_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_111_Pi__I,axiom,
! [F_7: arrow_1092341143e_indi > produc1832616231le_alt > $o,B_8: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o,A_11: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_11 )
=> ( member1362619835_alt_o @ ( F_7 @ X ) @ ( B_8 @ X ) ) )
=> ( member1561882372_alt_o @ F_7 @ ( pi_Arr418143960_alt_o @ A_11 @ B_8 ) ) ) ).
thf(fact_112_funcsetI,axiom,
! [F_6: produc1832616231le_alt > arrow_1092341143e_indi,B_7: arrow_1092341143e_indi > $o,A_10: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] :
( ( member545531028le_alt @ X @ A_10 )
=> ( member1714766084e_indi @ ( F_6 @ X ) @ B_7 ) )
=> ( member1486844321e_indi @ F_6
@ ( pi_Pro1535452471e_indi @ A_10
@ ^ [Uu: produc1832616231le_alt] : B_7 ) ) ) ).
thf(fact_113_funcsetI,axiom,
! [F_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_7: arrow_1092341143e_indi > $o,A_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_10 )
=> ( member1714766084e_indi @ ( F_6 @ X ) @ B_7 ) )
=> ( member1208133347e_indi @ F_6
@ ( pi_Arr170420797e_indi @ A_10
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_114_funcsetI,axiom,
! [F_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_7: $o > $o,A_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_10 )
=> ( member_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1754345465lt_o_o @ F_6
@ ( pi_Arr1767527177lt_o_o @ A_10
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_115_funcsetI,axiom,
! [F_6: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_7: arrow_1092341143e_indi > $o,A_10: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ A_10 )
=> ( member1714766084e_indi @ ( F_6 @ X ) @ B_7 ) )
=> ( member1255309082e_indi @ F_6
@ ( pi_Pro1340600692e_indi @ A_10
@ ^ [Uu: produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_116_funcsetI,axiom,
! [F_6: ( produc1832616231le_alt > $o ) > $o,B_7: $o > $o,A_10: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ A_10 )
=> ( member_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1949484546lt_o_o @ F_6
@ ( pi_Pro410810898lt_o_o @ A_10
@ ^ [Uu: produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_117_funcsetI,axiom,
! [F_6: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_7: arrow_1092341143e_indi > $o,A_10: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ X @ A_10 )
=> ( member1714766084e_indi @ ( F_6 @ X ) @ B_7 ) )
=> ( member986213183e_indi @ F_6
@ ( pi_Arr1941314005e_indi @ A_10
@ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_118_funcsetI,axiom,
! [F_6: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_7: $o > $o,A_10: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ X @ A_10 )
=> ( member_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member903234717lt_o_o @ F_6
@ ( pi_Arr1422400881lt_o_o @ A_10
@ ^ [Uu: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_119_funcsetI,axiom,
! [F_6: arrow_1092341143e_indi > produc1832616231le_alt,B_7: produc1832616231le_alt > $o,A_10: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_10 )
=> ( member545531028le_alt @ ( F_6 @ X ) @ B_7 ) )
=> ( member1621875105le_alt @ F_6
@ ( pi_Arr1055270199le_alt @ A_10
@ ^ [Uu: arrow_1092341143e_indi] : B_7 ) ) ) ).
thf(fact_120_funcsetI,axiom,
! [F_6: $o > produc1832616231le_alt,B_7: produc1832616231le_alt > $o,A_10: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_10 )
=> ( member545531028le_alt @ ( F_6 @ X ) @ B_7 ) )
=> ( member1368218865le_alt @ F_6
@ ( pi_o_P988780107le_alt @ A_10
@ ^ [Uu: $o] : B_7 ) ) ) ).
thf(fact_121_funcsetI,axiom,
! [F_6: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,B_7: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_10: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_10 )
=> ( member1561882372_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1079651021_alt_o @ F_6
@ ( pi_Arr651234977_alt_o @ A_10
@ ^ [Uu: arrow_1092341143e_indi] : B_7 ) ) ) ).
thf(fact_122_funcsetI,axiom,
! [F_6: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,B_7: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_10: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_10 )
=> ( member1561882372_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member537117565_alt_o @ F_6
@ ( pi_o_A71242893_alt_o @ A_10
@ ^ [Uu: $o] : B_7 ) ) ) ).
