TPTP Problem File: SCT170^2.p

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%------------------------------------------------------------------------------
% File     : SCT170^2 : TPTP v7.2.0. Released v5.3.0.
% Domain   : Social Choice Theory
% Problem  : Arrow's Impossibility Theorem line 204, 500 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : arrow_500_thf_l204 [Bla11]

% Status   : Theorem
% Rating   : 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0
% Syntax   : Number of formulae    : 1031 (   0 unit; 325 type;   0 defn)
%            Number of atoms       : 8536 ( 488 equality;4827 variable)
%            Maximal formula depth :   20 (   8 average)
%            Number of connectives : 7121 ( 267   ~;  50   |;  90   &;5700   @)
%                                         ( 120 <=>; 894  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 3576 (3576   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  330 ( 325   :;   0   =)
%            Number of variables   : 2228 (  80 sgn;2049   !;  51   ?; 128   ^)
%                                         (2228   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 19:24:06
%------------------------------------------------------------------------------
%----Should-be-implicit typings (29)
thf(ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    arrow_475358991le_alt: $tType )).

thf(ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    arrow_1429601828e_indi: $tType )).

thf(ty_ty_tc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv,type,(
    list_A518015091_alt_o: $tType )).

thf(ty_ty_tc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oind,type,(
    list_A524553945_alt_o: $tType )).

thf(ty_ty_tc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvl,type,(
    list_P1178103901_alt_o: $tType )).

thf(ty_ty_tc__List__Olist_I_Eo_J,type,(
    list_o: $tType )).

thf(ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_J,type,(
    list_A2115238852le_alt: $tType )).

thf(ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_J,type,(
    list_A1484739013e_indi: $tType )).

thf(ty_ty_tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilv,type,(
    list_l1475218533le_alt: $tType )).

thf(ty_ty_tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
    list_P736798472le_alt: $tType )).

thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,(
    list_P1295265784le_alt: $tType )).

thf(ty_ty_tc__Nat__Onat,type,(
    nat: $tType )).

thf(ty_ty_tc__prod_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    produc344885491_alt_o: $tType )).

thf(ty_ty_tc__prod_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062,type,(
    produc634020647_alt_o: $tType )).

thf(ty_ty_tc__prod_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O,type,(
    produc603869735_alt_o: $tType )).

thf(ty_ty_tc__prod_I_Eo_M_Eo_J,type,(
    product_prod_o_o: $tType )).

thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc__Arrow__,type,(
    produc1501160679le_alt: $tType )).

thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mtc__Arrow_,type,(
    produc1091721111e_indi: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mirabelle____,type,(
    produc1362754407_alt_o: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle____lcilvl,type,(
    produc2070394625_alt_o: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle,type,(
    produc1361459593_alt_o: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_I_Eo_J_Mtc__List__Olist_I_Eo_J_J,type,(
    produc1191881495list_o: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
    produc1362454231le_alt: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___001,type,(
    produc343559527e_indi: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,(
    produc938956263le_alt: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____lc,type,(
    produc347927591le_alt: $tType )).

thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__,type,(
    produc1884787239le_alt: $tType )).

thf(ty_ty_tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mt,type,(
    produc1076844957le_alt: $tType )).

thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lc,type,(
    produc1787997437le_alt: $tType )).

%----Explicit typings (296)
thf(sy_c_All2,type,(
    all2: ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_All1,type,(
    all1: ( produc1362454231le_alt > $o ) > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OIIA,type,(
    arrow_797024463le_IIA: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OLin,type,(
    arrow_823908191le_Lin: ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OProf,type,(
    arrow_734252939e_Prof: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Oabove,type,(
    arrow_789600939_above: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Obelow,type,(
    arrow_2098199487_below: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Odictator,type,(
    arrow_1212662430ctator: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Omkbot,type,(
    arrow_2054445623_mkbot: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Omktop,type,(
    arrow_55669061_mktop: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o )).

thf(sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Ounanimity,type,(
    arrow_1706409458nimity: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Ex2,type,(
    ex2: ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Ex1,type,(
    ex1: ( produc1362454231le_alt > $o ) > $o )).

thf(sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000t,type,(
    in_rel1252994498le_alt: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o )).

thf(sy_c_FunDef_Oin__rel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcil,type,(
    in_rel1156631736le_alt: ( produc1362454231le_alt > $o ) > list_A2115238852le_alt > list_A2115238852le_alt > $o )).

thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O,type,(
    pi_Arr195212324lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_002,type,(
    pi_Arr1005837828le_alt: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_003,type,(
    pi_Arr338314351e_indi: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_004,type,(
    pi_Arr2076738722le_alt: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M,type,(
    pi_Arr1304755663_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_005,type,(
    pi_Arr952516694lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_006,type,(
    pi_Arr1483346486le_alt: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_007,type,(
    pi_Arr1232280765e_indi: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_008,type,(
    pi_Arr1957214192le_alt: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz,type,(
    pi_Pro422690258lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_009,type,(
    pi_Pro1868152754le_alt: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_010,type,(
    pi_Pro468373057e_indi: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o )).

thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_011,type,(
    pi_Pro1678345076le_alt: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > produc1362454231le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvl,type,(
    pi_o_A1186128886_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
    pi_o_A1182933120_alt_o: ( $o > $o ) > ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lc,type,(
    pi_o_P553196292_alt_o: ( $o > $o ) > ( $o > ( produc1501160679le_alt > $o ) > $o ) > ( $o > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk,type,(
    pi_o_P657324555le_alt: ( $o > $o ) > ( $o > produc1501160679le_alt > $o ) > ( $o > produc1501160679le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000_062_,type,(
    pi_Arr515871190_alt_o: ( arrow_475358991le_alt > $o ) > ( arrow_475358991le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000_062__012,type,(
    pi_Arr578767520_alt_o: ( arrow_475358991le_alt > $o ) > ( arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000_062__013,type,(
    pi_Arr1520776484_alt_o: ( arrow_475358991le_alt > $o ) > ( arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_475358991le_alt > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000tc__p,type,(
    pi_Arr1786181611le_alt: ( arrow_475358991le_alt > $o ) > ( arrow_475358991le_alt > produc1501160679le_alt > $o ) > ( arrow_475358991le_alt > produc1501160679le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062,type,(
    pi_Arr1564509167_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062_014,type,(
    pi_Arr1060328391_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062_015,type,(
    pi_Arr1929480907_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000tc__,type,(
    pi_Arr329216900le_alt: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal,type,(
    pi_Pro1701359055_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o > $o ) > ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_016,type,(
    pi_Pro315446191le_alt: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > arrow_475358991le_alt > $o ) > ( produc1501160679le_alt > arrow_475358991le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_017,type,(
    pi_Pro1767455108e_indi: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > arrow_1429601828e_indi > $o ) > ( produc1501160679le_alt > arrow_1429601828e_indi ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_018,type,(
    pi_Pro666407479le_alt: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > produc1362454231le_alt > $o ) > ( produc1501160679le_alt > produc1362454231le_alt ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,(
    pi_Pro441468706_alt_o: ( produc1362454231le_alt > $o ) > ( produc1362454231le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___019,type,(
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thf(sy_c_List_Oinsert_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
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thf(sy_c_List_Olist_ONil_000_Eo,type,(
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thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    nil_Ar1286194111le_alt: list_A2115238852le_alt )).

thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    nil_Ar380161396e_indi: list_A1484739013e_indi )).

thf(sy_c_List_Olist_ONil_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcil,type,(
    nil_li1907286804le_alt: list_l1475218533le_alt )).

thf(sy_c_List_Olist_ONil_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_,type,(
    nil_Pr861385783le_alt: list_P736798472le_alt )).

thf(sy_c_List_Olist_ONil_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,(
    nil_Pr365739559le_alt: list_P1295265784le_alt )).

thf(sy_c_List_Olist_Olist__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,(
    list_c1623890103le_alt: list_A2115238852le_alt > ( arrow_475358991le_alt > list_A2115238852le_alt > list_A2115238852le_alt ) > list_A2115238852le_alt > list_A2115238852le_alt )).

thf(sy_c_List_Olistrel1_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    listre2064003096le_alt: ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o )).

thf(sy_c_List_Olistrel1_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilv,type,(
    listre620555643le_alt: ( produc1362454231le_alt > $o ) > produc938956263le_alt > $o )).

thf(sy_c_List_Olistrel_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    listre1920655591le_alt: ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o )).

thf(sy_c_List_Olistrel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvl,type,(
    listre623166444le_alt: ( produc1362454231le_alt > $o ) > produc938956263le_alt > $o )).

thf(sy_c_List_Olistrelp_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    listre1213162009le_alt: ( arrow_475358991le_alt > arrow_475358991le_alt > $o ) > list_A2115238852le_alt > list_A2115238852le_alt > $o )).

thf(sy_c_List_Olistrelp_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilv,type,(
    listre816681018le_alt: ( list_A2115238852le_alt > list_A2115238852le_alt > $o ) > list_l1475218533le_alt > list_l1475218533le_alt > $o )).

thf(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    null_A1520965063le_alt: list_A2115238852le_alt > $o )).

thf(sy_c_List_Opartition_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    partit1487577784le_alt: ( arrow_475358991le_alt > $o ) > list_A2115238852le_alt > produc1362454231le_alt )).

thf(sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    replic1511538809le_alt: nat > arrow_475358991le_alt > list_A2115238852le_alt )).

thf(sy_c_List_Orev_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin,type,(
    rev_Ar5548482_alt_o: list_A518015091_alt_o > list_A518015091_alt_o )).

thf(sy_c_List_Orev_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_0,type,(
    rev_Ar413755828_alt_o: list_A524553945_alt_o > list_A524553945_alt_o )).

thf(sy_c_List_Orev_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_,type,(
    rev_Pr1006783032_alt_o: list_P1178103901_alt_o > list_P1178103901_alt_o )).

thf(sy_c_List_Orev_000_Eo,type,(
    rev_o: list_o > list_o )).

thf(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt )).

thf(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    rev_Ar501922580e_indi: list_A1484739013e_indi > list_A1484739013e_indi )).

thf(sy_c_List_Orev_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_,type,(
    rev_Pr1216324055le_alt: list_P736798472le_alt > list_P736798472le_alt )).

thf(sy_c_List_Orev_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,(
    rev_Pr1619606471le_alt: list_P1295265784le_alt > list_P1295265784le_alt )).

thf(sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    rotate335349260le_alt: list_A2115238852le_alt > list_A2115238852le_alt )).

thf(sy_c_List_Oset_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin,type,(
    set_Ar1356274881_alt_o: list_A518015091_alt_o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_List_Oset_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_0,type,(
    set_Ar571341173_alt_o: list_A524553945_alt_o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_List_Oset_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_,type,(
    set_Pr592386425_alt_o: list_P1178103901_alt_o > ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_List_Oset_000_Eo,type,(
    set_o: list_o > $o > $o )).

thf(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    set_Ar577454304le_alt: list_A2115238852le_alt > arrow_475358991le_alt > $o )).

thf(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    set_Ar778541203e_indi: list_A1484739013e_indi > arrow_1429601828e_indi > $o )).

thf(sy_c_List_Oset_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv,type,(
    set_li1631982259le_alt: list_l1475218533le_alt > list_A2115238852le_alt > $o )).

thf(sy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_,type,(
    set_Pr1525059414le_alt: list_P736798472le_alt > produc1501160679le_alt > $o )).

thf(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,(
    set_Pr412222150le_alt: list_P1295265784le_alt > produc1362454231le_alt > $o )).

thf(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    splice1520898450le_alt: list_A2115238852le_alt > list_A2115238852le_alt > list_A2115238852le_alt )).

thf(sy_c_List_OtakeWhile_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkz,type,(
    takeWh877796585_alt_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > list_A518015091_alt_o > list_A518015091_alt_o )).

thf(sy_c_List_OtakeWhile_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin,type,(
    takeWh1825606477_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > list_A524553945_alt_o > list_A524553945_alt_o )).

thf(sy_c_List_OtakeWhile_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilv,type,(
    takeWh1715715921_alt_o: ( ( produc1501160679le_alt > $o ) > $o ) > list_P1178103901_alt_o > list_P1178103901_alt_o )).

thf(sy_c_List_OtakeWhile_000_Eo,type,(
    takeWhile_o: ( $o > $o ) > list_o > list_o )).

thf(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    takeWh1696291512le_alt: ( arrow_475358991le_alt > $o ) > list_A2115238852le_alt > list_A2115238852le_alt )).

thf(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    takeWh831911099e_indi: ( arrow_1429601828e_indi > $o ) > list_A1484739013e_indi > list_A1484739013e_indi )).

thf(sy_c_List_OtakeWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_,type,(
    takeWh302148478le_alt: ( produc1501160679le_alt > $o ) > list_P736798472le_alt > list_P736798472le_alt )).

thf(sy_c_List_OtakeWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,(
    takeWh1571807982le_alt: ( produc1362454231le_alt > $o ) > list_P1295265784le_alt > list_P1295265784le_alt )).

thf(sy_c_List_Otl_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oind,type,(
    tl_Arr2017860491_alt_o: list_A518015091_alt_o > list_A518015091_alt_o )).

thf(sy_c_List_Otl_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_06,type,(
    tl_Arr1704054571_alt_o: list_A524553945_alt_o > list_A524553945_alt_o )).

thf(sy_c_List_Otl_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
    tl_Pro1735316527_alt_o: list_P1178103901_alt_o > list_P1178103901_alt_o )).

thf(sy_c_List_Otl_000_Eo,type,(
    tl_o: list_o > list_o )).

thf(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    tl_Arr465451158le_alt: list_A2115238852le_alt > list_A2115238852le_alt )).

thf(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    tl_Arr25726557e_indi: list_A1484739013e_indi > list_A1484739013e_indi )).

thf(sy_c_List_Otl_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M,type,(
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thf(sy_c_List_Otl_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____l,type,(
    tl_Pro1448262032le_alt: list_P1295265784le_alt > list_P1295265784le_alt )).

thf(sy_c_Nat_OSuc,type,(
    suc: nat > nat )).

thf(sy_c_Nat_Onat_Onat__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,(
    nat_ca2147365008le_alt: list_A2115238852le_alt > ( nat > list_A2115238852le_alt ) > nat > list_A2115238852le_alt )).

thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,(
    size_s1858781230le_alt: list_A2115238852le_alt > nat )).

thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Or,type,(
    size_s1911906171le_alt: list_l1475218533le_alt > nat )).

thf(sy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabel,type,(
    order_1995917111le_alt: ( arrow_475358991le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,(
    ord_less_nat: nat > nat > $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,(
    ord_less_eq_nat: nat > nat > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_I_062_Itc__Arrow____Order____Mirab,type,(
    top_to1969627639lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__,type,(
    top_to2122763103lt_o_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__prod_Itc__Arrow____Order____M,type,(
    top_to1842727771lt_o_o: ( produc1501160679le_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____lcil,type,(
    top_to728987956_alt_o: arrow_475358991le_alt > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____lcil_022,type,(
    top_to988227749indi_o: arrow_1429601828e_indi > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel,type,(
    top_to1841428258_alt_o: produc1501160679le_alt > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow___,type,(
    top_to1039387826_alt_o: produc1362454231le_alt > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_Eo,type,(
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thf(sy_c_Product__Type_OPair_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilv,type,(
    produc434968681_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc344885491_alt_o )).

thf(sy_c_Product__Type_OPair_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_,type,(
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thf(sy_c_Product__Type_OPair_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____l,type,(
    produc548346135_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc603869735_alt_o )).

thf(sy_c_Product__Type_OPair_000_Eo_000_Eo,type,(
    product_Pair_o_o: $o > $o > product_prod_o_o )).

thf(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_,type,(
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thf(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_062_I_062_Itc__Arrow____Order____M,type,(
    produc385333463_alt_o: list_A518015091_alt_o > list_A518015091_alt_o > produc1362754407_alt_o )).

thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_062_Itc__Arrow____Order____Mirabel,type,(
    produc1301429239_alt_o: list_A524553945_alt_o > list_A524553945_alt_o > produc2070394625_alt_o )).

thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order_,type,(
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_Eo_J_000tc__List__Olist_I_Eo_J,type,(
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,(
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_____023,type,(
    produc1195920727e_indi: list_A1484739013e_indi > list_A1484739013e_indi > produc343559527e_indi )).

thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order,type,(
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mir,type,(
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arro,type,(
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlk,type,(
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mir,type,(
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thf(sy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
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thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,(
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thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____lcilv,type,(
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thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M,type,(
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thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_024,type,(
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thf(sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
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thf(sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_,type,(
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thf(sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk,type,(
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thf(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
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thf(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
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thf(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa,type,(
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thf(sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O,type,(
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thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__,type,(
    member1823529808lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___025,type,(
    member474974512le_alt: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___026,type,(
    member1452482393e_indi: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___027,type,(
    member845447052le_alt: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_,type,(
    member616898751_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__028,type,(
    member939334982lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__029,type,(
    member1596146470le_alt: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__030,type,(
    member44294883e_indi: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__031,type,(
    member1849320470le_alt: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk,type,(
    member1961363906lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( ( produc1501160679le_alt > $o ) > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_032,type,(
    member1524522914le_alt: ( ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > ( ( ( produc1501160679le_alt > $o ) > arrow_475358991le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_033,type,(
    member304866663e_indi: ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o )).

thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_034,type,(
    member1099563162le_alt: ( ( produc1501160679le_alt > $o ) > produc1362454231le_alt ) > ( ( ( produc1501160679le_alt > $o ) > produc1362454231le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlk,type,(
    member1957863580_alt_o: ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O,type,(
    member1394214384_alt_o: ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lci,type,(
    member1862122484_alt_o: ( $o > produc1501160679le_alt > $o ) > ( ( $o > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz,type,(
    member492167345le_alt: ( $o > produc1501160679le_alt ) > ( ( $o > produc1501160679le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M_062_I,type,(
    member89384572_alt_o: ( arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M_062_I_035,type,(
    member1876989968_alt_o: ( arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M_062_I_036,type,(
    member1908358676_alt_o: ( arrow_475358991le_alt > produc1501160679le_alt > $o ) > ( ( arrow_475358991le_alt > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc__pr,type,(
    member712472209le_alt: ( arrow_475358991le_alt > produc1501160679le_alt ) > ( ( arrow_475358991le_alt > produc1501160679le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062_,type,(
    member811956313_alt_o: ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062__037,type,(
    member1234151027_alt_o: ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062__038,type,(
    member526088951_alt_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mtc__p,type,(
    member351225838le_alt: ( arrow_1429601828e_indi > produc1501160679le_alt ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa,type,(
    member377231867_alt_o: ( produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_039,type,(
    member1416774619le_alt: ( produc1501160679le_alt > arrow_475358991le_alt ) > ( ( produc1501160679le_alt > arrow_475358991le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_040,type,(
    member1640632174e_indi: ( produc1501160679le_alt > arrow_1429601828e_indi ) > ( ( produc1501160679le_alt > arrow_1429601828e_indi ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_041,type,(
    member220989473le_alt: ( produc1501160679le_alt > produc1362454231le_alt ) > ( ( produc1501160679le_alt > produc1362454231le_alt ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,(
    member654997644_alt_o: ( produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__042,type,(
    member392452608_alt_o: ( produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__043,type,(
    member2082473988_alt_o: ( produc1362454231le_alt > produc1501160679le_alt > $o ) > ( ( produc1362454231le_alt > produc1501160679le_alt > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__044,type,(
    member428957857le_alt: ( produc1362454231le_alt > produc1501160679le_alt ) > ( ( produc1362454231le_alt > produc1501160679le_alt ) > $o ) > $o )).