thf(fact_123_funcsetI,axiom,
! [F_6: $o > produc1832616231le_alt > $o,B_7: ( produc1832616231le_alt > $o ) > $o,A_10: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_10 )
=> ( member1362619835_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1099673524_alt_o @ F_6
@ ( pi_o_P1538584260_alt_o @ A_10
@ ^ [Uu: $o] : B_7 ) ) ) ).
thf(fact_124_funcsetI,axiom,
! [F_6: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_7: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_10: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_10 )
=> ( member733327538_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member24189887_alt_o @ F_6
@ ( pi_Arr1140519125_alt_o @ A_10
@ ^ [Uu: arrow_1092341143e_indi] : B_7 ) ) ) ).
thf(fact_125_funcsetI,axiom,
! [F_6: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_7: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_10: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_10 )
=> ( member733327538_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1710515983_alt_o @ F_6
@ ( pi_o_A1302557673_alt_o @ A_10
@ ^ [Uu: $o] : B_7 ) ) ) ).
thf(fact_126_funcsetI,axiom,
! [F_6: produc1832616231le_alt > $o,B_7: $o > $o,A_10: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] :
( ( member545531028le_alt @ X @ A_10 )
=> ( member_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1362619835_alt_o @ F_6
@ ( pi_Pro539263375_alt_o @ A_10
@ ^ [Uu: produc1832616231le_alt] : B_7 ) ) ) ).
thf(fact_127_funcsetI,axiom,
! [F_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_7: ( produc1832616231le_alt > $o ) > $o,A_10: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_10 )
=> ( member1362619835_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member733327538_alt_o @ F_6
@ ( pi_Arr1021537730_alt_o @ A_10
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : B_7 ) ) ) ).
thf(fact_128_funcsetI,axiom,
! [F_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,B_7: ( produc1832616231le_alt > $o ) > $o,A_10: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_10 )
=> ( member1362619835_alt_o @ ( F_6 @ X ) @ B_7 ) )
=> ( member1561882372_alt_o @ F_6
@ ( pi_Arr418143960_alt_o @ A_10
@ ^ [Uu: arrow_1092341143e_indi] : B_7 ) ) ) ).
thf(fact_129_linear__alt,axiom,
? [L: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ L @ arrow_1751445586le_Lin ) ).
thf(fact_130_Pi__I_H,axiom,
! [F_5: produc1832616231le_alt > arrow_1092341143e_indi,B_6: produc1832616231le_alt > arrow_1092341143e_indi > $o,A_9: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] :
( ( member545531028le_alt @ X @ A_9 )
=> ( member1714766084e_indi @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1486844321e_indi @ F_5 @ ( pi_Pro1535452471e_indi @ A_9 @ B_6 ) ) ) ).
thf(fact_131_Pi__I_H,axiom,
! [F_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o,A_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_9 )
=> ( member1714766084e_indi @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1208133347e_indi @ F_5 @ ( pi_Arr170420797e_indi @ A_9 @ B_6 ) ) ) ).
thf(fact_132_Pi__I_H,axiom,
! [F_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,B_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o > $o,A_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_9 )
=> ( member_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1754345465lt_o_o @ F_5 @ ( pi_Arr1767527177lt_o_o @ A_9 @ B_6 ) ) ) ).
thf(fact_133_Pi__I_H,axiom,
! [F_5: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_6: ( produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o,A_9: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ A_9 )
=> ( member1714766084e_indi @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1255309082e_indi @ F_5 @ ( pi_Pro1340600692e_indi @ A_9 @ B_6 ) ) ) ).
thf(fact_134_Pi__I_H,axiom,
! [F_5: ( produc1832616231le_alt > $o ) > $o,B_6: ( produc1832616231le_alt > $o ) > $o > $o,A_9: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] :
( ( member1362619835_alt_o @ X @ A_9 )
=> ( member_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1949484546lt_o_o @ F_5 @ ( pi_Pro410810898lt_o_o @ A_9 @ B_6 ) ) ) ).
thf(fact_135_Pi__I_H,axiom,
! [F_5: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi,B_6: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > arrow_1092341143e_indi > $o,A_9: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ X @ A_9 )
=> ( member1714766084e_indi @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member986213183e_indi @ F_5 @ ( pi_Arr1941314005e_indi @ A_9 @ B_6 ) ) ) ).