thf(sy_c_member_000_Eo,type,(
    member_o: $o > ( $o > $o ) > $o )).

thf(sy_c_member_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,(
    member84363362le_alt: arrow_475358991le_alt > ( arrow_475358991le_alt > $o ) > $o )).

thf(sy_c_member_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi,type,(
    member2052026769e_indi: arrow_1429601828e_indi > ( arrow_1429601828e_indi > $o ) > $o )).

thf(sy_c_member_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O,type,(
    member998134961le_alt: list_A2115238852le_alt > ( list_A2115238852le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkk,type,(
    member1909339872_alt_o: produc344885491_alt_o > ( produc344885491_alt_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oi,type,(
    member423327892_alt_o: produc634020647_alt_o > ( produc634020647_alt_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcil,type,(
    member1998617236_alt_o: produc603869735_alt_o > ( produc603869735_alt_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_I_Eo_M_Eo_J,type,(
    member1392690260od_o_o: product_prod_o_o > ( product_prod_o_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc,type,(
    member214075476le_alt: produc1501160679le_alt > ( produc1501160679le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mt,type,(
    member1239815300e_indi: produc1091721111e_indi > ( produc1091721111e_indi > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mira,type,(
    member119836116_alt_o: produc1362754407_alt_o > ( produc1362754407_alt_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle_,type,(
    member1890873582_alt_o: produc2070394625_alt_o > ( produc2070394625_alt_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____,type,(
    member79660662_alt_o: produc1361459593_alt_o > ( produc1361459593_alt_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_I_Eo_J_Mtc__List__Olist_I_Eo_J_J,type,(
    member806300420list_o: produc1191881495list_o > ( produc1191881495list_o > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lci,type,(
    member28618436le_alt: produc1362454231le_alt > ( produc1362454231le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lci_045,type,(
    member1618636500e_indi: produc343559527e_indi > ( produc343559527e_indi > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order___,type,(
    member1732936276le_alt: produc938956263le_alt > ( produc938956263le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabe,type,(
    member475755924le_alt: produc347927591le_alt > ( produc347927591le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow__,type,(
    member608607380le_alt: produc1884787239le_alt > ( produc1884787239le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv,type,(
    member1664185994le_alt: produc1076844957le_alt > ( produc1076844957le_alt > $o ) > $o )).

thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,(
    member902484714le_alt: produc1787997437le_alt > ( produc1787997437le_alt > $o ) > $o )).

thf(sy_v_F,type,(
    f: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o )).

thf(sy_v_P_H____,type,(
    p_1: arrow_1429601828e_indi > produc1501160679le_alt > $o )).

thf(sy_v_P____,type,(
    p: arrow_1429601828e_indi > produc1501160679le_alt > $o )).

thf(sy_v_a____,type,(
    a: arrow_475358991le_alt )).

thf(sy_v_b____,type,(
    b: arrow_475358991le_alt )).

thf(sy_v_c____,type,(
    c: arrow_475358991le_alt )).

%----Relevant facts (700)
thf(fact_0__096P_A_058_AProf_096,axiom,
    ( member526088951_alt_o @ p @ arrow_734252939e_Prof )).

thf(fact_1_assms_I3_J,axiom,
    ( arrow_797024463le_IIA @ f )).

thf(fact_2_u,axiom,
    ( arrow_1706409458nimity @ f )).

thf(fact_3__096a_A_126_061_Ab_096,axiom,(
    a != b )).

thf(fact_4_dist,axiom,
    ( distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ) )).

thf(fact_5_iff,axiom,(
    ! [I: arrow_1429601828e_indi] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) )
    <=> ( member214075476le_alt @ ( produc1347929815le_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_2: arrow_475358991le_alt] :
        ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ C_2 @ nil_Ar1286194111le_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,
    ( member526088951_alt_o
    @ ^ [P_30: arrow_1429601828e_indi] :
        ( arrow_2098199487_below @ ( arrow_2098199487_below @ ( p @ P_30 ) @ c @ b ) @ b @ a )
    @ arrow_734252939e_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,
    ( member526088951_alt_o
    @ ^ [P_30: arrow_1429601828e_indi] :
        ( arrow_2098199487_below @ ( arrow_2098199487_below @ ( arrow_2098199487_below @ ( p @ P_30 ) @ c @ b ) @ b @ a ) @ a @ c )
    @ arrow_734252939e_Prof )).

thf(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
    ( member526088951_alt_o
    @ ^ [P_30: arrow_1429601828e_indi] :
        ( arrow_2098199487_below @ ( p @ P_30 ) @ c @ b )
    @ arrow_734252939e_Prof )).

thf(fact_10_in__mkbot,axiom,(
    ! [X: arrow_475358991le_alt,Y: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o,Z_1: arrow_475358991le_alt] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ ( arrow_2054445623_mkbot @ L_1 @ Z_1 ) )
    <=> ( ( Y != Z_1 )
        & ( ( X = Z_1 )
         => ( X != Y ) )
        & ( ( X != Z_1 )
         => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) ) ) )).

thf(fact_11_in__mktop,axiom,(
    ! [X: arrow_475358991le_alt,Y: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o,Z_1: arrow_475358991le_alt] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ ( arrow_55669061_mktop @ L_1 @ Z_1 ) )
    <=> ( ( X != Z_1 )
        & ( ( Y = Z_1 )
         => ( X != Y ) )
        & ( ( Y != Z_1 )
         => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) ) ) )).

thf(fact_12_in__below,axiom,(
    ! [X: arrow_475358991le_alt,Y: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o,A_24: arrow_475358991le_alt,B_17: arrow_475358991le_alt] :
      ( ( A_24 != B_17 )
     => ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
       => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ ( arrow_2098199487_below @ L_1 @ A_24 @ B_17 ) )
        <=> ( ( X != Y )
            & ( ( Y = A_24 )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ B_17 ) @ L_1 ) )
            & ( ( Y != A_24 )
             => ( ( ( X = A_24 )
                 => ( ( Y = B_17 )
                    | ( member214075476le_alt @ ( produc1347929815le_alt @ B_17 @ Y ) @ L_1 ) ) )
                & ( ( X != A_24 )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) ) ) ) ) ) ) )).

thf(fact_13_split__paired__All,axiom,(
    ! [P_33: produc1362454231le_alt > $o] :
      ( ( all1 @ P_33 )
    <=> ! [A: list_A2115238852le_alt,B: list_A2115238852le_alt] :
          ( P_33 @ ( produc776457805le_alt @ A @ B ) ) ) )).

thf(fact_14_split__paired__All,axiom,(
    ! [P_33: produc1501160679le_alt > $o] :
      ( ( all2 @ P_33 )
    <=> ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
          ( P_33 @ ( produc1347929815le_alt @ A @ B ) ) ) )).

thf(fact_15_Pair__eq,axiom,(
    ! [A_30: list_A2115238852le_alt,B_23: list_A2115238852le_alt,A_29: list_A2115238852le_alt,B_22: list_A2115238852le_alt] :
      ( ( ( produc776457805le_alt @ A_30 @ B_23 )
        = ( produc776457805le_alt @ A_29 @ B_22 ) )
    <=> ( ( A_30 = A_29 )
        & ( B_23 = B_22 ) ) ) )).

thf(fact_16_Pair__eq,axiom,(
    ! [A_30: arrow_475358991le_alt,B_23: arrow_475358991le_alt,A_29: arrow_475358991le_alt,B_22: arrow_475358991le_alt] :
      ( ( ( produc1347929815le_alt @ A_30 @ B_23 )
        = ( produc1347929815le_alt @ A_29 @ B_22 ) )
    <=> ( ( A_30 = A_29 )
        & ( B_23 = B_22 ) ) ) )).

thf(fact_17_Pair__inject,axiom,(
    ! [A_28: list_A2115238852le_alt,B_21: list_A2115238852le_alt,A_27: list_A2115238852le_alt,B_20: list_A2115238852le_alt] :
      ( ( ( produc776457805le_alt @ A_28 @ B_21 )
        = ( produc776457805le_alt @ A_27 @ B_20 ) )
     => ~ ( ( A_28 = A_27 )
         => ( B_21 != B_20 ) ) ) )).

thf(fact_18_Pair__inject,axiom,(
    ! [A_28: arrow_475358991le_alt,B_21: arrow_475358991le_alt,A_27: arrow_475358991le_alt,B_20: arrow_475358991le_alt] :
      ( ( ( produc1347929815le_alt @ A_28 @ B_21 )
        = ( produc1347929815le_alt @ A_27 @ B_20 ) )
     => ~ ( ( A_28 = A_27 )
         => ( B_21 != B_20 ) ) ) )).

thf(fact_19_in__rel__def,axiom,(
    ! [R_40: produc1362454231le_alt > $o,X_75: list_A2115238852le_alt,Y_27: list_A2115238852le_alt] :
      ( ( in_rel1156631736le_alt @ R_40 @ X_75 @ Y_27 )
    <=> ( member28618436le_alt @ ( produc776457805le_alt @ X_75 @ Y_27 ) @ R_40 ) ) )).

thf(fact_20_in__rel__def,axiom,(
    ! [R_40: produc1501160679le_alt > $o,X_75: arrow_475358991le_alt,Y_27: arrow_475358991le_alt] :
      ( ( in_rel1252994498le_alt @ R_40 @ X_75 @ Y_27 )
    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ X_75 @ Y_27 ) @ R_40 ) ) )).

thf(fact_21_below__Lin,axiom,(
    ! [L_1: produc1501160679le_alt > $o,X: arrow_475358991le_alt,Y: arrow_475358991le_alt] :
      ( ( X != Y )
     => ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
       => ( member377231867_alt_o @ ( arrow_2098199487_below @ L_1 @ X @ Y ) @ arrow_823908191le_Lin ) ) ) )).

thf(fact_22__096P_H_A_058_AProf_096,axiom,
    ( member526088951_alt_o @ p_1 @ arrow_734252939e_Prof )).

thf(fact_23__C1_C,axiom,(
    ! [P_32: arrow_1429601828e_indi > produc1501160679le_alt > $o,P_31: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_26: arrow_475358991le_alt,B_19: arrow_475358991le_alt,A_25: arrow_475358991le_alt,B_18: arrow_475358991le_alt] :
      ( ( A_25 != B_18 )
     => ( ( A_26 != B_19 )
       => ( ( A_25 != B_19 )
         => ( ( B_18 != A_26 )
           => ( ( member526088951_alt_o @ P_31 @ arrow_734252939e_Prof )
             => ( ( member526088951_alt_o @ P_32 @ arrow_734252939e_Prof )
               => ( ! [I: arrow_1429601828e_indi] :
                      ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_25 @ B_18 ) @ ( P_31 @ I ) )
                    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ A_26 @ B_19 ) @ ( P_32 @ I ) ) )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_25 @ B_18 ) @ ( f @ P_31 ) )
                   => ( member214075476le_alt @ ( produc1347929815le_alt @ A_26 @ B_19 ) @ ( f @ P_32 ) ) ) ) ) ) ) ) ) ) )).

thf(fact_24__C2_C,axiom,(
    ! [P_32: arrow_1429601828e_indi > produc1501160679le_alt > $o,P_31: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_26: arrow_475358991le_alt,B_19: arrow_475358991le_alt,A_25: arrow_475358991le_alt,B_18: arrow_475358991le_alt] :
      ( ( A_25 != B_18 )
     => ( ( A_26 != B_19 )
       => ( ( A_25 != B_19 )
         => ( ( B_18 != A_26 )
           => ( ( member526088951_alt_o @ P_31 @ arrow_734252939e_Prof )
             => ( ( member526088951_alt_o @ P_32 @ arrow_734252939e_Prof )
               => ( ! [I: arrow_1429601828e_indi] :
                      ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_25 @ B_18 ) @ ( P_31 @ I ) )
                    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ A_26 @ B_19 ) @ ( P_32 @ I ) ) )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_25 @ B_18 ) @ ( f @ P_31 ) )
                  <=> ( member214075476le_alt @ ( produc1347929815le_alt @ A_26 @ B_19 ) @ ( f @ P_32 ) ) ) ) ) ) ) ) ) ) )).

thf(fact_25_assms_I1_J,axiom,
    ( member616898751_alt_o @ f
    @ ( pi_Arr1304755663_alt_o @ arrow_734252939e_Prof
      @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : arrow_823908191le_Lin ) )).

thf(fact_26_const__Lin__Prof,axiom,(
    ! [L_1: produc1501160679le_alt > $o] :
      ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
     => ( member526088951_alt_o
        @ ^ [P_30: arrow_1429601828e_indi] : L_1
        @ arrow_734252939e_Prof ) ) )).

thf(fact_27_mkbot__Lin,axiom,(
    ! [X: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o] :
      ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
     => ( member377231867_alt_o @ ( arrow_2054445623_mkbot @ L_1 @ X ) @ arrow_823908191le_Lin ) ) )).

thf(fact_28_mktop__Lin,axiom,(
    ! [X: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o] :
      ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
     => ( member377231867_alt_o @ ( arrow_55669061_mktop @ L_1 @ X ) @ arrow_823908191le_Lin ) ) )).

thf(fact_29_Lin__irrefl,axiom,(
    ! [A_24: arrow_475358991le_alt,B_17: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o] :
      ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
     => ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_24 @ B_17 ) @ L_1 )
       => ~ ( member214075476le_alt @ ( produc1347929815le_alt @ B_17 @ A_24 ) @ L_1 ) ) ) )).

thf(fact_30_notin__Lin__iff,axiom,(
    ! [X: arrow_475358991le_alt,Y: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o] :
      ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
     => ( ( X != Y )
       => ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ L_1 )
        <=> ( member214075476le_alt @ ( produc1347929815le_alt @ Y @ X ) @ L_1 ) ) ) ) )).

thf(fact_31_third__alt,axiom,(
    ! [A_24: arrow_475358991le_alt,B_17: arrow_475358991le_alt] :
      ( ( A_24 != B_17 )
     => ? [C_2: arrow_475358991le_alt] :
          ( distin236324274le_alt @ ( cons_A228743023le_alt @ A_24 @ ( cons_A228743023le_alt @ B_17 @ ( cons_A228743023le_alt @ C_2 @ nil_Ar1286194111le_alt ) ) ) ) ) )).

thf(fact_32_IIA__def,axiom,(
    ! [F_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( ( arrow_797024463le_IIA @ F_14 )
    <=> ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ arrow_734252939e_Prof )
         => ! [Xa: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
              ( ( member526088951_alt_o @ Xa @ arrow_734252939e_Prof )
             => ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
                  ( ! [I: arrow_1429601828e_indi] :
                      ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( X_2 @ I ) )
                    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( Xa @ I ) ) )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( F_14 @ X_2 ) )
                  <=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( F_14 @ Xa ) ) ) ) ) ) ) )).

thf(fact_33_unanimity__def,axiom,(
    ! [F_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( ( arrow_1706409458nimity @ F_14 )
    <=> ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ arrow_734252939e_Prof )
         => ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
              ( ! [I: arrow_1429601828e_indi] :
                  ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( X_2 @ I ) )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( F_14 @ X_2 ) ) ) ) ) )).

thf(fact_34_complete__Lin,axiom,(
    ! [A_24: arrow_475358991le_alt,B_17: arrow_475358991le_alt] :
      ( ( A_24 != B_17 )
     => ? [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ arrow_823908191le_Lin )
          & ( member214075476le_alt @ ( produc1347929815le_alt @ A_24 @ B_17 ) @ X_2 ) ) ) )).

thf(fact_35_in__above,axiom,(
    ! [X: arrow_475358991le_alt,Y: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o,A_24: arrow_475358991le_alt,B_17: arrow_475358991le_alt] :
      ( ( A_24 != B_17 )
     => ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
       => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ ( arrow_789600939_above @ L_1 @ A_24 @ B_17 ) )
        <=> ( ( X != Y )
            & ( ( X = B_17 )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ A_24 @ Y ) @ L_1 ) )
            & ( ( X != B_17 )
             => ( ( ( Y = B_17 )
                 => ( ( X = A_24 )
                    | ( member214075476le_alt @ ( produc1347929815le_alt @ X @ A_24 ) @ L_1 ) ) )
                & ( ( Y != B_17 )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) ) ) ) ) ) ) )).

thf(fact_36_distinct_Osimps_I1_J,axiom,
    ( distin236324274le_alt @ nil_Ar1286194111le_alt )).

thf(fact_37_list_Osimps_I2_J,axiom,(
    ! [A_23: arrow_475358991le_alt,List_4: list_A2115238852le_alt] :
      ( nil_Ar1286194111le_alt
     != ( cons_A228743023le_alt @ A_23 @ List_4 ) ) )).

thf(fact_38_list_Osimps_I3_J,axiom,(
    ! [A_22: arrow_475358991le_alt,List_3: list_A2115238852le_alt] :
      ( ( cons_A228743023le_alt @ A_22 @ List_3 )
     != nil_Ar1286194111le_alt ) )).

thf(fact_39_alt3,axiom,(
    ? [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C_2: arrow_475358991le_alt] :
      ( distin236324274le_alt @ ( cons_A228743023le_alt @ A @ ( cons_A228743023le_alt @ B @ ( cons_A228743023le_alt @ C_2 @ nil_Ar1286194111le_alt ) ) ) ) )).

thf(fact_40_linear__alt,axiom,(
    ? [L_2: produc1501160679le_alt > $o] :
      ( member377231867_alt_o @ L_2 @ arrow_823908191le_Lin ) )).

thf(fact_41_list_Oinject,axiom,(
    ! [A_21: arrow_475358991le_alt,List_2: list_A2115238852le_alt,A_20: arrow_475358991le_alt,List_1: list_A2115238852le_alt] :
      ( ( ( cons_A228743023le_alt @ A_21 @ List_2 )
        = ( cons_A228743023le_alt @ A_20 @ List_1 ) )
    <=> ( ( A_21 = A_20 )
        & ( List_2 = List_1 ) ) ) )).

thf(fact_42_not__Cons__self2,axiom,(
    ! [X_74: arrow_475358991le_alt,Xs_127: list_A2115238852le_alt] :
      ( ( cons_A228743023le_alt @ X_74 @ Xs_127 )
     != Xs_127 ) )).

thf(fact_43_not__Cons__self,axiom,(
    ! [Xs_126: list_A2115238852le_alt,X_73: arrow_475358991le_alt] :
      ( Xs_126
     != ( cons_A228743023le_alt @ X_73 @ Xs_126 ) ) )).

thf(fact_44_above__Lin,axiom,(
    ! [L_1: produc1501160679le_alt > $o,X: arrow_475358991le_alt,Y: arrow_475358991le_alt] :
      ( ( X != Y )
     => ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
       => ( member377231867_alt_o @ ( arrow_789600939_above @ L_1 @ X @ Y ) @ arrow_823908191le_Lin ) ) ) )).