thf(fact_136_Pi__I_H,axiom,
! [F_5: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,B_6: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o > $o,A_9: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( member733327538_alt_o @ X @ A_9 )
=> ( member_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member903234717lt_o_o @ F_5 @ ( pi_Arr1422400881lt_o_o @ A_9 @ B_6 ) ) ) ).
thf(fact_137_Pi__I_H,axiom,
! [F_5: arrow_1092341143e_indi > produc1832616231le_alt,B_6: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_9: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_9 )
=> ( member545531028le_alt @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1621875105le_alt @ F_5 @ ( pi_Arr1055270199le_alt @ A_9 @ B_6 ) ) ) ).
thf(fact_138_Pi__I_H,axiom,
! [F_5: $o > produc1832616231le_alt,B_6: $o > produc1832616231le_alt > $o,A_9: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_9 )
=> ( member545531028le_alt @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1368218865le_alt @ F_5 @ ( pi_o_P988780107le_alt @ A_9 @ B_6 ) ) ) ).
thf(fact_139_Pi__I_H,axiom,
! [F_5: arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o,B_6: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_9: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_9 )
=> ( member1561882372_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1079651021_alt_o @ F_5 @ ( pi_Arr651234977_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_140_Pi__I_H,axiom,
! [F_5: $o > arrow_1092341143e_indi > produc1832616231le_alt > $o,B_6: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o,A_9: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_9 )
=> ( member1561882372_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member537117565_alt_o @ F_5 @ ( pi_o_A71242893_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_141_Pi__I_H,axiom,
! [F_5: $o > produc1832616231le_alt > $o,B_6: $o > ( produc1832616231le_alt > $o ) > $o,A_9: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_9 )
=> ( member1362619835_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1099673524_alt_o @ F_5 @ ( pi_o_P1538584260_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_142_Pi__I_H,axiom,
! [F_5: arrow_1092341143e_indi > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_6: arrow_1092341143e_indi > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_9: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_9 )
=> ( member733327538_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member24189887_alt_o @ F_5 @ ( pi_Arr1140519125_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_143_Pi__I_H,axiom,
! [F_5: $o > ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_6: $o > ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o,A_9: $o > $o] :
( ! [X: $o] :
( ( member_o @ X @ A_9 )
=> ( member733327538_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1710515983_alt_o @ F_5 @ ( pi_o_A1302557673_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_144_Pi__I_H,axiom,
! [F_5: produc1832616231le_alt > $o,B_6: produc1832616231le_alt > $o > $o,A_9: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] :
( ( member545531028le_alt @ X @ A_9 )
=> ( member_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1362619835_alt_o @ F_5 @ ( pi_Pro539263375_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_145_Pi__I_H,axiom,
! [F_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,B_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o,A_9: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ X @ A_9 )
=> ( member1362619835_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member733327538_alt_o @ F_5 @ ( pi_Arr1021537730_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_146_Pi__I_H,axiom,
! [F_5: arrow_1092341143e_indi > produc1832616231le_alt > $o,B_6: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o,A_9: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ X @ A_9 )
=> ( member1362619835_alt_o @ ( F_5 @ X ) @ ( B_6 @ X ) ) )
=> ( member1561882372_alt_o @ F_5 @ ( pi_Arr418143960_alt_o @ A_9 @ B_6 ) ) ) ).
thf(fact_147_Pi__cong,axiom,
! [B_5: produc1832616231le_alt > $o > $o,G: produc1832616231le_alt > $o,F_4: produc1832616231le_alt > $o,A_8: produc1832616231le_alt > $o] :
( ! [W: produc1832616231le_alt] :
( ( member545531028le_alt @ W @ A_8 )
=> ( ( F_4 @ W )
<=> ( G @ W ) ) )
=> ( ( member1362619835_alt_o @ F_4 @ ( pi_Pro539263375_alt_o @ A_8 @ B_5 ) )
<=> ( member1362619835_alt_o @ G @ ( pi_Pro539263375_alt_o @ A_8 @ B_5 ) ) ) ) ).
thf(fact_148_Pi__cong,axiom,
! [B_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > $o,F_4: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,G: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o,A_8: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [W: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( member1561882372_alt_o @ W @ A_8 )
=> ( ( F_4 @ W )
= ( G @ W ) ) )
=> ( ( member733327538_alt_o @ F_4 @ ( pi_Arr1021537730_alt_o @ A_8 @ B_5 ) )
<=> ( member733327538_alt_o @ G @ ( pi_Arr1021537730_alt_o @ A_8 @ B_5 ) ) ) ) ).