thf(fact_45_dictatorI,axiom,(
    ! [I_1: arrow_1429601828e_indi,F_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( ( member616898751_alt_o @ F_14
        @ ( pi_Arr1304755663_alt_o @ arrow_734252939e_Prof
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : arrow_823908191le_Lin ) )
     => ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
            ( ( member526088951_alt_o @ X_2 @ arrow_734252939e_Prof )
           => ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
                ( ( A != B )
               => ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( X_2 @ I_1 ) )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( F_14 @ X_2 ) ) ) ) )
       => ( arrow_1212662430ctator @ F_14 @ I_1 ) ) ) )).

thf(fact_46_PiE,axiom,(
    ! [X_72: produc1501160679le_alt,F_15: produc1501160679le_alt > $o,A_19: produc1501160679le_alt > $o,B_16: produc1501160679le_alt > $o > $o] :
      ( ( member377231867_alt_o @ F_15 @ ( pi_Pro1701359055_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member214075476le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_47_PiE,axiom,(
    ! [X_72: arrow_475358991le_alt,F_15: arrow_475358991le_alt > produc1501160679le_alt,A_19: arrow_475358991le_alt > $o,B_16: arrow_475358991le_alt > produc1501160679le_alt > $o] :
      ( ( member712472209le_alt @ F_15 @ ( pi_Arr1786181611le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member214075476le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member84363362le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_48_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi,F_15: arrow_1429601828e_indi > produc1501160679le_alt,A_19: arrow_1429601828e_indi > $o,B_16: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( ( member351225838le_alt @ F_15 @ ( pi_Arr329216900le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member214075476le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member2052026769e_indi @ X_72 @ A_19 ) ) ) )).

thf(fact_49_PiE,axiom,(
    ! [X_72: produc1362454231le_alt,F_15: produc1362454231le_alt > produc1501160679le_alt,A_19: produc1362454231le_alt > $o,B_16: produc1362454231le_alt > produc1501160679le_alt > $o] :
      ( ( member428957857le_alt @ F_15 @ ( pi_Pro1708969783le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member214075476le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member28618436le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_50_PiE,axiom,(
    ! [X_72: $o,F_15: $o > produc1501160679le_alt,A_19: $o > $o,B_16: $o > produc1501160679le_alt > $o] :
      ( ( member492167345le_alt @ F_15 @ ( pi_o_P657324555le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member214075476le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member_o @ X_72 @ A_19 ) ) ) )).

thf(fact_51_PiE,axiom,(
    ! [X_72: arrow_475358991le_alt,F_15: arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_19: arrow_475358991le_alt > $o,B_16: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1876989968_alt_o @ F_15 @ ( pi_Arr578767520_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member526088951_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member84363362le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_52_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi,F_15: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_19: arrow_1429601828e_indi > $o,B_16: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1234151027_alt_o @ F_15 @ ( pi_Arr1060328391_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member526088951_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member2052026769e_indi @ X_72 @ A_19 ) ) ) )).

thf(fact_53_PiE,axiom,(
    ! [X_72: produc1362454231le_alt,F_15: produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_19: produc1362454231le_alt > $o,B_16: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member392452608_alt_o @ F_15 @ ( pi_Pro121963604_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member526088951_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member28618436le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_54_PiE,axiom,(
    ! [X_72: $o,F_15: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_19: $o > $o,B_16: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1394214384_alt_o @ F_15 @ ( pi_o_A1182933120_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member526088951_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member_o @ X_72 @ A_19 ) ) ) )).

thf(fact_55_PiE,axiom,(
    ! [X_72: arrow_475358991le_alt,F_15: arrow_475358991le_alt > produc1501160679le_alt > $o,A_19: arrow_475358991le_alt > $o,B_16: arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member1908358676_alt_o @ F_15 @ ( pi_Arr1520776484_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member84363362le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_56_PiE,axiom,(
    ! [X_72: produc1362454231le_alt,F_15: produc1362454231le_alt > produc1501160679le_alt > $o,A_19: produc1362454231le_alt > $o,B_16: produc1362454231le_alt > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member2082473988_alt_o @ F_15 @ ( pi_Pro589599960_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member28618436le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_57_PiE,axiom,(
    ! [X_72: $o,F_15: $o > produc1501160679le_alt > $o,A_19: $o > $o,B_16: $o > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member1862122484_alt_o @ F_15 @ ( pi_o_P553196292_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member_o @ X_72 @ A_19 ) ) ) )).

thf(fact_58_PiE,axiom,(
    ! [X_72: arrow_475358991le_alt,F_15: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_19: arrow_475358991le_alt > $o,B_16: arrow_475358991le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member89384572_alt_o @ F_15 @ ( pi_Arr515871190_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member616898751_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member84363362le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_59_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi,F_15: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_19: arrow_1429601828e_indi > $o,B_16: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member811956313_alt_o @ F_15 @ ( pi_Arr1564509167_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member616898751_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member2052026769e_indi @ X_72 @ A_19 ) ) ) )).

thf(fact_60_PiE,axiom,(
    ! [X_72: produc1362454231le_alt,F_15: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_19: produc1362454231le_alt > $o,B_16: produc1362454231le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member654997644_alt_o @ F_15 @ ( pi_Pro441468706_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member616898751_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member28618436le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_61_PiE,axiom,(
    ! [X_72: $o,F_15: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_19: $o > $o,B_16: $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member1957863580_alt_o @ F_15 @ ( pi_o_A1186128886_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member616898751_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member_o @ X_72 @ A_19 ) ) ) )).

thf(fact_62_PiE,axiom,(
    ! [X_72: produc1501160679le_alt,F_15: produc1501160679le_alt > arrow_475358991le_alt,A_19: produc1501160679le_alt > $o,B_16: produc1501160679le_alt > arrow_475358991le_alt > $o] :
      ( ( member1416774619le_alt @ F_15 @ ( pi_Pro315446191le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member84363362le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member214075476le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_63_PiE,axiom,(
    ! [X_72: produc1501160679le_alt,F_15: produc1501160679le_alt > arrow_1429601828e_indi,A_19: produc1501160679le_alt > $o,B_16: produc1501160679le_alt > arrow_1429601828e_indi > $o] :
      ( ( member1640632174e_indi @ F_15 @ ( pi_Pro1767455108e_indi @ A_19 @ B_16 ) )
     => ( ~ ( member2052026769e_indi @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member214075476le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_64_PiE,axiom,(
    ! [X_72: produc1501160679le_alt,F_15: produc1501160679le_alt > produc1362454231le_alt,A_19: produc1501160679le_alt > $o,B_16: produc1501160679le_alt > produc1362454231le_alt > $o] :
      ( ( member220989473le_alt @ F_15 @ ( pi_Pro666407479le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member28618436le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member214075476le_alt @ X_72 @ A_19 ) ) ) )).

thf(fact_65_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_19: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o] :
      ( ( member1596146470le_alt @ F_15 @ ( pi_Arr1483346486le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member84363362le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member526088951_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_66_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_19: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
      ( ( member44294883e_indi @ F_15 @ ( pi_Arr1232280765e_indi @ A_19 @ B_16 ) )
     => ( ~ ( member2052026769e_indi @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member526088951_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_67_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt,A_19: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o] :
      ( ( member1849320470le_alt @ F_15 @ ( pi_Arr1957214192le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member28618436le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member526088951_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_68_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_19: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o] :
      ( ( member939334982lt_o_o @ F_15 @ ( pi_Arr952516694lt_o_o @ A_19 @ B_16 ) )
     => ( ~ ( member_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member526088951_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_69_PiE,axiom,(
    ! [X_72: produc1501160679le_alt > $o,F_15: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_19: ( produc1501160679le_alt > $o ) > $o,B_16: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o] :
      ( ( member1524522914le_alt @ F_15 @ ( pi_Pro1868152754le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member84363362le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member377231867_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_70_PiE,axiom,(
    ! [X_72: produc1501160679le_alt > $o,F_15: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_19: ( produc1501160679le_alt > $o ) > $o,B_16: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
      ( ( member304866663e_indi @ F_15 @ ( pi_Pro468373057e_indi @ A_19 @ B_16 ) )
     => ( ~ ( member2052026769e_indi @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member377231867_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_71_PiE,axiom,(
    ! [X_72: produc1501160679le_alt > $o,F_15: ( produc1501160679le_alt > $o ) > produc1362454231le_alt,A_19: ( produc1501160679le_alt > $o ) > $o,B_16: ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o] :
      ( ( member1099563162le_alt @ F_15 @ ( pi_Pro1678345076le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member28618436le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member377231867_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_72_PiE,axiom,(
    ! [X_72: produc1501160679le_alt > $o,F_15: ( produc1501160679le_alt > $o ) > $o,A_19: ( produc1501160679le_alt > $o ) > $o,B_16: ( produc1501160679le_alt > $o ) > $o > $o] :
      ( ( member1961363906lt_o_o @ F_15 @ ( pi_Pro422690258lt_o_o @ A_19 @ B_16 ) )
     => ( ~ ( member_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member377231867_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_73_PiE,axiom,(
    ! [X_72: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_19: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o] :
      ( ( member474974512le_alt @ F_15 @ ( pi_Arr1005837828le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member84363362le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member616898751_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_74_PiE,axiom,(
    ! [X_72: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_19: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
      ( ( member1452482393e_indi @ F_15 @ ( pi_Arr338314351e_indi @ A_19 @ B_16 ) )
     => ( ~ ( member2052026769e_indi @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member616898751_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_75_PiE,axiom,(
    ! [X_72: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt,A_19: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o] :
      ( ( member845447052le_alt @ F_15 @ ( pi_Arr2076738722le_alt @ A_19 @ B_16 ) )
     => ( ~ ( member28618436le_alt @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member616898751_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_76_PiE,axiom,(
    ! [X_72: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_19: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o] :
      ( ( member1823529808lt_o_o @ F_15 @ ( pi_Arr195212324lt_o_o @ A_19 @ B_16 ) )
     => ( ~ ( member_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member616898751_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_77_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_19: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member616898751_alt_o @ F_15 @ ( pi_Arr1304755663_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member526088951_alt_o @ X_72 @ A_19 ) ) ) )).

thf(fact_78_PiE,axiom,(
    ! [X_72: arrow_1429601828e_indi,F_15: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_19: arrow_1429601828e_indi > $o,B_16: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ F_15 @ ( pi_Arr1929480907_alt_o @ A_19 @ B_16 ) )
     => ( ~ ( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) )
       => ~ ( member2052026769e_indi @ X_72 @ A_19 ) ) ) )).

thf(fact_79_list_Oexhaust,axiom,(
    ! [Y_26: list_A2115238852le_alt] :
      ( ( Y_26 != nil_Ar1286194111le_alt )
     => ~ ! [A: arrow_475358991le_alt,List: list_A2115238852le_alt] :
            ( Y_26
           != ( cons_A228743023le_alt @ A @ List ) ) ) )).

thf(fact_80_neq__Nil__conv,axiom,(
    ! [Xs_125: list_A2115238852le_alt] :
      ( ( Xs_125 != nil_Ar1286194111le_alt )
    <=> ? [Y_1: arrow_475358991le_alt,Ys: list_A2115238852le_alt] :
          ( Xs_125
          = ( cons_A228743023le_alt @ Y_1 @ Ys ) ) ) )).

thf(fact_81_dictator__def,axiom,(
    ! [F_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,I_1: arrow_1429601828e_indi] :
      ( ( arrow_1212662430ctator @ F_14 @ I_1 )
    <=> ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ arrow_734252939e_Prof )
         => ( ( F_14 @ X_2 )
            = ( X_2 @ I_1 ) ) ) ) )).

thf(fact_82_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt,F_13: produc1501160679le_alt > $o,A_18: produc1501160679le_alt > $o,B_15: $o > $o] :
      ( ( member377231867_alt_o @ F_13
        @ ( pi_Pro1701359055_alt_o @ A_18
          @ ^ [Uu: produc1501160679le_alt] : B_15 ) )
     => ( ( member214075476le_alt @ X_71 @ A_18 )
       => ( member_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_83_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt,F_13: produc1501160679le_alt > arrow_475358991le_alt,A_18: produc1501160679le_alt > $o,B_15: arrow_475358991le_alt > $o] :
      ( ( member1416774619le_alt @ F_13
        @ ( pi_Pro315446191le_alt @ A_18
          @ ^ [Uu: produc1501160679le_alt] : B_15 ) )
     => ( ( member214075476le_alt @ X_71 @ A_18 )
       => ( member84363362le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_84_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt,F_13: produc1501160679le_alt > arrow_1429601828e_indi,A_18: produc1501160679le_alt > $o,B_15: arrow_1429601828e_indi > $o] :
      ( ( member1640632174e_indi @ F_13
        @ ( pi_Pro1767455108e_indi @ A_18
          @ ^ [Uu: produc1501160679le_alt] : B_15 ) )
     => ( ( member214075476le_alt @ X_71 @ A_18 )
       => ( member2052026769e_indi @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_85_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt,F_13: produc1501160679le_alt > produc1362454231le_alt,A_18: produc1501160679le_alt > $o,B_15: produc1362454231le_alt > $o] :
      ( ( member220989473le_alt @ F_13
        @ ( pi_Pro666407479le_alt @ A_18
          @ ^ [Uu: produc1501160679le_alt] : B_15 ) )
     => ( ( member214075476le_alt @ X_71 @ A_18 )
       => ( member28618436le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_86_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_18: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_15: arrow_475358991le_alt > $o] :
      ( ( member1596146470le_alt @ F_13
        @ ( pi_Arr1483346486le_alt @ A_18
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member526088951_alt_o @ X_71 @ A_18 )
       => ( member84363362le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_87_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_18: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_15: arrow_1429601828e_indi > $o] :
      ( ( member44294883e_indi @ F_13
        @ ( pi_Arr1232280765e_indi @ A_18
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member526088951_alt_o @ X_71 @ A_18 )
       => ( member2052026769e_indi @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_88_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt,A_18: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_15: produc1362454231le_alt > $o] :
      ( ( member1849320470le_alt @ F_13
        @ ( pi_Arr1957214192le_alt @ A_18
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member526088951_alt_o @ X_71 @ A_18 )
       => ( member28618436le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_89_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_18: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_15: $o > $o] :
      ( ( member939334982lt_o_o @ F_13
        @ ( pi_Arr952516694lt_o_o @ A_18
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member526088951_alt_o @ X_71 @ A_18 )
       => ( member_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_90_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt > $o,F_13: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_18: ( produc1501160679le_alt > $o ) > $o,B_15: arrow_475358991le_alt > $o] :
      ( ( member1524522914le_alt @ F_13
        @ ( pi_Pro1868152754le_alt @ A_18
          @ ^ [Uu: produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member377231867_alt_o @ X_71 @ A_18 )
       => ( member84363362le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_91_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt > $o,F_13: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_18: ( produc1501160679le_alt > $o ) > $o,B_15: arrow_1429601828e_indi > $o] :
      ( ( member304866663e_indi @ F_13
        @ ( pi_Pro468373057e_indi @ A_18
          @ ^ [Uu: produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member377231867_alt_o @ X_71 @ A_18 )
       => ( member2052026769e_indi @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_92_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt > $o,F_13: ( produc1501160679le_alt > $o ) > produc1362454231le_alt,A_18: ( produc1501160679le_alt > $o ) > $o,B_15: produc1362454231le_alt > $o] :
      ( ( member1099563162le_alt @ F_13
        @ ( pi_Pro1678345076le_alt @ A_18
          @ ^ [Uu: produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member377231867_alt_o @ X_71 @ A_18 )
       => ( member28618436le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_93_funcset__mem,axiom,(
    ! [X_71: produc1501160679le_alt > $o,F_13: ( produc1501160679le_alt > $o ) > $o,A_18: ( produc1501160679le_alt > $o ) > $o,B_15: $o > $o] :
      ( ( member1961363906lt_o_o @ F_13
        @ ( pi_Pro422690258lt_o_o @ A_18
          @ ^ [Uu: produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member377231867_alt_o @ X_71 @ A_18 )
       => ( member_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_94_funcset__mem,axiom,(
    ! [X_71: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_18: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_15: arrow_475358991le_alt > $o] :
      ( ( member474974512le_alt @ F_13
        @ ( pi_Arr1005837828le_alt @ A_18
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member616898751_alt_o @ X_71 @ A_18 )
       => ( member84363362le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_95_funcset__mem,axiom,(
    ! [X_71: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_18: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_15: arrow_1429601828e_indi > $o] :
      ( ( member1452482393e_indi @ F_13
        @ ( pi_Arr338314351e_indi @ A_18
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member616898751_alt_o @ X_71 @ A_18 )
       => ( member2052026769e_indi @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_96_funcset__mem,axiom,(
    ! [X_71: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt,A_18: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_15: produc1362454231le_alt > $o] :
      ( ( member845447052le_alt @ F_13
        @ ( pi_Arr2076738722le_alt @ A_18
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member616898751_alt_o @ X_71 @ A_18 )
       => ( member28618436le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_97_funcset__mem,axiom,(
    ! [X_71: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_18: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_15: $o > $o] :
      ( ( member1823529808lt_o_o @ F_13
        @ ( pi_Arr195212324lt_o_o @ A_18
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member616898751_alt_o @ X_71 @ A_18 )
       => ( member_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_98_funcset__mem,axiom,(
    ! [X_71: arrow_475358991le_alt,F_13: arrow_475358991le_alt > produc1501160679le_alt,A_18: arrow_475358991le_alt > $o,B_15: produc1501160679le_alt > $o] :
      ( ( member712472209le_alt @ F_13
        @ ( pi_Arr1786181611le_alt @ A_18
          @ ^ [Uu: arrow_475358991le_alt] : B_15 ) )
     => ( ( member84363362le_alt @ X_71 @ A_18 )
       => ( member214075476le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_99_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi,F_13: arrow_1429601828e_indi > produc1501160679le_alt,A_18: arrow_1429601828e_indi > $o,B_15: produc1501160679le_alt > $o] :
      ( ( member351225838le_alt @ F_13
        @ ( pi_Arr329216900le_alt @ A_18
          @ ^ [Uu: arrow_1429601828e_indi] : B_15 ) )
     => ( ( member2052026769e_indi @ X_71 @ A_18 )
       => ( member214075476le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_100_funcset__mem,axiom,(
    ! [X_71: produc1362454231le_alt,F_13: produc1362454231le_alt > produc1501160679le_alt,A_18: produc1362454231le_alt > $o,B_15: produc1501160679le_alt > $o] :
      ( ( member428957857le_alt @ F_13
        @ ( pi_Pro1708969783le_alt @ A_18
          @ ^ [Uu: produc1362454231le_alt] : B_15 ) )
     => ( ( member28618436le_alt @ X_71 @ A_18 )
       => ( member214075476le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_101_funcset__mem,axiom,(
    ! [X_71: $o,F_13: $o > produc1501160679le_alt,A_18: $o > $o,B_15: produc1501160679le_alt > $o] :
      ( ( member492167345le_alt @ F_13
        @ ( pi_o_P657324555le_alt @ A_18
          @ ^ [Uu: $o] : B_15 ) )
     => ( ( member_o @ X_71 @ A_18 )
       => ( member214075476le_alt @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_102_funcset__mem,axiom,(
    ! [X_71: arrow_475358991le_alt,F_13: arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_18: arrow_475358991le_alt > $o,B_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1876989968_alt_o @ F_13
        @ ( pi_Arr578767520_alt_o @ A_18
          @ ^ [Uu: arrow_475358991le_alt] : B_15 ) )
     => ( ( member84363362le_alt @ X_71 @ A_18 )
       => ( member526088951_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_103_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi,F_13: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_18: arrow_1429601828e_indi > $o,B_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1234151027_alt_o @ F_13
        @ ( pi_Arr1060328391_alt_o @ A_18
          @ ^ [Uu: arrow_1429601828e_indi] : B_15 ) )
     => ( ( member2052026769e_indi @ X_71 @ A_18 )
       => ( member526088951_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_104_funcset__mem,axiom,(
    ! [X_71: produc1362454231le_alt,F_13: produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_18: produc1362454231le_alt > $o,B_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member392452608_alt_o @ F_13
        @ ( pi_Pro121963604_alt_o @ A_18
          @ ^ [Uu: produc1362454231le_alt] : B_15 ) )
     => ( ( member28618436le_alt @ X_71 @ A_18 )
       => ( member526088951_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_105_funcset__mem,axiom,(
    ! [X_71: $o,F_13: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_18: $o > $o,B_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1394214384_alt_o @ F_13
        @ ( pi_o_A1182933120_alt_o @ A_18
          @ ^ [Uu: $o] : B_15 ) )
     => ( ( member_o @ X_71 @ A_18 )
       => ( member526088951_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_106_funcset__mem,axiom,(
    ! [X_71: arrow_475358991le_alt,F_13: arrow_475358991le_alt > produc1501160679le_alt > $o,A_18: arrow_475358991le_alt > $o,B_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member1908358676_alt_o @ F_13
        @ ( pi_Arr1520776484_alt_o @ A_18
          @ ^ [Uu: arrow_475358991le_alt] : B_15 ) )
     => ( ( member84363362le_alt @ X_71 @ A_18 )
       => ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_107_funcset__mem,axiom,(
    ! [X_71: produc1362454231le_alt,F_13: produc1362454231le_alt > produc1501160679le_alt > $o,A_18: produc1362454231le_alt > $o,B_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member2082473988_alt_o @ F_13
        @ ( pi_Pro589599960_alt_o @ A_18
          @ ^ [Uu: produc1362454231le_alt] : B_15 ) )
     => ( ( member28618436le_alt @ X_71 @ A_18 )
       => ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_108_funcset__mem,axiom,(
    ! [X_71: $o,F_13: $o > produc1501160679le_alt > $o,A_18: $o > $o,B_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member1862122484_alt_o @ F_13
        @ ( pi_o_P553196292_alt_o @ A_18
          @ ^ [Uu: $o] : B_15 ) )
     => ( ( member_o @ X_71 @ A_18 )
       => ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_109_funcset__mem,axiom,(
    ! [X_71: arrow_475358991le_alt,F_13: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_18: arrow_475358991le_alt > $o,B_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member89384572_alt_o @ F_13
        @ ( pi_Arr515871190_alt_o @ A_18
          @ ^ [Uu: arrow_475358991le_alt] : B_15 ) )
     => ( ( member84363362le_alt @ X_71 @ A_18 )
       => ( member616898751_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_110_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi,F_13: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_18: arrow_1429601828e_indi > $o,B_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member811956313_alt_o @ F_13
        @ ( pi_Arr1564509167_alt_o @ A_18
          @ ^ [Uu: arrow_1429601828e_indi] : B_15 ) )
     => ( ( member2052026769e_indi @ X_71 @ A_18 )
       => ( member616898751_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_111_funcset__mem,axiom,(
    ! [X_71: produc1362454231le_alt,F_13: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_18: produc1362454231le_alt > $o,B_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member654997644_alt_o @ F_13
        @ ( pi_Pro441468706_alt_o @ A_18
          @ ^ [Uu: produc1362454231le_alt] : B_15 ) )
     => ( ( member28618436le_alt @ X_71 @ A_18 )
       => ( member616898751_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_112_funcset__mem,axiom,(
    ! [X_71: $o,F_13: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_18: $o > $o,B_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member1957863580_alt_o @ F_13
        @ ( pi_o_A1186128886_alt_o @ A_18
          @ ^ [Uu: $o] : B_15 ) )
     => ( ( member_o @ X_71 @ A_18 )
       => ( member616898751_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_113_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_18: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member616898751_alt_o @ F_13
        @ ( pi_Arr1304755663_alt_o @ A_18
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_15 ) )
     => ( ( member526088951_alt_o @ X_71 @ A_18 )
       => ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_114_funcset__mem,axiom,(
    ! [X_71: arrow_1429601828e_indi,F_13: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_18: arrow_1429601828e_indi > $o,B_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ F_13
        @ ( pi_Arr1929480907_alt_o @ A_18
          @ ^ [Uu: arrow_1429601828e_indi] : B_15 ) )
     => ( ( member2052026769e_indi @ X_71 @ A_18 )
       => ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) )).

thf(fact_115_splice_Osimps_I2_J,axiom,(
    ! [V_2: arrow_475358991le_alt,Va: list_A2115238852le_alt] :
      ( ( splice1520898450le_alt @ ( cons_A228743023le_alt @ V_2 @ Va ) @ nil_Ar1286194111le_alt )
      = ( cons_A228743023le_alt @ V_2 @ Va ) ) )).

thf(fact_116_splice_Osimps_I3_J,axiom,(
    ! [X_70: arrow_475358991le_alt,Xs_124: list_A2115238852le_alt,Y_25: arrow_475358991le_alt,Ys_56: list_A2115238852le_alt] :
      ( ( splice1520898450le_alt @ ( cons_A228743023le_alt @ X_70 @ Xs_124 ) @ ( cons_A228743023le_alt @ Y_25 @ Ys_56 ) )
      = ( cons_A228743023le_alt @ X_70 @ ( cons_A228743023le_alt @ Y_25 @ ( splice1520898450le_alt @ Xs_124 @ Ys_56 ) ) ) ) )).

thf(fact_117_splice_Osimps_I1_J,axiom,(
    ! [Ys_55: list_A2115238852le_alt] :
      ( ( splice1520898450le_alt @ nil_Ar1286194111le_alt @ Ys_55 )
      = Ys_55 ) )).

thf(fact_118_splice__Nil2,axiom,(
    ! [Xs_123: list_A2115238852le_alt] :
      ( ( splice1520898450le_alt @ Xs_123 @ nil_Ar1286194111le_alt )
      = Xs_123 ) )).

thf(fact_119_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt,F_12: produc1501160679le_alt > $o,A_17: produc1501160679le_alt > $o,B_14: produc1501160679le_alt > $o > $o] :
      ( ( member377231867_alt_o @ F_12 @ ( pi_Pro1701359055_alt_o @ A_17 @ B_14 ) )
     => ( ( member214075476le_alt @ X_69 @ A_17 )
       => ( member_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_120_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt,F_12: produc1501160679le_alt > arrow_475358991le_alt,A_17: produc1501160679le_alt > $o,B_14: produc1501160679le_alt > arrow_475358991le_alt > $o] :
      ( ( member1416774619le_alt @ F_12 @ ( pi_Pro315446191le_alt @ A_17 @ B_14 ) )
     => ( ( member214075476le_alt @ X_69 @ A_17 )
       => ( member84363362le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_121_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt,F_12: produc1501160679le_alt > arrow_1429601828e_indi,A_17: produc1501160679le_alt > $o,B_14: produc1501160679le_alt > arrow_1429601828e_indi > $o] :
      ( ( member1640632174e_indi @ F_12 @ ( pi_Pro1767455108e_indi @ A_17 @ B_14 ) )
     => ( ( member214075476le_alt @ X_69 @ A_17 )
       => ( member2052026769e_indi @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_122_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt,F_12: produc1501160679le_alt > produc1362454231le_alt,A_17: produc1501160679le_alt > $o,B_14: produc1501160679le_alt > produc1362454231le_alt > $o] :
      ( ( member220989473le_alt @ F_12 @ ( pi_Pro666407479le_alt @ A_17 @ B_14 ) )
     => ( ( member214075476le_alt @ X_69 @ A_17 )
       => ( member28618436le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_123_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_17: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o] :
      ( ( member1596146470le_alt @ F_12 @ ( pi_Arr1483346486le_alt @ A_17 @ B_14 ) )
     => ( ( member526088951_alt_o @ X_69 @ A_17 )
       => ( member84363362le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_124_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_17: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
      ( ( member44294883e_indi @ F_12 @ ( pi_Arr1232280765e_indi @ A_17 @ B_14 ) )
     => ( ( member526088951_alt_o @ X_69 @ A_17 )
       => ( member2052026769e_indi @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_125_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt,A_17: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o] :
      ( ( member1849320470le_alt @ F_12 @ ( pi_Arr1957214192le_alt @ A_17 @ B_14 ) )
     => ( ( member526088951_alt_o @ X_69 @ A_17 )
       => ( member28618436le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_126_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_17: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o] :
      ( ( member939334982lt_o_o @ F_12 @ ( pi_Arr952516694lt_o_o @ A_17 @ B_14 ) )
     => ( ( member526088951_alt_o @ X_69 @ A_17 )
       => ( member_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_127_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt > $o,F_12: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_17: ( produc1501160679le_alt > $o ) > $o,B_14: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o] :
      ( ( member1524522914le_alt @ F_12 @ ( pi_Pro1868152754le_alt @ A_17 @ B_14 ) )
     => ( ( member377231867_alt_o @ X_69 @ A_17 )
       => ( member84363362le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_128_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt > $o,F_12: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_17: ( produc1501160679le_alt > $o ) > $o,B_14: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
      ( ( member304866663e_indi @ F_12 @ ( pi_Pro468373057e_indi @ A_17 @ B_14 ) )
     => ( ( member377231867_alt_o @ X_69 @ A_17 )
       => ( member2052026769e_indi @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_129_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt > $o,F_12: ( produc1501160679le_alt > $o ) > produc1362454231le_alt,A_17: ( produc1501160679le_alt > $o ) > $o,B_14: ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o] :
      ( ( member1099563162le_alt @ F_12 @ ( pi_Pro1678345076le_alt @ A_17 @ B_14 ) )
     => ( ( member377231867_alt_o @ X_69 @ A_17 )
       => ( member28618436le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_130_Pi__mem,axiom,(
    ! [X_69: produc1501160679le_alt > $o,F_12: ( produc1501160679le_alt > $o ) > $o,A_17: ( produc1501160679le_alt > $o ) > $o,B_14: ( produc1501160679le_alt > $o ) > $o > $o] :
      ( ( member1961363906lt_o_o @ F_12 @ ( pi_Pro422690258lt_o_o @ A_17 @ B_14 ) )
     => ( ( member377231867_alt_o @ X_69 @ A_17 )
       => ( member_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_131_Pi__mem,axiom,(
    ! [X_69: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt,A_17: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o] :
      ( ( member474974512le_alt @ F_12 @ ( pi_Arr1005837828le_alt @ A_17 @ B_14 ) )
     => ( ( member616898751_alt_o @ X_69 @ A_17 )
       => ( member84363362le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_132_Pi__mem,axiom,(
    ! [X_69: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,A_17: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
      ( ( member1452482393e_indi @ F_12 @ ( pi_Arr338314351e_indi @ A_17 @ B_14 ) )
     => ( ( member616898751_alt_o @ X_69 @ A_17 )
       => ( member2052026769e_indi @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_133_Pi__mem,axiom,(
    ! [X_69: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt,A_17: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o] :
      ( ( member845447052le_alt @ F_12 @ ( pi_Arr2076738722le_alt @ A_17 @ B_14 ) )
     => ( ( member616898751_alt_o @ X_69 @ A_17 )
       => ( member28618436le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_134_Pi__mem,axiom,(
    ! [X_69: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,F_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_17: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o] :
      ( ( member1823529808lt_o_o @ F_12 @ ( pi_Arr195212324lt_o_o @ A_17 @ B_14 ) )
     => ( ( member616898751_alt_o @ X_69 @ A_17 )
       => ( member_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_135_Pi__mem,axiom,(
    ! [X_69: arrow_475358991le_alt,F_12: arrow_475358991le_alt > produc1501160679le_alt,A_17: arrow_475358991le_alt > $o,B_14: arrow_475358991le_alt > produc1501160679le_alt > $o] :
      ( ( member712472209le_alt @ F_12 @ ( pi_Arr1786181611le_alt @ A_17 @ B_14 ) )
     => ( ( member84363362le_alt @ X_69 @ A_17 )
       => ( member214075476le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_136_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi,F_12: arrow_1429601828e_indi > produc1501160679le_alt,A_17: arrow_1429601828e_indi > $o,B_14: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( ( member351225838le_alt @ F_12 @ ( pi_Arr329216900le_alt @ A_17 @ B_14 ) )
     => ( ( member2052026769e_indi @ X_69 @ A_17 )
       => ( member214075476le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_137_Pi__mem,axiom,(
    ! [X_69: produc1362454231le_alt,F_12: produc1362454231le_alt > produc1501160679le_alt,A_17: produc1362454231le_alt > $o,B_14: produc1362454231le_alt > produc1501160679le_alt > $o] :
      ( ( member428957857le_alt @ F_12 @ ( pi_Pro1708969783le_alt @ A_17 @ B_14 ) )
     => ( ( member28618436le_alt @ X_69 @ A_17 )
       => ( member214075476le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_138_Pi__mem,axiom,(
    ! [X_69: $o,F_12: $o > produc1501160679le_alt,A_17: $o > $o,B_14: $o > produc1501160679le_alt > $o] :
      ( ( member492167345le_alt @ F_12 @ ( pi_o_P657324555le_alt @ A_17 @ B_14 ) )
     => ( ( member_o @ X_69 @ A_17 )
       => ( member214075476le_alt @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_139_Pi__mem,axiom,(
    ! [X_69: arrow_475358991le_alt,F_12: arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_17: arrow_475358991le_alt > $o,B_14: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1876989968_alt_o @ F_12 @ ( pi_Arr578767520_alt_o @ A_17 @ B_14 ) )
     => ( ( member84363362le_alt @ X_69 @ A_17 )
       => ( member526088951_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_140_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi,F_12: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_17: arrow_1429601828e_indi > $o,B_14: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1234151027_alt_o @ F_12 @ ( pi_Arr1060328391_alt_o @ A_17 @ B_14 ) )
     => ( ( member2052026769e_indi @ X_69 @ A_17 )
       => ( member526088951_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_141_Pi__mem,axiom,(
    ! [X_69: produc1362454231le_alt,F_12: produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_17: produc1362454231le_alt > $o,B_14: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member392452608_alt_o @ F_12 @ ( pi_Pro121963604_alt_o @ A_17 @ B_14 ) )
     => ( ( member28618436le_alt @ X_69 @ A_17 )
       => ( member526088951_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_142_Pi__mem,axiom,(
    ! [X_69: $o,F_12: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,A_17: $o > $o,B_14: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member1394214384_alt_o @ F_12 @ ( pi_o_A1182933120_alt_o @ A_17 @ B_14 ) )
     => ( ( member_o @ X_69 @ A_17 )
       => ( member526088951_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_143_Pi__mem,axiom,(
    ! [X_69: arrow_475358991le_alt,F_12: arrow_475358991le_alt > produc1501160679le_alt > $o,A_17: arrow_475358991le_alt > $o,B_14: arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member1908358676_alt_o @ F_12 @ ( pi_Arr1520776484_alt_o @ A_17 @ B_14 ) )
     => ( ( member84363362le_alt @ X_69 @ A_17 )
       => ( member377231867_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_144_Pi__mem,axiom,(
    ! [X_69: produc1362454231le_alt,F_12: produc1362454231le_alt > produc1501160679le_alt > $o,A_17: produc1362454231le_alt > $o,B_14: produc1362454231le_alt > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member2082473988_alt_o @ F_12 @ ( pi_Pro589599960_alt_o @ A_17 @ B_14 ) )
     => ( ( member28618436le_alt @ X_69 @ A_17 )
       => ( member377231867_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_145_Pi__mem,axiom,(
    ! [X_69: $o,F_12: $o > produc1501160679le_alt > $o,A_17: $o > $o,B_14: $o > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member1862122484_alt_o @ F_12 @ ( pi_o_P553196292_alt_o @ A_17 @ B_14 ) )
     => ( ( member_o @ X_69 @ A_17 )
       => ( member377231867_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_146_Pi__mem,axiom,(
    ! [X_69: arrow_475358991le_alt,F_12: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_17: arrow_475358991le_alt > $o,B_14: arrow_475358991le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member89384572_alt_o @ F_12 @ ( pi_Arr515871190_alt_o @ A_17 @ B_14 ) )
     => ( ( member84363362le_alt @ X_69 @ A_17 )
       => ( member616898751_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_147_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi,F_12: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_17: arrow_1429601828e_indi > $o,B_14: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member811956313_alt_o @ F_12 @ ( pi_Arr1564509167_alt_o @ A_17 @ B_14 ) )
     => ( ( member2052026769e_indi @ X_69 @ A_17 )
       => ( member616898751_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_148_Pi__mem,axiom,(
    ! [X_69: produc1362454231le_alt,F_12: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_17: produc1362454231le_alt > $o,B_14: produc1362454231le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member654997644_alt_o @ F_12 @ ( pi_Pro441468706_alt_o @ A_17 @ B_14 ) )
     => ( ( member28618436le_alt @ X_69 @ A_17 )
       => ( member616898751_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_149_Pi__mem,axiom,(
    ! [X_69: $o,F_12: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_17: $o > $o,B_14: $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member1957863580_alt_o @ F_12 @ ( pi_o_A1186128886_alt_o @ A_17 @ B_14 ) )
     => ( ( member_o @ X_69 @ A_17 )
       => ( member616898751_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_150_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi > produc1501160679le_alt > $o,F_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_17: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member616898751_alt_o @ F_12 @ ( pi_Arr1304755663_alt_o @ A_17 @ B_14 ) )
     => ( ( member526088951_alt_o @ X_69 @ A_17 )
       => ( member377231867_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_151_Pi__mem,axiom,(
    ! [X_69: arrow_1429601828e_indi,F_12: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_17: arrow_1429601828e_indi > $o,B_14: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ F_12 @ ( pi_Arr1929480907_alt_o @ A_17 @ B_14 ) )
     => ( ( member2052026769e_indi @ X_69 @ A_17 )
       => ( member377231867_alt_o @ ( F_12 @ X_69 ) @ ( B_14 @ X_69 ) ) ) ) )).

thf(fact_152_Pi__I,axiom,(
    ! [F_11: produc1501160679le_alt > arrow_475358991le_alt,B_13: produc1501160679le_alt > arrow_475358991le_alt > $o,A_16: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_16 )
         => ( member84363362le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1416774619le_alt @ F_11 @ ( pi_Pro315446191le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_153_Pi__I,axiom,(
    ! [F_11: produc1501160679le_alt > arrow_1429601828e_indi,B_13: produc1501160679le_alt > arrow_1429601828e_indi > $o,A_16: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_16 )
         => ( member2052026769e_indi @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1640632174e_indi @ F_11 @ ( pi_Pro1767455108e_indi @ A_16 @ B_13 ) ) ) )).