thf(fact_149_Pi__cong,axiom,
! [B_5: arrow_1092341143e_indi > ( produc1832616231le_alt > $o ) > $o,F_4: arrow_1092341143e_indi > produc1832616231le_alt > $o,G: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_8: arrow_1092341143e_indi > $o] :
( ! [W: arrow_1092341143e_indi] :
( ( member1714766084e_indi @ W @ A_8 )
=> ( ( F_4 @ W )
= ( G @ W ) ) )
=> ( ( member1561882372_alt_o @ F_4 @ ( pi_Arr418143960_alt_o @ A_8 @ B_5 ) )
<=> ( member1561882372_alt_o @ G @ ( pi_Arr418143960_alt_o @ A_8 @ B_5 ) ) ) ) ).
thf(fact_150_splice_Osimps_I2_J,axiom,
! [V: arrow_1346734812le_alt,Va: list_A1528105233le_alt] :
( ( splice244790623le_alt @ ( cons_A1100118844le_alt @ V @ Va ) @ nil_Ar10086284le_alt )
= ( cons_A1100118844le_alt @ V @ Va ) ) ).
thf(fact_151_splice_Osimps_I3_J,axiom,
! [X_10: arrow_1346734812le_alt,Xs_8: list_A1528105233le_alt,Y_3: arrow_1346734812le_alt,Ys_1: list_A1528105233le_alt] :
( ( splice244790623le_alt @ ( cons_A1100118844le_alt @ X_10 @ Xs_8 ) @ ( cons_A1100118844le_alt @ Y_3 @ Ys_1 ) )
= ( cons_A1100118844le_alt @ X_10 @ ( cons_A1100118844le_alt @ Y_3 @ ( splice244790623le_alt @ Xs_8 @ Ys_1 ) ) ) ) ).
thf(fact_152_splice_Osimps_I1_J,axiom,
! [Ys: list_A1528105233le_alt] :
( ( splice244790623le_alt @ nil_Ar10086284le_alt @ Ys )
= Ys ) ).
thf(fact_153_splice__Nil2,axiom,
! [Xs_7: list_A1528105233le_alt] :
( ( splice244790623le_alt @ Xs_7 @ nil_Ar10086284le_alt )
= Xs_7 ) ).
thf(fact_154_pred__equals__eq2,axiom,
! [S: produc1832616231le_alt > $o,R: produc1832616231le_alt > $o] :
( ! [X: arrow_1346734812le_alt,Xa: arrow_1346734812le_alt] :
( ( member545531028le_alt @ ( produc990411159le_alt @ X @ Xa ) @ R )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ X @ Xa ) @ S ) )
<=> ( R = S ) ) ).
thf(fact_155_prod_Oexhaust,axiom,
! [Y_2: produc1832616231le_alt] :
~ ! [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] :
( Y_2
!= ( produc990411159le_alt @ A_7 @ B_4 ) ) ).
thf(fact_156_PairE,axiom,
! [P_3: produc1832616231le_alt] :
~ ! [X: arrow_1346734812le_alt,Y_1: arrow_1346734812le_alt] :
( P_3
!= ( produc990411159le_alt @ X @ Y_1 ) ) ).
thf(fact_157_split__paired__Ex,axiom,
! [P_2: produc1832616231le_alt > $o] :
( ( ex @ P_2 )
<=> ? [A_7: arrow_1346734812le_alt,B_4: arrow_1346734812le_alt] : ( P_2 @ ( produc990411159le_alt @ A_7 @ B_4 ) ) ) ).
thf(fact_158_insert__Nil,axiom,
! [X_9: arrow_1346734812le_alt] :
( ( insert844458914le_alt @ X_9 @ nil_Ar10086284le_alt )
= ( cons_A1100118844le_alt @ X_9 @ nil_Ar10086284le_alt ) ) ).
thf(fact_159_distinct__insert,axiom,
! [X_8: arrow_1346734812le_alt,Xs_6: list_A1528105233le_alt] :
( ( distin1107700095le_alt @ Xs_6 )
=> ( distin1107700095le_alt @ ( insert844458914le_alt @ X_8 @ Xs_6 ) ) ) ).