thf(fact_154_Pi__I,axiom,(
    ! [F_11: produc1501160679le_alt > produc1362454231le_alt,B_13: produc1501160679le_alt > produc1362454231le_alt > $o,A_16: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_16 )
         => ( member28618436le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member220989473le_alt @ F_11 @ ( pi_Pro666407479le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_155_Pi__I,axiom,(
    ! [F_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o,A_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_16 )
         => ( member84363362le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1596146470le_alt @ F_11 @ ( pi_Arr1483346486le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_156_Pi__I,axiom,(
    ! [F_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o,A_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_16 )
         => ( member2052026769e_indi @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member44294883e_indi @ F_11 @ ( pi_Arr1232280765e_indi @ A_16 @ B_13 ) ) ) )).

thf(fact_157_Pi__I,axiom,(
    ! [F_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt,B_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o,A_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_16 )
         => ( member28618436le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1849320470le_alt @ F_11 @ ( pi_Arr1957214192le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_158_Pi__I,axiom,(
    ! [F_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o,A_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_16 )
         => ( member_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member939334982lt_o_o @ F_11 @ ( pi_Arr952516694lt_o_o @ A_16 @ B_13 ) ) ) )).

thf(fact_159_Pi__I,axiom,(
    ! [F_11: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_13: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o,A_16: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_16 )
         => ( member84363362le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1524522914le_alt @ F_11 @ ( pi_Pro1868152754le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_160_Pi__I,axiom,(
    ! [F_11: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_13: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o,A_16: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_16 )
         => ( member2052026769e_indi @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member304866663e_indi @ F_11 @ ( pi_Pro468373057e_indi @ A_16 @ B_13 ) ) ) )).

thf(fact_161_Pi__I,axiom,(
    ! [F_11: ( produc1501160679le_alt > $o ) > produc1362454231le_alt,B_13: ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o,A_16: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_16 )
         => ( member28618436le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1099563162le_alt @ F_11 @ ( pi_Pro1678345076le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_162_Pi__I,axiom,(
    ! [F_11: ( produc1501160679le_alt > $o ) > $o,B_13: ( produc1501160679le_alt > $o ) > $o > $o,A_16: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_16 )
         => ( member_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1961363906lt_o_o @ F_11 @ ( pi_Pro422690258lt_o_o @ A_16 @ B_13 ) ) ) )).

thf(fact_163_Pi__I,axiom,(
    ! [F_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o,A_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_16 )
         => ( member84363362le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member474974512le_alt @ F_11 @ ( pi_Arr1005837828le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_164_Pi__I,axiom,(
    ! [F_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o,A_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_16 )
         => ( member2052026769e_indi @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1452482393e_indi @ F_11 @ ( pi_Arr338314351e_indi @ A_16 @ B_13 ) ) ) )).

thf(fact_165_Pi__I,axiom,(
    ! [F_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt,B_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o,A_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_16 )
         => ( member28618436le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member845447052le_alt @ F_11 @ ( pi_Arr2076738722le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_166_Pi__I,axiom,(
    ! [F_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_13: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o,A_16: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_16 )
         => ( member_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1823529808lt_o_o @ F_11 @ ( pi_Arr195212324lt_o_o @ A_16 @ B_13 ) ) ) )).

thf(fact_167_Pi__I,axiom,(
    ! [F_11: arrow_475358991le_alt > produc1501160679le_alt,B_13: arrow_475358991le_alt > produc1501160679le_alt > $o,A_16: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_16 )
         => ( member214075476le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member712472209le_alt @ F_11 @ ( pi_Arr1786181611le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_168_Pi__I,axiom,(
    ! [F_11: arrow_1429601828e_indi > produc1501160679le_alt,B_13: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_16: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_16 )
         => ( member214075476le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member351225838le_alt @ F_11 @ ( pi_Arr329216900le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_169_Pi__I,axiom,(
    ! [F_11: produc1362454231le_alt > produc1501160679le_alt,B_13: produc1362454231le_alt > produc1501160679le_alt > $o,A_16: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_16 )
         => ( member214075476le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member428957857le_alt @ F_11 @ ( pi_Pro1708969783le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_170_Pi__I,axiom,(
    ! [F_11: $o > produc1501160679le_alt,B_13: $o > produc1501160679le_alt > $o,A_16: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_16 )
         => ( member214075476le_alt @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member492167345le_alt @ F_11 @ ( pi_o_P657324555le_alt @ A_16 @ B_13 ) ) ) )).

thf(fact_171_Pi__I,axiom,(
    ! [F_11: arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_13: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_16: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_16 )
         => ( member526088951_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1876989968_alt_o @ F_11 @ ( pi_Arr578767520_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_172_Pi__I,axiom,(
    ! [F_11: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_13: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_16: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_16 )
         => ( member526088951_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1234151027_alt_o @ F_11 @ ( pi_Arr1060328391_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_173_Pi__I,axiom,(
    ! [F_11: produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_13: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_16: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_16 )
         => ( member526088951_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member392452608_alt_o @ F_11 @ ( pi_Pro121963604_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_174_Pi__I,axiom,(
    ! [F_11: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_13: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_16: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_16 )
         => ( member526088951_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1394214384_alt_o @ F_11 @ ( pi_o_A1182933120_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_175_Pi__I,axiom,(
    ! [F_11: arrow_475358991le_alt > produc1501160679le_alt > $o,B_13: arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > $o,A_16: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_16 )
         => ( member377231867_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1908358676_alt_o @ F_11 @ ( pi_Arr1520776484_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_176_Pi__I,axiom,(
    ! [F_11: produc1362454231le_alt > produc1501160679le_alt > $o,B_13: produc1362454231le_alt > ( produc1501160679le_alt > $o ) > $o,A_16: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_16 )
         => ( member377231867_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member2082473988_alt_o @ F_11 @ ( pi_Pro589599960_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_177_Pi__I,axiom,(
    ! [F_11: $o > produc1501160679le_alt > $o,B_13: $o > ( produc1501160679le_alt > $o ) > $o,A_16: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_16 )
         => ( member377231867_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1862122484_alt_o @ F_11 @ ( pi_o_P553196292_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_178_Pi__I,axiom,(
    ! [F_11: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_13: arrow_475358991le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_16: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_16 )
         => ( member616898751_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member89384572_alt_o @ F_11 @ ( pi_Arr515871190_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_179_Pi__I,axiom,(
    ! [F_11: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_13: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_16: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_16 )
         => ( member616898751_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member811956313_alt_o @ F_11 @ ( pi_Arr1564509167_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_180_Pi__I,axiom,(
    ! [F_11: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_13: produc1362454231le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_16: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_16 )
         => ( member616898751_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member654997644_alt_o @ F_11 @ ( pi_Pro441468706_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_181_Pi__I,axiom,(
    ! [F_11: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_13: $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_16: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_16 )
         => ( member616898751_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member1957863580_alt_o @ F_11 @ ( pi_o_A1186128886_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_182_Pi__I,axiom,(
    ! [F_11: produc1501160679le_alt > $o,B_13: produc1501160679le_alt > $o > $o,A_16: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_16 )
         => ( member_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member377231867_alt_o @ F_11 @ ( pi_Pro1701359055_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_183_Pi__I,axiom,(
    ! [F_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,A_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_16 )
         => ( member377231867_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member616898751_alt_o @ F_11 @ ( pi_Arr1304755663_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_184_Pi__I,axiom,(
    ! [F_11: arrow_1429601828e_indi > produc1501160679le_alt > $o,B_13: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,A_16: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_16 )
         => ( member377231867_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) )
     => ( member526088951_alt_o @ F_11 @ ( pi_Arr1929480907_alt_o @ A_16 @ B_13 ) ) ) )).

thf(fact_185_funcsetI,axiom,(
    ! [F_10: produc1501160679le_alt > arrow_475358991le_alt,B_12: arrow_475358991le_alt > $o,A_15: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_15 )
         => ( member84363362le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1416774619le_alt @ F_10
        @ ( pi_Pro315446191le_alt @ A_15
          @ ^ [Uu: produc1501160679le_alt] : B_12 ) ) ) )).

thf(fact_186_funcsetI,axiom,(
    ! [F_10: produc1501160679le_alt > arrow_1429601828e_indi,B_12: arrow_1429601828e_indi > $o,A_15: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_15 )
         => ( member2052026769e_indi @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1640632174e_indi @ F_10
        @ ( pi_Pro1767455108e_indi @ A_15
          @ ^ [Uu: produc1501160679le_alt] : B_12 ) ) ) )).

thf(fact_187_funcsetI,axiom,(
    ! [F_10: produc1501160679le_alt > produc1362454231le_alt,B_12: produc1362454231le_alt > $o,A_15: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_15 )
         => ( member28618436le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member220989473le_alt @ F_10
        @ ( pi_Pro666407479le_alt @ A_15
          @ ^ [Uu: produc1501160679le_alt] : B_12 ) ) ) )).

thf(fact_188_funcsetI,axiom,(
    ! [F_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_12: arrow_475358991le_alt > $o,A_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_15 )
         => ( member84363362le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1596146470le_alt @ F_10
        @ ( pi_Arr1483346486le_alt @ A_15
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_189_funcsetI,axiom,(
    ! [F_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_12: arrow_1429601828e_indi > $o,A_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_15 )
         => ( member2052026769e_indi @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member44294883e_indi @ F_10
        @ ( pi_Arr1232280765e_indi @ A_15
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_190_funcsetI,axiom,(
    ! [F_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt,B_12: produc1362454231le_alt > $o,A_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_15 )
         => ( member28618436le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1849320470le_alt @ F_10
        @ ( pi_Arr1957214192le_alt @ A_15
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_191_funcsetI,axiom,(
    ! [F_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_12: $o > $o,A_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_15 )
         => ( member_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member939334982lt_o_o @ F_10
        @ ( pi_Arr952516694lt_o_o @ A_15
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_192_funcsetI,axiom,(
    ! [F_10: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_12: arrow_475358991le_alt > $o,A_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_15 )
         => ( member84363362le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1524522914le_alt @ F_10
        @ ( pi_Pro1868152754le_alt @ A_15
          @ ^ [Uu: produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_193_funcsetI,axiom,(
    ! [F_10: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_12: arrow_1429601828e_indi > $o,A_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_15 )
         => ( member2052026769e_indi @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member304866663e_indi @ F_10
        @ ( pi_Pro468373057e_indi @ A_15
          @ ^ [Uu: produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_194_funcsetI,axiom,(
    ! [F_10: ( produc1501160679le_alt > $o ) > produc1362454231le_alt,B_12: produc1362454231le_alt > $o,A_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_15 )
         => ( member28618436le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1099563162le_alt @ F_10
        @ ( pi_Pro1678345076le_alt @ A_15
          @ ^ [Uu: produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_195_funcsetI,axiom,(
    ! [F_10: ( produc1501160679le_alt > $o ) > $o,B_12: $o > $o,A_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_15 )
         => ( member_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1961363906lt_o_o @ F_10
        @ ( pi_Pro422690258lt_o_o @ A_15
          @ ^ [Uu: produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_196_funcsetI,axiom,(
    ! [F_10: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_12: arrow_475358991le_alt > $o,A_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_15 )
         => ( member84363362le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member474974512le_alt @ F_10
        @ ( pi_Arr1005837828le_alt @ A_15
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_197_funcsetI,axiom,(
    ! [F_10: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_12: arrow_1429601828e_indi > $o,A_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_15 )
         => ( member2052026769e_indi @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1452482393e_indi @ F_10
        @ ( pi_Arr338314351e_indi @ A_15
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_198_funcsetI,axiom,(
    ! [F_10: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt,B_12: produc1362454231le_alt > $o,A_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_15 )
         => ( member28618436le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member845447052le_alt @ F_10
        @ ( pi_Arr2076738722le_alt @ A_15
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_199_funcsetI,axiom,(
    ! [F_10: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_12: $o > $o,A_15: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_15 )
         => ( member_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1823529808lt_o_o @ F_10
        @ ( pi_Arr195212324lt_o_o @ A_15
          @ ^ [Uu: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_200_funcsetI,axiom,(
    ! [F_10: arrow_475358991le_alt > produc1501160679le_alt,B_12: produc1501160679le_alt > $o,A_15: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_15 )
         => ( member214075476le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member712472209le_alt @ F_10
        @ ( pi_Arr1786181611le_alt @ A_15
          @ ^ [Uu: arrow_475358991le_alt] : B_12 ) ) ) )).

thf(fact_201_funcsetI,axiom,(
    ! [F_10: arrow_1429601828e_indi > produc1501160679le_alt,B_12: produc1501160679le_alt > $o,A_15: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_15 )
         => ( member214075476le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member351225838le_alt @ F_10
        @ ( pi_Arr329216900le_alt @ A_15
          @ ^ [Uu: arrow_1429601828e_indi] : B_12 ) ) ) )).

thf(fact_202_funcsetI,axiom,(
    ! [F_10: produc1362454231le_alt > produc1501160679le_alt,B_12: produc1501160679le_alt > $o,A_15: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_15 )
         => ( member214075476le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member428957857le_alt @ F_10
        @ ( pi_Pro1708969783le_alt @ A_15
          @ ^ [Uu: produc1362454231le_alt] : B_12 ) ) ) )).

thf(fact_203_funcsetI,axiom,(
    ! [F_10: $o > produc1501160679le_alt,B_12: produc1501160679le_alt > $o,A_15: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_15 )
         => ( member214075476le_alt @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member492167345le_alt @ F_10
        @ ( pi_o_P657324555le_alt @ A_15
          @ ^ [Uu: $o] : B_12 ) ) ) )).

thf(fact_204_funcsetI,axiom,(
    ! [F_10: arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_15: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_15 )
         => ( member526088951_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1876989968_alt_o @ F_10
        @ ( pi_Arr578767520_alt_o @ A_15
          @ ^ [Uu: arrow_475358991le_alt] : B_12 ) ) ) )).

thf(fact_205_funcsetI,axiom,(
    ! [F_10: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_15: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_15 )
         => ( member526088951_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1234151027_alt_o @ F_10
        @ ( pi_Arr1060328391_alt_o @ A_15
          @ ^ [Uu: arrow_1429601828e_indi] : B_12 ) ) ) )).

thf(fact_206_funcsetI,axiom,(
    ! [F_10: produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_15: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_15 )
         => ( member526088951_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member392452608_alt_o @ F_10
        @ ( pi_Pro121963604_alt_o @ A_15
          @ ^ [Uu: produc1362454231le_alt] : B_12 ) ) ) )).

thf(fact_207_funcsetI,axiom,(
    ! [F_10: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_15: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_15 )
         => ( member526088951_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1394214384_alt_o @ F_10
        @ ( pi_o_A1182933120_alt_o @ A_15
          @ ^ [Uu: $o] : B_12 ) ) ) )).

thf(fact_208_funcsetI,axiom,(
    ! [F_10: arrow_475358991le_alt > produc1501160679le_alt > $o,B_12: ( produc1501160679le_alt > $o ) > $o,A_15: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_15 )
         => ( member377231867_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1908358676_alt_o @ F_10
        @ ( pi_Arr1520776484_alt_o @ A_15
          @ ^ [Uu: arrow_475358991le_alt] : B_12 ) ) ) )).

thf(fact_209_funcsetI,axiom,(
    ! [F_10: produc1362454231le_alt > produc1501160679le_alt > $o,B_12: ( produc1501160679le_alt > $o ) > $o,A_15: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_15 )
         => ( member377231867_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member2082473988_alt_o @ F_10
        @ ( pi_Pro589599960_alt_o @ A_15
          @ ^ [Uu: produc1362454231le_alt] : B_12 ) ) ) )).

thf(fact_210_funcsetI,axiom,(
    ! [F_10: $o > produc1501160679le_alt > $o,B_12: ( produc1501160679le_alt > $o ) > $o,A_15: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_15 )
         => ( member377231867_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1862122484_alt_o @ F_10
        @ ( pi_o_P553196292_alt_o @ A_15
          @ ^ [Uu: $o] : B_12 ) ) ) )).

thf(fact_211_funcsetI,axiom,(
    ! [F_10: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_15: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_15 )
         => ( member616898751_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member89384572_alt_o @ F_10
        @ ( pi_Arr515871190_alt_o @ A_15
          @ ^ [Uu: arrow_475358991le_alt] : B_12 ) ) ) )).

thf(fact_212_funcsetI,axiom,(
    ! [F_10: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_15: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_15 )
         => ( member616898751_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member811956313_alt_o @ F_10
        @ ( pi_Arr1564509167_alt_o @ A_15
          @ ^ [Uu: arrow_1429601828e_indi] : B_12 ) ) ) )).

thf(fact_213_funcsetI,axiom,(
    ! [F_10: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_15: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_15 )
         => ( member616898751_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member654997644_alt_o @ F_10
        @ ( pi_Pro441468706_alt_o @ A_15
          @ ^ [Uu: produc1362454231le_alt] : B_12 ) ) ) )).

thf(fact_214_funcsetI,axiom,(
    ! [F_10: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_15: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_15 )
         => ( member616898751_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member1957863580_alt_o @ F_10
        @ ( pi_o_A1186128886_alt_o @ A_15
          @ ^ [Uu: $o] : B_12 ) ) ) )).

thf(fact_215_funcsetI,axiom,(
    ! [F_10: produc1501160679le_alt > $o,B_12: $o > $o,A_15: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_15 )
         => ( member_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member377231867_alt_o @ F_10
        @ ( pi_Pro1701359055_alt_o @ A_15
          @ ^ [Uu: produc1501160679le_alt] : B_12 ) ) ) )).

thf(fact_216_funcsetI,axiom,(
    ! [F_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_12: ( produc1501160679le_alt > $o ) > $o,A_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_15 )
         => ( member377231867_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member616898751_alt_o @ F_10
        @ ( pi_Arr1304755663_alt_o @ A_15
          @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B_12 ) ) ) )).

thf(fact_217_funcsetI,axiom,(
    ! [F_10: arrow_1429601828e_indi > produc1501160679le_alt > $o,B_12: ( produc1501160679le_alt > $o ) > $o,A_15: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_15 )
         => ( member377231867_alt_o @ ( F_10 @ X_2 ) @ B_12 ) )
     => ( member526088951_alt_o @ F_10
        @ ( pi_Arr1929480907_alt_o @ A_15
          @ ^ [Uu: arrow_1429601828e_indi] : B_12 ) ) ) )).

thf(fact_218_Pi__I_H,axiom,(
    ! [F_9: produc1501160679le_alt > arrow_475358991le_alt,B_11: produc1501160679le_alt > arrow_475358991le_alt > $o,A_14: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_14 )
         => ( member84363362le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1416774619le_alt @ F_9 @ ( pi_Pro315446191le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_219_Pi__I_H,axiom,(
    ! [F_9: produc1501160679le_alt > arrow_1429601828e_indi,B_11: produc1501160679le_alt > arrow_1429601828e_indi > $o,A_14: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_14 )
         => ( member2052026769e_indi @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1640632174e_indi @ F_9 @ ( pi_Pro1767455108e_indi @ A_14 @ B_11 ) ) ) )).

thf(fact_220_Pi__I_H,axiom,(
    ! [F_9: produc1501160679le_alt > produc1362454231le_alt,B_11: produc1501160679le_alt > produc1362454231le_alt > $o,A_14: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_14 )
         => ( member28618436le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member220989473le_alt @ F_9 @ ( pi_Pro666407479le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_221_Pi__I_H,axiom,(
    ! [F_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o,A_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_14 )
         => ( member84363362le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1596146470le_alt @ F_9 @ ( pi_Arr1483346486le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_222_Pi__I_H,axiom,(
    ! [F_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o,A_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_14 )
         => ( member2052026769e_indi @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member44294883e_indi @ F_9 @ ( pi_Arr1232280765e_indi @ A_14 @ B_11 ) ) ) )).