thf(fact_160_mem__def,axiom,
! [X_7: arrow_1092341143e_indi,A_6: arrow_1092341143e_indi > $o] :
( ( member1714766084e_indi @ X_7 @ A_6 )
<=> ( A_6 @ X_7 ) ) ).
thf(fact_161_mem__def,axiom,
! [X_7: $o,A_6: $o > $o] :
( ( member_o @ X_7 @ A_6 )
<=> ( A_6 @ X_7 ) ) ).
thf(fact_162_mem__def,axiom,
! [X_7: produc1832616231le_alt,A_6: produc1832616231le_alt > $o] :
( ( member545531028le_alt @ X_7 @ A_6 )
<=> ( A_6 @ X_7 ) ) ).
thf(fact_163_mem__def,axiom,
! [X_7: arrow_1092341143e_indi > produc1832616231le_alt > $o,A_6: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( member1561882372_alt_o @ X_7 @ A_6 )
<=> ( A_6 @ X_7 ) ) ).
thf(fact_164_mem__def,axiom,
! [X_7: produc1832616231le_alt > $o,A_6: ( produc1832616231le_alt > $o ) > $o] :
( ( member1362619835_alt_o @ X_7 @ A_6 )
<=> ( A_6 @ X_7 ) ) ).
thf(fact_165_mem__def,axiom,
! [X_7: ( 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_7 @ A_6 )
<=> ( A_6 @ X_7 ) ) ).
thf(fact_166_Collect__def,axiom,
! [P_1: arrow_1092341143e_indi > $o] :
( ( collec1832628290e_indi @ P_1 )
= P_1 ) ).
thf(fact_167_list__nonempty__induct,axiom,
! [P: list_A1528105233le_alt > $o,Xs_4: list_A1528105233le_alt] :
( ( Xs_4 != nil_Ar10086284le_alt )
=> ( ! [X: arrow_1346734812le_alt] : ( P @ ( cons_A1100118844le_alt @ X @ nil_Ar10086284le_alt ) )
=> ( ! [X: arrow_1346734812le_alt,Xs_5: list_A1528105233le_alt] :
( ( Xs_5 != nil_Ar10086284le_alt )
=> ( ( P @ Xs_5 )
=> ( P @ ( cons_A1100118844le_alt @ X @ Xs_5 ) ) ) )
=> ( P @ Xs_4 ) ) ) ) ).
thf(fact_168_curry__def,axiom,
! [X: produc1832616231le_alt > $o,Xa: arrow_1346734812le_alt,Xb: arrow_1346734812le_alt] :
( ( produc443407182_alt_o @ X @ Xa @ Xb )
<=> ( X @ ( produc990411159le_alt @ Xa @ Xb ) ) ) ).
thf(fact_169_curryI,axiom,
! [F_3: produc1832616231le_alt > $o,A_5: arrow_1346734812le_alt,B_3: arrow_1346734812le_alt] :
( ( F_3 @ ( produc990411159le_alt @ A_5 @ B_3 ) )
=> ( produc443407182_alt_o @ F_3 @ A_5 @ B_3 ) ) ).
thf(fact_170_curryE,axiom,
! [F_2: produc1832616231le_alt > $o,A_4: arrow_1346734812le_alt,B_2: arrow_1346734812le_alt] :
( ( produc443407182_alt_o @ F_2 @ A_4 @ B_2 )
=> ( F_2 @ ( produc990411159le_alt @ A_4 @ B_2 ) ) ) ).
thf(fact_171_curryD,axiom,
! [F_1: produc1832616231le_alt > $o,A_3: arrow_1346734812le_alt,B_1: arrow_1346734812le_alt] :
( ( produc443407182_alt_o @ F_1 @ A_3 @ B_1 )
=> ( F_1 @ ( produc990411159le_alt @ A_3 @ B_1 ) ) ) ).
thf(fact_172_curry__conv,axiom,
! [F: produc1832616231le_alt > $o,A_2: arrow_1346734812le_alt,B: arrow_1346734812le_alt] :
( ( produc443407182_alt_o @ F @ A_2 @ B )
<=> ( F @ ( produc990411159le_alt @ A_2 @ B ) ) ) ).
thf(fact_173_eq__Nil__null,axiom,
! [Xs_3: list_A1528105233le_alt] :
( ( Xs_3 = nil_Ar10086284le_alt )
<=> ( null_A244857236le_alt @ Xs_3 ) ) ).
thf(fact_174_List_Onull__def,axiom,
! [Xs_2: list_A1528105233le_alt] :
( ( null_A244857236le_alt @ Xs_2 )
<=> ( Xs_2 = nil_Ar10086284le_alt ) ) ).
thf(fact_175_null__rec_I1_J,axiom,
! [X_6: arrow_1346734812le_alt,Xs_1: list_A1528105233le_alt] :
~ ( null_A244857236le_alt @ ( cons_A1100118844le_alt @ X_6 @ Xs_1 ) ) ).
thf(fact_176_null__rec_I2_J,axiom,
null_A244857236le_alt @ nil_Ar10086284le_alt ).
thf(fact_177_equal__Nil__null,axiom,
! [Xs: list_A1528105233le_alt] :
( ( equal_2044961839le_alt @ Xs @ nil_Ar10086284le_alt )
<=> ( null_A244857236le_alt @ Xs ) ) ).
thf(fact_178_Prof__def,axiom,
( arrow_1605628760e_Prof
= ( pi_Arr418143960_alt_o @ top_to527331954indi_o
@ ^ [Uu: arrow_1092341143e_indi] : arrow_1751445586le_Lin ) ) ).
thf(fact_179_top1I,axiom,
! [X_5: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( top_to1049332548lt_o_o @ X_5 ) ).
thf(fact_180_top1I,axiom,
! [X_5: produc1832616231le_alt > $o] : ( top_to1830848411lt_o_o @ X_5 ) ).
thf(fact_181_top1I,axiom,
! [X_5: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( top_to790289938lt_o_o @ X_5 ) ).
thf(fact_182_top1I,axiom,
! [X_5: produc1832616231le_alt] : ( top_to679332578_alt_o @ X_5 ) ).
thf(fact_183_top1I,axiom,
! [X_5: arrow_1092341143e_indi] : ( top_to527331954indi_o @ X_5 ) ).
thf(fact_184_Pi__UNIV,axiom,
! [A_1: produc1832616231le_alt > $o] :
( ( pi_Pro539263375_alt_o @ A_1
@ ^ [Uu: produc1832616231le_alt] : top_top_o_o )
= top_to1830848411lt_o_o ) ).
thf(fact_185_Pi__UNIV,axiom,
! [A_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ( pi_Arr1021537730_alt_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi > produc1832616231le_alt > $o] : top_to1830848411lt_o_o )
= top_to1049332548lt_o_o ) ).
thf(fact_186_Pi__UNIV,axiom,
! [A_1: arrow_1092341143e_indi > $o] :
( ( pi_Arr418143960_alt_o @ A_1
@ ^ [Uu: arrow_1092341143e_indi] : top_to1830848411lt_o_o )
= top_to790289938lt_o_o ) ).
thf(fact_187_equal__list__def,axiom,
! [X_4: list_A1528105233le_alt,Y: list_A1528105233le_alt] :
( ( equal_2044961839le_alt @ X_4 @ Y )
<=> ( X_4 = Y ) ) ).
thf(fact_188_iso__tuple__UNIV__I,axiom,
! [X_3: $o] : ( member_o @ X_3 @ top_top_o_o ) ).
thf(fact_189_iso__tuple__UNIV__I,axiom,
! [X_3: arrow_1092341143e_indi] : ( member1714766084e_indi @ X_3 @ top_to527331954indi_o ) ).
thf(fact_190_iso__tuple__UNIV__I,axiom,
! [X_3: produc1832616231le_alt] : ( member545531028le_alt @ X_3 @ top_to679332578_alt_o ) ).
thf(fact_191_iso__tuple__UNIV__I,axiom,
! [X_3: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X_3 @ top_to790289938lt_o_o ) ).
thf(fact_192_iso__tuple__UNIV__I,axiom,
! [X_3: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X_3 @ top_to1830848411lt_o_o ) ).
thf(fact_193_iso__tuple__UNIV__I,axiom,
! [X_3: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X_3 @ top_to1049332548lt_o_o ) ).
thf(fact_194_UNIV__I,axiom,
! [X_2: $o] : ( member_o @ X_2 @ top_top_o_o ) ).
thf(fact_195_UNIV__I,axiom,
! [X_2: arrow_1092341143e_indi] : ( member1714766084e_indi @ X_2 @ top_to527331954indi_o ) ).