thf(fact_223_Pi__I_H,axiom,(
    ! [F_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt,B_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o,A_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_14 )
         => ( member28618436le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1849320470le_alt @ F_9 @ ( pi_Arr1957214192le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_224_Pi__I_H,axiom,(
    ! [F_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,B_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o,A_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_14 )
         => ( member_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member939334982lt_o_o @ F_9 @ ( pi_Arr952516694lt_o_o @ A_14 @ B_11 ) ) ) )).

thf(fact_225_Pi__I_H,axiom,(
    ! [F_9: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_11: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o,A_14: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_14 )
         => ( member84363362le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1524522914le_alt @ F_9 @ ( pi_Pro1868152754le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_226_Pi__I_H,axiom,(
    ! [F_9: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_11: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o,A_14: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_14 )
         => ( member2052026769e_indi @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member304866663e_indi @ F_9 @ ( pi_Pro468373057e_indi @ A_14 @ B_11 ) ) ) )).

thf(fact_227_Pi__I_H,axiom,(
    ! [F_9: ( produc1501160679le_alt > $o ) > produc1362454231le_alt,B_11: ( produc1501160679le_alt > $o ) > produc1362454231le_alt > $o,A_14: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_14 )
         => ( member28618436le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1099563162le_alt @ F_9 @ ( pi_Pro1678345076le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_228_Pi__I_H,axiom,(
    ! [F_9: ( produc1501160679le_alt > $o ) > $o,B_11: ( produc1501160679le_alt > $o ) > $o > $o,A_14: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ A_14 )
         => ( member_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1961363906lt_o_o @ F_9 @ ( pi_Pro422690258lt_o_o @ A_14 @ B_11 ) ) ) )).

thf(fact_229_Pi__I_H,axiom,(
    ! [F_9: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt,B_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_475358991le_alt > $o,A_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_14 )
         => ( member84363362le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member474974512le_alt @ F_9 @ ( pi_Arr1005837828le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_230_Pi__I_H,axiom,(
    ! [F_9: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,B_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o,A_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_14 )
         => ( member2052026769e_indi @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1452482393e_indi @ F_9 @ ( pi_Arr338314351e_indi @ A_14 @ B_11 ) ) ) )).

thf(fact_231_Pi__I_H,axiom,(
    ! [F_9: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt,B_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > produc1362454231le_alt > $o,A_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_14 )
         => ( member28618436le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member845447052le_alt @ F_9 @ ( pi_Arr2076738722le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_232_Pi__I_H,axiom,(
    ! [F_9: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B_11: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o,A_14: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ A_14 )
         => ( member_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1823529808lt_o_o @ F_9 @ ( pi_Arr195212324lt_o_o @ A_14 @ B_11 ) ) ) )).

thf(fact_233_Pi__I_H,axiom,(
    ! [F_9: arrow_475358991le_alt > produc1501160679le_alt,B_11: arrow_475358991le_alt > produc1501160679le_alt > $o,A_14: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_14 )
         => ( member214075476le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member712472209le_alt @ F_9 @ ( pi_Arr1786181611le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_234_Pi__I_H,axiom,(
    ! [F_9: arrow_1429601828e_indi > produc1501160679le_alt,B_11: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_14: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_14 )
         => ( member214075476le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member351225838le_alt @ F_9 @ ( pi_Arr329216900le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_235_Pi__I_H,axiom,(
    ! [F_9: produc1362454231le_alt > produc1501160679le_alt,B_11: produc1362454231le_alt > produc1501160679le_alt > $o,A_14: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_14 )
         => ( member214075476le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member428957857le_alt @ F_9 @ ( pi_Pro1708969783le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_236_Pi__I_H,axiom,(
    ! [F_9: $o > produc1501160679le_alt,B_11: $o > produc1501160679le_alt > $o,A_14: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_14 )
         => ( member214075476le_alt @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member492167345le_alt @ F_9 @ ( pi_o_P657324555le_alt @ A_14 @ B_11 ) ) ) )).

thf(fact_237_Pi__I_H,axiom,(
    ! [F_9: arrow_475358991le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_11: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_14: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_14 )
         => ( member526088951_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1876989968_alt_o @ F_9 @ ( pi_Arr578767520_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_238_Pi__I_H,axiom,(
    ! [F_9: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_11: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_14: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_14 )
         => ( member526088951_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1234151027_alt_o @ F_9 @ ( pi_Arr1060328391_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_239_Pi__I_H,axiom,(
    ! [F_9: produc1362454231le_alt > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_11: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_14: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_14 )
         => ( member526088951_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member392452608_alt_o @ F_9 @ ( pi_Pro121963604_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_240_Pi__I_H,axiom,(
    ! [F_9: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,B_11: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,A_14: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_14 )
         => ( member526088951_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1394214384_alt_o @ F_9 @ ( pi_o_A1182933120_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_241_Pi__I_H,axiom,(
    ! [F_9: arrow_475358991le_alt > produc1501160679le_alt > $o,B_11: arrow_475358991le_alt > ( produc1501160679le_alt > $o ) > $o,A_14: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_14 )
         => ( member377231867_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1908358676_alt_o @ F_9 @ ( pi_Arr1520776484_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_242_Pi__I_H,axiom,(
    ! [F_9: produc1362454231le_alt > produc1501160679le_alt > $o,B_11: produc1362454231le_alt > ( produc1501160679le_alt > $o ) > $o,A_14: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_14 )
         => ( member377231867_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member2082473988_alt_o @ F_9 @ ( pi_Pro589599960_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_243_Pi__I_H,axiom,(
    ! [F_9: $o > produc1501160679le_alt > $o,B_11: $o > ( produc1501160679le_alt > $o ) > $o,A_14: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_14 )
         => ( member377231867_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1862122484_alt_o @ F_9 @ ( pi_o_P553196292_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_244_Pi__I_H,axiom,(
    ! [F_9: arrow_475358991le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_11: arrow_475358991le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_14: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ A_14 )
         => ( member616898751_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member89384572_alt_o @ F_9 @ ( pi_Arr515871190_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_245_Pi__I_H,axiom,(
    ! [F_9: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_11: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_14: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_14 )
         => ( member616898751_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member811956313_alt_o @ F_9 @ ( pi_Arr1564509167_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_246_Pi__I_H,axiom,(
    ! [F_9: produc1362454231le_alt > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_11: produc1362454231le_alt > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_14: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ A_14 )
         => ( member616898751_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member654997644_alt_o @ F_9 @ ( pi_Pro441468706_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_247_Pi__I_H,axiom,(
    ! [F_9: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_11: $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,A_14: $o > $o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ A_14 )
         => ( member616898751_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member1957863580_alt_o @ F_9 @ ( pi_o_A1186128886_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_248_Pi__I_H,axiom,(
    ! [F_9: produc1501160679le_alt > $o,B_11: produc1501160679le_alt > $o > $o,A_14: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ A_14 )
         => ( member_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member377231867_alt_o @ F_9 @ ( pi_Pro1701359055_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_249_Pi__I_H,axiom,(
    ! [F_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,A_14: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ A_14 )
         => ( member377231867_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member616898751_alt_o @ F_9 @ ( pi_Arr1304755663_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_250_Pi__I_H,axiom,(
    ! [F_9: arrow_1429601828e_indi > produc1501160679le_alt > $o,B_11: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,A_14: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ A_14 )
         => ( member377231867_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) )
     => ( member526088951_alt_o @ F_9 @ ( pi_Arr1929480907_alt_o @ A_14 @ B_11 ) ) ) )).

thf(fact_251_Pi__cong,axiom,(
    ! [B_10: produc1501160679le_alt > $o > $o,G: produc1501160679le_alt > $o,F_8: produc1501160679le_alt > $o,A_13: produc1501160679le_alt > $o] :
      ( ! [W: produc1501160679le_alt] :
          ( ( member214075476le_alt @ W @ A_13 )
         => ( ( F_8 @ W )
          <=> ( G @ W ) ) )
     => ( ( member377231867_alt_o @ F_8 @ ( pi_Pro1701359055_alt_o @ A_13 @ B_10 ) )
      <=> ( member377231867_alt_o @ G @ ( pi_Pro1701359055_alt_o @ A_13 @ B_10 ) ) ) ) )).

thf(fact_252_Pi__cong,axiom,(
    ! [B_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,F_8: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,G: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [W: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ W @ A_13 )
         => ( ( F_8 @ W )
            = ( G @ W ) ) )
     => ( ( member616898751_alt_o @ F_8 @ ( pi_Arr1304755663_alt_o @ A_13 @ B_10 ) )
      <=> ( member616898751_alt_o @ G @ ( pi_Arr1304755663_alt_o @ A_13 @ B_10 ) ) ) ) )).

thf(fact_253_Pi__cong,axiom,(
    ! [B_10: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,F_8: arrow_1429601828e_indi > produc1501160679le_alt > $o,G: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_13: arrow_1429601828e_indi > $o] :
      ( ! [W: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ W @ A_13 )
         => ( ( F_8 @ W )
            = ( G @ W ) ) )
     => ( ( member526088951_alt_o @ F_8 @ ( pi_Arr1929480907_alt_o @ A_13 @ B_10 ) )
      <=> ( member526088951_alt_o @ G @ ( pi_Arr1929480907_alt_o @ A_13 @ B_10 ) ) ) ) )).

thf(fact_254_pred__equals__eq2,axiom,(
    ! [S_1: produc1362454231le_alt > $o,R_39: produc1362454231le_alt > $o] :
      ( ! [X_2: list_A2115238852le_alt,Xa: list_A2115238852le_alt] :
          ( ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Xa ) @ R_39 )
        <=> ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Xa ) @ S_1 ) )
    <=> ( R_39 = S_1 ) ) )).

thf(fact_255_pred__equals__eq2,axiom,(
    ! [S_1: produc1501160679le_alt > $o,R_39: produc1501160679le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt,Xa: arrow_475358991le_alt] :
          ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Xa ) @ R_39 )
        <=> ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Xa ) @ S_1 ) )
    <=> ( R_39 = S_1 ) ) )).

thf(fact_256_prod_Oexhaust,axiom,(
    ! [Y_24: produc1362454231le_alt] :
      ~ ! [A: list_A2115238852le_alt,B: list_A2115238852le_alt] :
          ( Y_24
         != ( produc776457805le_alt @ A @ B ) ) )).

thf(fact_257_prod_Oexhaust,axiom,(
    ! [Y_24: produc1501160679le_alt] :
      ~ ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
          ( Y_24
         != ( produc1347929815le_alt @ A @ B ) ) )).

thf(fact_258_PairE,axiom,(
    ! [P_29: produc1362454231le_alt] :
      ~ ! [X_2: list_A2115238852le_alt,Y_1: list_A2115238852le_alt] :
          ( P_29
         != ( produc776457805le_alt @ X_2 @ Y_1 ) ) )).

thf(fact_259_PairE,axiom,(
    ! [P_29: produc1501160679le_alt] :
      ~ ! [X_2: arrow_475358991le_alt,Y_1: arrow_475358991le_alt] :
          ( P_29
         != ( produc1347929815le_alt @ X_2 @ Y_1 ) ) )).

thf(fact_260_split__paired__Ex,axiom,(
    ! [P_28: produc1362454231le_alt > $o] :
      ( ( ex1 @ P_28 )
    <=> ? [A: list_A2115238852le_alt,B: list_A2115238852le_alt] :
          ( P_28 @ ( produc776457805le_alt @ A @ B ) ) ) )).

thf(fact_261_split__paired__Ex,axiom,(
    ! [P_28: produc1501160679le_alt > $o] :
      ( ( ex2 @ P_28 )
    <=> ? [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
          ( P_28 @ ( produc1347929815le_alt @ A @ B ) ) ) )).

thf(fact_262_insert__Nil,axiom,(
    ! [X_68: arrow_475358991le_alt] :
      ( ( insert2120566741le_alt @ X_68 @ nil_Ar1286194111le_alt )
      = ( cons_A228743023le_alt @ X_68 @ nil_Ar1286194111le_alt ) ) )).

thf(fact_263_distinct__insert,axiom,(
    ! [X_67: arrow_475358991le_alt,Xs_122: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_122 )
     => ( distin236324274le_alt @ ( insert2120566741le_alt @ X_67 @ Xs_122 ) ) ) )).

thf(fact_264_mem__def,axiom,(
    ! [X_66: arrow_475358991le_alt,A_12: arrow_475358991le_alt > $o] :
      ( ( member84363362le_alt @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_265_mem__def,axiom,(
    ! [X_66: arrow_1429601828e_indi,A_12: arrow_1429601828e_indi > $o] :
      ( ( member2052026769e_indi @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_266_mem__def,axiom,(
    ! [X_66: produc1362454231le_alt,A_12: produc1362454231le_alt > $o] :
      ( ( member28618436le_alt @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_267_mem__def,axiom,(
    ! [X_66: $o,A_12: $o > $o] :
      ( ( member_o @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_268_mem__def,axiom,(
    ! [X_66: produc1501160679le_alt,A_12: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_269_mem__def,axiom,(
    ! [X_66: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_270_mem__def,axiom,(
    ! [X_66: produc1501160679le_alt > $o,A_12: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member377231867_alt_o @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_271_mem__def,axiom,(
    ! [X_66: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,A_12: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ( member616898751_alt_o @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) )).

thf(fact_272_Collect__def,axiom,(
    ! [P_27: arrow_475358991le_alt > $o] :
      ( ( collec742074788le_alt @ P_27 )
      = P_27 ) )).

thf(fact_273_Collect__def,axiom,(
    ! [P_27: arrow_1429601828e_indi > $o] :
      ( ( collec22405327e_indi @ P_27 )
      = P_27 ) )).

thf(fact_274_Collect__def,axiom,(
    ! [P_27: ( produc1501160679le_alt > $o ) > $o] :
      ( ( collec94295101_alt_o @ P_27 )
      = P_27 ) )).

thf(fact_275_list__nonempty__induct,axiom,(
    ! [P_26: list_A2115238852le_alt > $o,Xs_121: list_A2115238852le_alt] :
      ( ( Xs_121 != nil_Ar1286194111le_alt )
     => ( ! [X_2: arrow_475358991le_alt] :
            ( P_26 @ ( cons_A228743023le_alt @ X_2 @ nil_Ar1286194111le_alt ) )
       => ( ! [X_2: arrow_475358991le_alt,Xs_21: list_A2115238852le_alt] :
              ( ( Xs_21 != nil_Ar1286194111le_alt )
             => ( ( P_26 @ Xs_21 )
               => ( P_26 @ ( cons_A228743023le_alt @ X_2 @ Xs_21 ) ) ) )
         => ( P_26 @ Xs_121 ) ) ) ) )).

thf(fact_276_curry__def,axiom,(
    ! [X_2: produc1501160679le_alt > $o,Xa: arrow_475358991le_alt,Xb: arrow_475358991le_alt] :
      ( ( produc910278158_alt_o @ X_2 @ Xa @ Xb )
    <=> ( X_2 @ ( produc1347929815le_alt @ Xa @ Xb ) ) ) )).

thf(fact_277_curryI,axiom,(
    ! [F_7: produc1362454231le_alt > $o,A_11: list_A2115238852le_alt,B_9: list_A2115238852le_alt] :
      ( ( F_7 @ ( produc776457805le_alt @ A_11 @ B_9 ) )
     => ( produc1739499928_alt_o @ F_7 @ A_11 @ B_9 ) ) )).

thf(fact_278_curryI,axiom,(
    ! [F_7: produc1501160679le_alt > $o,A_11: arrow_475358991le_alt,B_9: arrow_475358991le_alt] :
      ( ( F_7 @ ( produc1347929815le_alt @ A_11 @ B_9 ) )
     => ( produc910278158_alt_o @ F_7 @ A_11 @ B_9 ) ) )).

thf(fact_279_null__rec_I2_J,axiom,
    ( null_A1520965063le_alt @ nil_Ar1286194111le_alt )).

thf(fact_280_List_Onull__def,axiom,(
    ! [Xs_120: list_A2115238852le_alt] :
      ( ( null_A1520965063le_alt @ Xs_120 )
    <=> ( Xs_120 = nil_Ar1286194111le_alt ) ) )).

thf(fact_281_eq__Nil__null,axiom,(
    ! [Xs_119: list_A2115238852le_alt] :
      ( ( Xs_119 = nil_Ar1286194111le_alt )
    <=> ( null_A1520965063le_alt @ Xs_119 ) ) )).

thf(fact_282_null__rec_I1_J,axiom,(
    ! [X_65: arrow_475358991le_alt,Xs_118: list_A2115238852le_alt] :
      ~ ( null_A1520965063le_alt @ ( cons_A228743023le_alt @ X_65 @ Xs_118 ) ) )).

thf(fact_283_curryD,axiom,(
    ! [F_6: produc1362454231le_alt > $o,A_10: list_A2115238852le_alt,B_8: list_A2115238852le_alt] :
      ( ( produc1739499928_alt_o @ F_6 @ A_10 @ B_8 )
     => ( F_6 @ ( produc776457805le_alt @ A_10 @ B_8 ) ) ) )).

thf(fact_284_curryD,axiom,(
    ! [F_6: produc1501160679le_alt > $o,A_10: arrow_475358991le_alt,B_8: arrow_475358991le_alt] :
      ( ( produc910278158_alt_o @ F_6 @ A_10 @ B_8 )
     => ( F_6 @ ( produc1347929815le_alt @ A_10 @ B_8 ) ) ) )).

thf(fact_285_curryE,axiom,(
    ! [F_5: produc1362454231le_alt > $o,A_9: list_A2115238852le_alt,B_7: list_A2115238852le_alt] :
      ( ( produc1739499928_alt_o @ F_5 @ A_9 @ B_7 )
     => ( F_5 @ ( produc776457805le_alt @ A_9 @ B_7 ) ) ) )).

thf(fact_286_curryE,axiom,(
    ! [F_5: produc1501160679le_alt > $o,A_9: arrow_475358991le_alt,B_7: arrow_475358991le_alt] :
      ( ( produc910278158_alt_o @ F_5 @ A_9 @ B_7 )
     => ( F_5 @ ( produc1347929815le_alt @ A_9 @ B_7 ) ) ) )).

thf(fact_287_curry__conv,axiom,(
    ! [F_4: produc1501160679le_alt > $o,A_8: arrow_475358991le_alt,B_6: arrow_475358991le_alt] :
      ( ( produc910278158_alt_o @ F_4 @ A_8 @ B_6 )
    <=> ( F_4 @ ( produc1347929815le_alt @ A_8 @ B_6 ) ) ) )).

thf(fact_288_equal__Nil__null,axiom,(
    ! [Xs_117: list_A2115238852le_alt] :
      ( ( equal_484611810le_alt @ Xs_117 @ nil_Ar1286194111le_alt )
    <=> ( null_A1520965063le_alt @ Xs_117 ) ) )).

thf(fact_289_Prof__def,axiom,
    ( arrow_734252939e_Prof
    = ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
      @ ^ [Uu: arrow_1429601828e_indi] : arrow_823908191le_Lin ) )).

thf(fact_290_lexord__cons__cons,axiom,(
    ! [A_7: list_A2115238852le_alt,X_64: list_l1475218533le_alt,B_5: list_A2115238852le_alt,Y_23: list_l1475218533le_alt,R_38: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ A_7 @ X_64 ) @ ( cons_l635097956le_alt @ B_5 @ Y_23 ) ) @ ( lexord469916775le_alt @ R_38 ) )
    <=> ( ( member28618436le_alt @ ( produc776457805le_alt @ A_7 @ B_5 ) @ R_38 )
        | ( ( A_7 = B_5 )
          & ( member1732936276le_alt @ ( produc1317709143le_alt @ X_64 @ Y_23 ) @ ( lexord469916775le_alt @ R_38 ) ) ) ) ) )).

thf(fact_291_lexord__cons__cons,axiom,(
    ! [A_7: arrow_475358991le_alt,X_64: list_A2115238852le_alt,B_5: arrow_475358991le_alt,Y_23: list_A2115238852le_alt,R_38: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ A_7 @ X_64 ) @ ( cons_A228743023le_alt @ B_5 @ Y_23 ) ) @ ( lexord958095404le_alt @ R_38 ) )
    <=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_7 @ B_5 ) @ R_38 )
        | ( ( A_7 = B_5 )
          & ( member28618436le_alt @ ( produc776457805le_alt @ X_64 @ Y_23 ) @ ( lexord958095404le_alt @ R_38 ) ) ) ) ) )).

thf(fact_292_distinct__butlast,axiom,(
    ! [Xs_116: list_A2115238852le_alt] :
      ( ( Xs_116 != nil_Ar1286194111le_alt )
     => ( ( distin236324274le_alt @ Xs_116 )
       => ( distin236324274le_alt @ ( butlas274947851le_alt @ Xs_116 ) ) ) ) )).

thf(fact_293_last__ConsL,axiom,(
    ! [X_63: arrow_475358991le_alt,Xs_115: list_A2115238852le_alt] :
      ( ( Xs_115 = nil_Ar1286194111le_alt )
     => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_63 @ Xs_115 ) )
        = X_63 ) ) )).

thf(fact_294_last__ConsR,axiom,(
    ! [X_62: arrow_475358991le_alt,Xs_114: list_A2115238852le_alt] :
      ( ( Xs_114 != nil_Ar1286194111le_alt )
     => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_62 @ Xs_114 ) )
        = ( last_A1217315288le_alt @ Xs_114 ) ) ) )).

thf(fact_295_top1I,axiom,(
    ! [X_61: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( top_to1969627639lt_o_o @ X_61 ) )).

thf(fact_296_top1I,axiom,(
    ! [X_61: produc1501160679le_alt > $o] :
      ( top_to1842727771lt_o_o @ X_61 ) )).

thf(fact_297_top1I,axiom,(
    ! [X_61: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( top_to2122763103lt_o_o @ X_61 ) )).

thf(fact_298_top1I,axiom,(
    ! [X_61: produc1501160679le_alt] :
      ( top_to1841428258_alt_o @ X_61 ) )).

thf(fact_299_top1I,axiom,(
    ! [X_61: arrow_1429601828e_indi] :
      ( top_to988227749indi_o @ X_61 ) )).

thf(fact_300_top1I,axiom,(
    ! [X_61: arrow_475358991le_alt] :
      ( top_to728987956_alt_o @ X_61 ) )).

thf(fact_301_equal__list__def,axiom,(
    ! [X_60: list_A2115238852le_alt,Y_22: list_A2115238852le_alt] :
      ( ( equal_484611810le_alt @ X_60 @ Y_22 )
    <=> ( X_60 = Y_22 ) ) )).

thf(fact_302_Pi__UNIV,axiom,(
    ! [A_6: produc1501160679le_alt > $o] :
      ( ( pi_Pro1701359055_alt_o @ A_6
        @ ^ [Uu: produc1501160679le_alt] : top_top_o_o )
      = top_to1842727771lt_o_o ) )).

thf(fact_303_Pi__UNIV,axiom,(
    ! [A_6: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( pi_Arr1304755663_alt_o @ A_6
        @ ^ [Uu: arrow_1429601828e_indi > produc1501160679le_alt > $o] : top_to1842727771lt_o_o )
      = top_to1969627639lt_o_o ) )).

thf(fact_304_Pi__UNIV,axiom,(
    ! [A_6: arrow_1429601828e_indi > $o] :
      ( ( pi_Arr1929480907_alt_o @ A_6
        @ ^ [Uu: arrow_1429601828e_indi] : top_to1842727771lt_o_o )
      = top_to2122763103lt_o_o ) )).

thf(fact_305_butlast_Osimps_I1_J,axiom,
    ( ( butlas274947851le_alt @ nil_Ar1286194111le_alt )
    = nil_Ar1286194111le_alt )).

thf(fact_306_lexord__Nil__right,axiom,(
    ! [X_59: list_A2115238852le_alt,R_37: produc1501160679le_alt > $o] :
      ~ ( member28618436le_alt @ ( produc776457805le_alt @ X_59 @ nil_Ar1286194111le_alt ) @ ( lexord958095404le_alt @ R_37 ) ) )).

thf(fact_307_butlast_Osimps_I2_J,axiom,(
    ! [X_58: arrow_475358991le_alt,Xs_113: list_A2115238852le_alt] :
      ( ( ( Xs_113 = nil_Ar1286194111le_alt )
       => ( ( butlas274947851le_alt @ ( cons_A228743023le_alt @ X_58 @ Xs_113 ) )
          = nil_Ar1286194111le_alt ) )
      & ( ( Xs_113 != nil_Ar1286194111le_alt )
       => ( ( butlas274947851le_alt @ ( cons_A228743023le_alt @ X_58 @ Xs_113 ) )
          = ( cons_A228743023le_alt @ X_58 @ ( butlas274947851le_alt @ Xs_113 ) ) ) ) ) )).

thf(fact_308_last_Osimps,axiom,(
    ! [X_57: arrow_475358991le_alt,Xs_112: list_A2115238852le_alt] :
      ( ( ( Xs_112 = nil_Ar1286194111le_alt )
       => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_57 @ Xs_112 ) )
          = X_57 ) )
      & ( ( Xs_112 != nil_Ar1286194111le_alt )
       => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_57 @ Xs_112 ) )
          = ( last_A1217315288le_alt @ Xs_112 ) ) ) ) )).

thf(fact_309_lexord__Nil__left,axiom,(
    ! [Y_21: list_A2115238852le_alt,R_36: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ nil_Ar1286194111le_alt @ Y_21 ) @ ( lexord958095404le_alt @ R_36 ) )
    <=> ? [A: arrow_475358991le_alt,X_2: list_A2115238852le_alt] :
          ( Y_21
          = ( cons_A228743023le_alt @ A @ X_2 ) ) ) )).

thf(fact_310_lexord__irreflexive,axiom,(
    ! [Xs_111: list_l1475218533le_alt,R_35: produc1362454231le_alt > $o] :
      ( ! [X_2: list_A2115238852le_alt] :
          ~ ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ X_2 ) @ R_35 )
     => ~ ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_111 @ Xs_111 ) @ ( lexord469916775le_alt @ R_35 ) ) ) )).

thf(fact_311_lexord__irreflexive,axiom,(
    ! [Xs_111: list_A2115238852le_alt,R_35: produc1501160679le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ X_2 ) @ R_35 )
     => ~ ( member28618436le_alt @ ( produc776457805le_alt @ Xs_111 @ Xs_111 ) @ ( lexord958095404le_alt @ R_35 ) ) ) )).

thf(fact_312_lexord__linear,axiom,(
    ! [X_56: list_l1475218533le_alt,Y_20: list_l1475218533le_alt,R_34: produc1362454231le_alt > $o] :
      ( ! [A: list_A2115238852le_alt,B: list_A2115238852le_alt] :
          ( ( member28618436le_alt @ ( produc776457805le_alt @ A @ B ) @ R_34 )
          | ( A = B )
          | ( member28618436le_alt @ ( produc776457805le_alt @ B @ A ) @ R_34 ) )
     => ( ( member1732936276le_alt @ ( produc1317709143le_alt @ X_56 @ Y_20 ) @ ( lexord469916775le_alt @ R_34 ) )
        | ( X_56 = Y_20 )
        | ( member1732936276le_alt @ ( produc1317709143le_alt @ Y_20 @ X_56 ) @ ( lexord469916775le_alt @ R_34 ) ) ) ) )).

thf(fact_313_lexord__linear,axiom,(
    ! [X_56: list_A2115238852le_alt,Y_20: list_A2115238852le_alt,R_34: produc1501160679le_alt > $o] :
      ( ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
          ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ R_34 )
          | ( A = B )
          | ( member214075476le_alt @ ( produc1347929815le_alt @ B @ A ) @ R_34 ) )
     => ( ( member28618436le_alt @ ( produc776457805le_alt @ X_56 @ Y_20 ) @ ( lexord958095404le_alt @ R_34 ) )
        | ( X_56 = Y_20 )
        | ( member28618436le_alt @ ( produc776457805le_alt @ Y_20 @ X_56 ) @ ( lexord958095404le_alt @ R_34 ) ) ) ) )).

thf(fact_314_UNIV__I,axiom,(
    ! [X_55: produc1362454231le_alt] :
      ( member28618436le_alt @ X_55 @ top_to1039387826_alt_o ) )).

thf(fact_315_UNIV__I,axiom,(
    ! [X_55: $o] :
      ( member_o @ X_55 @ top_top_o_o ) )).

thf(fact_316_UNIV__I,axiom,(
    ! [X_55: arrow_1429601828e_indi] :
      ( member2052026769e_indi @ X_55 @ top_to988227749indi_o ) )).

thf(fact_317_UNIV__I,axiom,(
    ! [X_55: arrow_475358991le_alt] :
      ( member84363362le_alt @ X_55 @ top_to728987956_alt_o ) )).

thf(fact_318_UNIV__I,axiom,(
    ! [X_55: produc1501160679le_alt] :
      ( member214075476le_alt @ X_55 @ top_to1841428258_alt_o ) )).

thf(fact_319_UNIV__I,axiom,(
    ! [X_55: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( member526088951_alt_o @ X_55 @ top_to2122763103lt_o_o ) )).

thf(fact_320_UNIV__I,axiom,(
    ! [X_55: produc1501160679le_alt > $o] :
      ( member377231867_alt_o @ X_55 @ top_to1842727771lt_o_o ) )).

thf(fact_321_UNIV__I,axiom,(
    ! [X_55: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( member616898751_alt_o @ X_55 @ top_to1969627639lt_o_o ) )).

thf(fact_322_iso__tuple__UNIV__I,axiom,(
    ! [X_54: produc1362454231le_alt] :
      ( member28618436le_alt @ X_54 @ top_to1039387826_alt_o ) )).

thf(fact_323_iso__tuple__UNIV__I,axiom,(
    ! [X_54: $o] :
      ( member_o @ X_54 @ top_top_o_o ) )).

thf(fact_324_iso__tuple__UNIV__I,axiom,(
    ! [X_54: arrow_1429601828e_indi] :
      ( member2052026769e_indi @ X_54 @ top_to988227749indi_o ) )).

thf(fact_325_iso__tuple__UNIV__I,axiom,(
    ! [X_54: arrow_475358991le_alt] :
      ( member84363362le_alt @ X_54 @ top_to728987956_alt_o ) )).

thf(fact_326_iso__tuple__UNIV__I,axiom,(
    ! [X_54: produc1501160679le_alt] :
      ( member214075476le_alt @ X_54 @ top_to1841428258_alt_o ) )).

thf(fact_327_iso__tuple__UNIV__I,axiom,(
    ! [X_54: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( member526088951_alt_o @ X_54 @ top_to2122763103lt_o_o ) )).

thf(fact_328_iso__tuple__UNIV__I,axiom,(
    ! [X_54: produc1501160679le_alt > $o] :
      ( member377231867_alt_o @ X_54 @ top_to1842727771lt_o_o ) )).

thf(fact_329_iso__tuple__UNIV__I,axiom,(
    ! [X_54: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( member616898751_alt_o @ X_54 @ top_to1969627639lt_o_o ) )).

thf(fact_330_top__apply,axiom,(
    ! [X_53: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( ( top_to1969627639lt_o_o @ X_53 )
    <=> top_top_o ) )).

thf(fact_331_top__apply,axiom,(
    ! [X_53: produc1501160679le_alt > $o] :
      ( ( top_to1842727771lt_o_o @ X_53 )
    <=> top_top_o ) )).

thf(fact_332_top__apply,axiom,(
    ! [X_53: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( ( top_to2122763103lt_o_o @ X_53 )
    <=> top_top_o ) )).

thf(fact_333_top__apply,axiom,(
    ! [X_53: produc1501160679le_alt] :
      ( ( top_to1841428258_alt_o @ X_53 )
    <=> top_top_o ) )).

thf(fact_334_top__apply,axiom,(
    ! [X_53: arrow_1429601828e_indi] :
      ( ( top_to988227749indi_o @ X_53 )
    <=> top_top_o ) )).

thf(fact_335_top__apply,axiom,(
    ! [X_53: arrow_475358991le_alt] :
      ( ( top_to728987956_alt_o @ X_53 )
    <=> top_top_o ) )).

thf(fact_336_takeWhile__not__last,axiom,(
    ! [Xs_110: list_A2115238852le_alt] :
      ( ( Xs_110 != nil_Ar1286194111le_alt )
     => ( ( distin236324274le_alt @ Xs_110 )
       => ( ( takeWh1696291512le_alt
            @ ^ [Y_1: arrow_475358991le_alt] :
                ( (~)
                @ ( Y_1
                  = ( last_A1217315288le_alt @ Xs_110 ) ) )
            @ Xs_110 )
          = ( butlas274947851le_alt @ Xs_110 ) ) ) ) )).

thf(fact_337_partition_Osimps_I1_J,axiom,(
    ! [P_25: arrow_475358991le_alt > $o] :
      ( ( partit1487577784le_alt @ P_25 @ nil_Ar1286194111le_alt )
      = ( produc776457805le_alt @ nil_Ar1286194111le_alt @ nil_Ar1286194111le_alt ) ) )).

thf(fact_338_takeWhile_Osimps_I1_J,axiom,(
    ! [P_24: arrow_475358991le_alt > $o] :
      ( ( takeWh1696291512le_alt @ P_24 @ nil_Ar1286194111le_alt )
      = nil_Ar1286194111le_alt ) )).

thf(fact_339_distinct__takeWhile,axiom,(
    ! [P_23: arrow_475358991le_alt > $o,Xs_109: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_109 )
     => ( distin236324274le_alt @ ( takeWh1696291512le_alt @ P_23 @ Xs_109 ) ) ) )).

thf(fact_340_takeWhile_Osimps_I2_J,axiom,(
    ! [Xs_108: list_A2115238852le_alt,P_22: arrow_475358991le_alt > $o,X_52: arrow_475358991le_alt] :
      ( ( ( P_22 @ X_52 )
       => ( ( takeWh1696291512le_alt @ P_22 @ ( cons_A228743023le_alt @ X_52 @ Xs_108 ) )
          = ( cons_A228743023le_alt @ X_52 @ ( takeWh1696291512le_alt @ P_22 @ Xs_108 ) ) ) )
      & ( ~ ( P_22 @ X_52 )
       => ( ( takeWh1696291512le_alt @ P_22 @ ( cons_A228743023le_alt @ X_52 @ Xs_108 ) )
          = nil_Ar1286194111le_alt ) ) ) )).

thf(fact_341_UNIV__def,axiom,
    ( top_to1969627639lt_o_o
    = ( collec2009291517_alt_o
      @ ^ [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : $true ) )).

thf(fact_342_UNIV__def,axiom,
    ( top_to2122763103lt_o_o
    = ( collec682858041_alt_o
      @ ^ [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] : $true ) )).

thf(fact_343_UNIV__def,axiom,
    ( top_to1841428258_alt_o
    = ( collec869865362le_alt
      @ ^ [X_2: produc1501160679le_alt] : $true ) )).

thf(fact_344_UNIV__def,axiom,
    ( top_to988227749indi_o
    = ( collec22405327e_indi
      @ ^ [X_2: arrow_1429601828e_indi] : $true ) )).

thf(fact_345_UNIV__def,axiom,
    ( top_to728987956_alt_o
    = ( collec742074788le_alt
      @ ^ [X_2: arrow_475358991le_alt] : $true ) )).

thf(fact_346_UNIV__def,axiom,
    ( top_to1842727771lt_o_o
    = ( collec94295101_alt_o
      @ ^ [X_2: produc1501160679le_alt > $o] : $true ) )).

thf(fact_347_UNIV__eq__I,axiom,(
    ! [A_5: produc1362454231le_alt > $o] :
      ( ! [X_2: produc1362454231le_alt] :
          ( member28618436le_alt @ X_2 @ A_5 )
     => ( top_to1039387826_alt_o = A_5 ) ) )).

thf(fact_348_UNIV__eq__I,axiom,(
    ! [A_5: $o > $o] :
      ( ! [X_2: $o] :
          ( member_o @ X_2 @ A_5 )
     => ( top_top_o_o = A_5 ) ) )).

thf(fact_349_UNIV__eq__I,axiom,(
    ! [A_5: arrow_1429601828e_indi > $o] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( member2052026769e_indi @ X_2 @ A_5 )
     => ( top_to988227749indi_o = A_5 ) ) )).

thf(fact_350_UNIV__eq__I,axiom,(
    ! [A_5: arrow_475358991le_alt > $o] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( member84363362le_alt @ X_2 @ A_5 )
     => ( top_to728987956_alt_o = A_5 ) ) )).

thf(fact_351_UNIV__eq__I,axiom,(
    ! [A_5: produc1501160679le_alt > $o] :
      ( ! [X_2: produc1501160679le_alt] :
          ( member214075476le_alt @ X_2 @ A_5 )
     => ( top_to1841428258_alt_o = A_5 ) ) )).

thf(fact_352_UNIV__eq__I,axiom,(
    ! [A_5: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( member526088951_alt_o @ X_2 @ A_5 )
     => ( top_to2122763103lt_o_o = A_5 ) ) )).

thf(fact_353_UNIV__eq__I,axiom,(
    ! [A_5: ( produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( member377231867_alt_o @ X_2 @ A_5 )
     => ( top_to1842727771lt_o_o = A_5 ) ) )).

thf(fact_354_UNIV__eq__I,axiom,(
    ! [A_5: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( member616898751_alt_o @ X_2 @ A_5 )
     => ( top_to1969627639lt_o_o = A_5 ) ) )).

thf(fact_355_UNIV__witness,axiom,(
    ? [X_2: produc1362454231le_alt] :
      ( member28618436le_alt @ X_2 @ top_to1039387826_alt_o ) )).

thf(fact_356_UNIV__witness,axiom,(
    ? [X_2: $o] :
      ( member_o @ X_2 @ top_top_o_o ) )).

thf(fact_357_UNIV__witness,axiom,(
    ? [X_2: arrow_1429601828e_indi] :
      ( member2052026769e_indi @ X_2 @ top_to988227749indi_o ) )).