thf(fact_196_UNIV__I,axiom,
! [X_2: produc1832616231le_alt] : ( member545531028le_alt @ X_2 @ top_to679332578_alt_o ) ).
thf(fact_197_UNIV__I,axiom,
! [X_2: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X_2 @ top_to790289938lt_o_o ) ).
thf(fact_198_UNIV__I,axiom,
! [X_2: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X_2 @ top_to1830848411lt_o_o ) ).
thf(fact_199_UNIV__I,axiom,
! [X_2: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X_2 @ top_to1049332548lt_o_o ) ).
thf(fact_200_UNIV__def,axiom,
( top_to1049332548lt_o_o
= ( collec2125720304_alt_o
@ ^ [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : $true ) ) ).
thf(fact_201_UNIV__def,axiom,
( top_to1830848411lt_o_o
= ( collec1079683069_alt_o
@ ^ [X: produc1832616231le_alt > $o] : $true ) ) ).
thf(fact_202_UNIV__def,axiom,
( top_to790289938lt_o_o
= ( collec1718651462_alt_o
@ ^ [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] : $true ) ) ).
thf(fact_203_UNIV__def,axiom,
( top_to679332578_alt_o
= ( collec1201320914le_alt
@ ^ [X: produc1832616231le_alt] : $true ) ) ).
thf(fact_204_UNIV__def,axiom,
( top_to527331954indi_o
= ( collec1832628290e_indi
@ ^ [X: arrow_1092341143e_indi] : $true ) ) ).
thf(fact_205_top__apply,axiom,
! [X_1: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] :
( ( top_to1049332548lt_o_o @ X_1 )
<=> top_top_o ) ).
thf(fact_206_top__apply,axiom,
! [X_1: produc1832616231le_alt > $o] :
( ( top_to1830848411lt_o_o @ X_1 )
<=> top_top_o ) ).
thf(fact_207_top__apply,axiom,
! [X_1: arrow_1092341143e_indi > produc1832616231le_alt > $o] :
( ( top_to790289938lt_o_o @ X_1 )
<=> top_top_o ) ).
thf(fact_208_top__apply,axiom,
! [X_1: produc1832616231le_alt] :
( ( top_to679332578_alt_o @ X_1 )
<=> top_top_o ) ).
thf(fact_209_top__apply,axiom,
! [X_1: arrow_1092341143e_indi] :
( ( top_to527331954indi_o @ X_1 )
<=> top_top_o ) ).
thf(fact_210_UNIV__eq__I,axiom,
! [A: $o > $o] :
( ! [X: $o] : ( member_o @ X @ A )
=> ( top_top_o_o = A ) ) ).
thf(fact_211_UNIV__eq__I,axiom,
! [A: arrow_1092341143e_indi > $o] :
( ! [X: arrow_1092341143e_indi] : ( member1714766084e_indi @ X @ A )
=> ( top_to527331954indi_o = A ) ) ).
thf(fact_212_UNIV__eq__I,axiom,
! [A: produc1832616231le_alt > $o] :
( ! [X: produc1832616231le_alt] : ( member545531028le_alt @ X @ A )
=> ( top_to679332578_alt_o = A ) ) ).
thf(fact_213_UNIV__eq__I,axiom,
! [A: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > $o] :
( ! [X: arrow_1092341143e_indi > produc1832616231le_alt > $o] : ( member1561882372_alt_o @ X @ A )
=> ( top_to790289938lt_o_o = A ) ) ).
thf(fact_214_UNIV__eq__I,axiom,
! [A: ( produc1832616231le_alt > $o ) > $o] :
( ! [X: produc1832616231le_alt > $o] : ( member1362619835_alt_o @ X @ A )
=> ( top_to1830848411lt_o_o = A ) ) ).
thf(fact_215_UNIV__eq__I,axiom,
! [A: ( ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ) > $o] :
( ! [X: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o] : ( member733327538_alt_o @ X @ A )
=> ( top_to1049332548lt_o_o = A ) ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
! [I: arrow_1092341143e_indi] :
( ( member545531028le_alt @ ( produc990411159le_alt @ a @ b ) @ ( p @ I ) )
<=> ( member545531028le_alt @ ( produc990411159le_alt @ a @ c ) @ ( arrow_1760938802_below @ ( p @ I ) @ c @ b ) ) ) ).
%------------------------------------------------------------------------------