thf(fact_358_UNIV__witness,axiom,(
    ? [X_2: arrow_475358991le_alt] :
      ( member84363362le_alt @ X_2 @ top_to728987956_alt_o ) )).

thf(fact_359_UNIV__witness,axiom,(
    ? [X_2: produc1501160679le_alt] :
      ( member214075476le_alt @ X_2 @ top_to1841428258_alt_o ) )).

thf(fact_360_UNIV__witness,axiom,(
    ? [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
      ( member526088951_alt_o @ X_2 @ top_to2122763103lt_o_o ) )).

thf(fact_361_UNIV__witness,axiom,(
    ? [X_2: produc1501160679le_alt > $o] :
      ( member377231867_alt_o @ X_2 @ top_to1842727771lt_o_o ) )).

thf(fact_362_UNIV__witness,axiom,(
    ? [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
      ( member616898751_alt_o @ X_2 @ top_to1969627639lt_o_o ) )).

thf(fact_363_Lin__def,axiom,
    ( arrow_823908191le_Lin
    = ( collec94295101_alt_o @ ( order_1995917111le_alt @ top_to728987956_alt_o ) ) )).

thf(fact_364_append__butlast__last__id,axiom,(
    ! [Xs_107: list_A2115238852le_alt] :
      ( ( Xs_107 != nil_Ar1286194111le_alt )
     => ( ( append179082452le_alt @ ( butlas274947851le_alt @ Xs_107 ) @ ( cons_A228743023le_alt @ ( last_A1217315288le_alt @ Xs_107 ) @ nil_Ar1286194111le_alt ) )
        = Xs_107 ) ) )).

thf(fact_365_snoc__eq__iff__butlast,axiom,(
    ! [Xs_106: list_A2115238852le_alt,X_51: arrow_475358991le_alt,Ys_54: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_106 @ ( cons_A228743023le_alt @ X_51 @ nil_Ar1286194111le_alt ) )
        = Ys_54 )
    <=> ( ( Ys_54 != nil_Ar1286194111le_alt )
        & ( ( butlas274947851le_alt @ Ys_54 )
          = Xs_106 )
        & ( ( last_A1217315288le_alt @ Ys_54 )
          = X_51 ) ) ) )).

thf(fact_366_Nil2__notin__lex,axiom,(
    ! [Xs_105: list_A2115238852le_alt,R_33: produc1501160679le_alt > $o] :
      ~ ( member28618436le_alt @ ( produc776457805le_alt @ Xs_105 @ nil_Ar1286194111le_alt ) @ ( lex_Ar1415517219le_alt @ R_33 ) ) )).

thf(fact_367_Nil__notin__lex,axiom,(
    ! [Ys_53: list_A2115238852le_alt,R_32: produc1501160679le_alt > $o] :
      ~ ( member28618436le_alt @ ( produc776457805le_alt @ nil_Ar1286194111le_alt @ Ys_53 ) @ ( lex_Ar1415517219le_alt @ R_32 ) ) )).

thf(fact_368_append__eq__appendI,axiom,(
    ! [Ys_52: list_A2115238852le_alt,Us_3: list_A2115238852le_alt,Xs_104: list_A2115238852le_alt,Xs1_1: list_A2115238852le_alt,Zs_9: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_104 @ Xs1_1 )
        = Zs_9 )
     => ( ( Ys_52
          = ( append179082452le_alt @ Xs1_1 @ Us_3 ) )
       => ( ( append179082452le_alt @ Xs_104 @ Ys_52 )
          = ( append179082452le_alt @ Zs_9 @ Us_3 ) ) ) ) )).

thf(fact_369_append__same__eq,axiom,(
    ! [Ys_51: list_A2115238852le_alt,Xs_103: list_A2115238852le_alt,Zs_8: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Ys_51 @ Xs_103 )
        = ( append179082452le_alt @ Zs_8 @ Xs_103 ) )
    <=> ( Ys_51 = Zs_8 ) ) )).

thf(fact_370_same__append__eq,axiom,(
    ! [Xs_102: list_A2115238852le_alt,Ys_50: list_A2115238852le_alt,Zs_7: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_102 @ Ys_50 )
        = ( append179082452le_alt @ Xs_102 @ Zs_7 ) )
    <=> ( Ys_50 = Zs_7 ) ) )).

thf(fact_371_append__eq__append__conv2,axiom,(
    ! [Xs_101: list_A2115238852le_alt,Ys_49: list_A2115238852le_alt,Zs_6: list_A2115238852le_alt,Ts: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_101 @ Ys_49 )
        = ( append179082452le_alt @ Zs_6 @ Ts ) )
    <=> ? [Us: list_A2115238852le_alt] :
          ( ( ( Xs_101
              = ( append179082452le_alt @ Zs_6 @ Us ) )
            & ( ( append179082452le_alt @ Us @ Ys_49 )
              = Ts ) )
          | ( ( ( append179082452le_alt @ Xs_101 @ Us )
              = Zs_6 )
            & ( Ys_49
              = ( append179082452le_alt @ Us @ Ts ) ) ) ) ) )).

thf(fact_372_append__assoc,axiom,(
    ! [Xs_100: list_A2115238852le_alt,Ys_48: list_A2115238852le_alt,Zs_5: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( append179082452le_alt @ Xs_100 @ Ys_48 ) @ Zs_5 )
      = ( append179082452le_alt @ Xs_100 @ ( append179082452le_alt @ Ys_48 @ Zs_5 ) ) ) )).

thf(fact_373_append__Cons,axiom,(
    ! [X_50: arrow_475358991le_alt,Xs_99: list_A2115238852le_alt,Ys_47: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( cons_A228743023le_alt @ X_50 @ Xs_99 ) @ Ys_47 )
      = ( cons_A228743023le_alt @ X_50 @ ( append179082452le_alt @ Xs_99 @ Ys_47 ) ) ) )).

thf(fact_374_Cons__eq__appendI,axiom,(
    ! [Xs_98: list_A2115238852le_alt,Zs_4: list_A2115238852le_alt,X_49: arrow_475358991le_alt,Xs1: list_A2115238852le_alt,Ys_46: list_A2115238852le_alt] :
      ( ( ( cons_A228743023le_alt @ X_49 @ Xs1 )
        = Ys_46 )
     => ( ( Xs_98
          = ( append179082452le_alt @ Xs1 @ Zs_4 ) )
       => ( ( cons_A228743023le_alt @ X_49 @ Xs_98 )
          = ( append179082452le_alt @ Ys_46 @ Zs_4 ) ) ) ) )).

thf(fact_375_append__Nil,axiom,(
    ! [Ys_45: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_45 )
      = Ys_45 ) )).

thf(fact_376_Nil__is__append__conv,axiom,(
    ! [Xs_97: list_A2115238852le_alt,Ys_44: list_A2115238852le_alt] :
      ( ( nil_Ar1286194111le_alt
        = ( append179082452le_alt @ Xs_97 @ Ys_44 ) )
    <=> ( ( Xs_97 = nil_Ar1286194111le_alt )
        & ( Ys_44 = nil_Ar1286194111le_alt ) ) ) )).

thf(fact_377_append__Nil2,axiom,(
    ! [Xs_96: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ Xs_96 @ nil_Ar1286194111le_alt )
      = Xs_96 ) )).

thf(fact_378_self__append__conv,axiom,(
    ! [Xs_95: list_A2115238852le_alt,Ys_43: list_A2115238852le_alt] :
      ( ( Xs_95
        = ( append179082452le_alt @ Xs_95 @ Ys_43 ) )
    <=> ( Ys_43 = nil_Ar1286194111le_alt ) ) )).

thf(fact_379_self__append__conv2,axiom,(
    ! [Ys_42: list_A2115238852le_alt,Xs_94: list_A2115238852le_alt] :
      ( ( Ys_42
        = ( append179082452le_alt @ Xs_94 @ Ys_42 ) )
    <=> ( Xs_94 = nil_Ar1286194111le_alt ) ) )).

thf(fact_380_append__is__Nil__conv,axiom,(
    ! [Xs_93: list_A2115238852le_alt,Ys_41: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_93 @ Ys_41 )
        = nil_Ar1286194111le_alt )
    <=> ( ( Xs_93 = nil_Ar1286194111le_alt )
        & ( Ys_41 = nil_Ar1286194111le_alt ) ) ) )).

thf(fact_381_append__self__conv,axiom,(
    ! [Xs_92: list_A2115238852le_alt,Ys_40: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_92 @ Ys_40 )
        = Xs_92 )
    <=> ( Ys_40 = nil_Ar1286194111le_alt ) ) )).

thf(fact_382_append__self__conv2,axiom,(
    ! [Xs_91: list_A2115238852le_alt,Ys_39: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_91 @ Ys_39 )
        = Ys_39 )
    <=> ( Xs_91 = nil_Ar1286194111le_alt ) ) )).

thf(fact_383_eq__Nil__appendI,axiom,(
    ! [Xs_90: list_A2115238852le_alt,Ys_38: list_A2115238852le_alt] :
      ( ( Xs_90 = Ys_38 )
     => ( Xs_90
        = ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_38 ) ) ) )).

thf(fact_384_append__eq__Cons__conv,axiom,(
    ! [Ys_37: list_A2115238852le_alt,Zs_3: list_A2115238852le_alt,X_48: arrow_475358991le_alt,Xs_89: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Ys_37 @ Zs_3 )
        = ( cons_A228743023le_alt @ X_48 @ Xs_89 ) )
    <=> ( ( ( Ys_37 = nil_Ar1286194111le_alt )
          & ( Zs_3
            = ( cons_A228743023le_alt @ X_48 @ Xs_89 ) ) )
        | ? [Ys_36: list_A2115238852le_alt] :
            ( ( Ys_37
              = ( cons_A228743023le_alt @ X_48 @ Ys_36 ) )
            & ( ( append179082452le_alt @ Ys_36 @ Zs_3 )
              = Xs_89 ) ) ) ) )).

thf(fact_385_Cons__eq__append__conv,axiom,(
    ! [X_47: arrow_475358991le_alt,Xs_88: list_A2115238852le_alt,Ys_35: list_A2115238852le_alt,Zs_2: list_A2115238852le_alt] :
      ( ( ( cons_A228743023le_alt @ X_47 @ Xs_88 )
        = ( append179082452le_alt @ Ys_35 @ Zs_2 ) )
    <=> ( ( ( Ys_35 = nil_Ar1286194111le_alt )
          & ( ( cons_A228743023le_alt @ X_47 @ Xs_88 )
            = Zs_2 ) )
        | ? [Ys_36: list_A2115238852le_alt] :
            ( ( ( cons_A228743023le_alt @ X_47 @ Ys_36 )
              = Ys_35 )
            & ( Xs_88
              = ( append179082452le_alt @ Ys_36 @ Zs_2 ) ) ) ) ) )).

thf(fact_386_append1__eq__conv,axiom,(
    ! [Xs_87: list_A2115238852le_alt,X_46: arrow_475358991le_alt,Ys_34: list_A2115238852le_alt,Y_19: arrow_475358991le_alt] :
      ( ( ( append179082452le_alt @ Xs_87 @ ( cons_A228743023le_alt @ X_46 @ nil_Ar1286194111le_alt ) )
        = ( append179082452le_alt @ Ys_34 @ ( cons_A228743023le_alt @ Y_19 @ nil_Ar1286194111le_alt ) ) )
    <=> ( ( Xs_87 = Ys_34 )
        & ( X_46 = Y_19 ) ) ) )).

thf(fact_387_takeWhile__tail,axiom,(
    ! [Xs_86: list_A2115238852le_alt,L: list_A2115238852le_alt,P_21: arrow_475358991le_alt > $o,X_45: arrow_475358991le_alt] :
      ( ~ ( P_21 @ X_45 )
     => ( ( takeWh1696291512le_alt @ P_21 @ ( append179082452le_alt @ Xs_86 @ ( cons_A228743023le_alt @ X_45 @ L ) ) )
        = ( takeWh1696291512le_alt @ P_21 @ Xs_86 ) ) ) )).

thf(fact_388_butlast__append,axiom,(
    ! [Xs_85: list_A2115238852le_alt,Ys_33: list_A2115238852le_alt] :
      ( ( ( Ys_33 = nil_Ar1286194111le_alt )
       => ( ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_85 @ Ys_33 ) )
          = ( butlas274947851le_alt @ Xs_85 ) ) )
      & ( ( Ys_33 != nil_Ar1286194111le_alt )
       => ( ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_85 @ Ys_33 ) )
          = ( append179082452le_alt @ Xs_85 @ ( butlas274947851le_alt @ Ys_33 ) ) ) ) ) )).

thf(fact_389_last__append,axiom,(
    ! [Xs_84: list_A2115238852le_alt,Ys_32: list_A2115238852le_alt] :
      ( ( ( Ys_32 = nil_Ar1286194111le_alt )
       => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_84 @ Ys_32 ) )
          = ( last_A1217315288le_alt @ Xs_84 ) ) )
      & ( ( Ys_32 != nil_Ar1286194111le_alt )
       => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_84 @ Ys_32 ) )
          = ( last_A1217315288le_alt @ Ys_32 ) ) ) ) )).

thf(fact_390_last__appendR,axiom,(
    ! [Xs_83: list_A2115238852le_alt,Ys_31: list_A2115238852le_alt] :
      ( ( Ys_31 != nil_Ar1286194111le_alt )
     => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_83 @ Ys_31 ) )
        = ( last_A1217315288le_alt @ Ys_31 ) ) ) )).

thf(fact_391_last__appendL,axiom,(
    ! [Xs_82: list_A2115238852le_alt,Ys_30: list_A2115238852le_alt] :
      ( ( Ys_30 = nil_Ar1286194111le_alt )
     => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_82 @ Ys_30 ) )
        = ( last_A1217315288le_alt @ Xs_82 ) ) ) )).

thf(fact_392_lexord__append__leftI,axiom,(
    ! [X_44: list_A2115238852le_alt,U_2: list_A2115238852le_alt,V_1: list_A2115238852le_alt,R_31: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ U_2 @ V_1 ) @ ( lexord958095404le_alt @ R_31 ) )
     => ( member28618436le_alt @ ( produc776457805le_alt @ ( append179082452le_alt @ X_44 @ U_2 ) @ ( append179082452le_alt @ X_44 @ V_1 ) ) @ ( lexord958095404le_alt @ R_31 ) ) ) )).

thf(fact_393_butlast__snoc,axiom,(
    ! [Xs_81: list_A2115238852le_alt,X_43: arrow_475358991le_alt] :
      ( ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_81 @ ( cons_A228743023le_alt @ X_43 @ nil_Ar1286194111le_alt ) ) )
      = Xs_81 ) )).

thf(fact_394_last__snoc,axiom,(
    ! [Xs_80: list_A2115238852le_alt,X_42: arrow_475358991le_alt] :
      ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_80 @ ( cons_A228743023le_alt @ X_42 @ nil_Ar1286194111le_alt ) ) )
      = X_42 ) )).

thf(fact_395_lexord__append__left__rightI,axiom,(
    ! [U_1: list_A2115238852le_alt,X_41: list_A2115238852le_alt,Y_18: list_A2115238852le_alt,A_4: arrow_475358991le_alt,B_4: arrow_475358991le_alt,R_30: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ A_4 @ B_4 ) @ R_30 )
     => ( member28618436le_alt @ ( produc776457805le_alt @ ( append179082452le_alt @ U_1 @ ( cons_A228743023le_alt @ A_4 @ X_41 ) ) @ ( append179082452le_alt @ U_1 @ ( cons_A228743023le_alt @ B_4 @ Y_18 ) ) ) @ ( lexord958095404le_alt @ R_30 ) ) ) )).

thf(fact_396_lexord__append__left__rightI,axiom,(
    ! [U_1: list_l1475218533le_alt,X_41: list_l1475218533le_alt,Y_18: list_l1475218533le_alt,A_4: list_A2115238852le_alt,B_4: list_A2115238852le_alt,R_30: produc1362454231le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ A_4 @ B_4 ) @ R_30 )
     => ( member1732936276le_alt @ ( produc1317709143le_alt @ ( append1166001599le_alt @ U_1 @ ( cons_l635097956le_alt @ A_4 @ X_41 ) ) @ ( append1166001599le_alt @ U_1 @ ( cons_l635097956le_alt @ B_4 @ Y_18 ) ) ) @ ( lexord469916775le_alt @ R_30 ) ) ) )).

thf(fact_397_lexord__append__rightI,axiom,(
    ! [X_40: list_A2115238852le_alt,R_29: produc1501160679le_alt > $o,Y_17: list_A2115238852le_alt] :
      ( ? [B: arrow_475358991le_alt,Z: list_A2115238852le_alt] :
          ( Y_17
          = ( cons_A228743023le_alt @ B @ Z ) )
     => ( member28618436le_alt @ ( produc776457805le_alt @ X_40 @ ( append179082452le_alt @ X_40 @ Y_17 ) ) @ ( lexord958095404le_alt @ R_29 ) ) ) )).

thf(fact_398_lexord__append__leftD,axiom,(
    ! [X_39: list_l1475218533le_alt,U: list_l1475218533le_alt,V: list_l1475218533le_alt,R_28: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( append1166001599le_alt @ X_39 @ U ) @ ( append1166001599le_alt @ X_39 @ V ) ) @ ( lexord469916775le_alt @ R_28 ) )
     => ( ! [A: list_A2115238852le_alt] :
            ~ ( member28618436le_alt @ ( produc776457805le_alt @ A @ A ) @ R_28 )
       => ( member1732936276le_alt @ ( produc1317709143le_alt @ U @ V ) @ ( lexord469916775le_alt @ R_28 ) ) ) ) )).

thf(fact_399_lexord__append__leftD,axiom,(
    ! [X_39: list_A2115238852le_alt,U: list_A2115238852le_alt,V: list_A2115238852le_alt,R_28: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( append179082452le_alt @ X_39 @ U ) @ ( append179082452le_alt @ X_39 @ V ) ) @ ( lexord958095404le_alt @ R_28 ) )
     => ( ! [A: arrow_475358991le_alt] :
            ~ ( member214075476le_alt @ ( produc1347929815le_alt @ A @ A ) @ R_28 )
       => ( member28618436le_alt @ ( produc776457805le_alt @ U @ V ) @ ( lexord958095404le_alt @ R_28 ) ) ) ) )).

thf(fact_400_rev__induct,axiom,(
    ! [Xs_79: list_A2115238852le_alt,P_20: list_A2115238852le_alt > $o] :
      ( ( P_20 @ nil_Ar1286194111le_alt )
     => ( ! [X_2: arrow_475358991le_alt,Xs_21: list_A2115238852le_alt] :
            ( ( P_20 @ Xs_21 )
           => ( P_20 @ ( append179082452le_alt @ Xs_21 @ ( cons_A228743023le_alt @ X_2 @ nil_Ar1286194111le_alt ) ) ) )
       => ( P_20 @ Xs_79 ) ) ) )).

thf(fact_401_rev__cases,axiom,(
    ! [Xs_78: list_A2115238852le_alt] :
      ( ( Xs_78 != nil_Ar1286194111le_alt )
     => ~ ! [Ys: list_A2115238852le_alt,Y_1: arrow_475358991le_alt] :
            ( Xs_78
           != ( append179082452le_alt @ Ys @ ( cons_A228743023le_alt @ Y_1 @ nil_Ar1286194111le_alt ) ) ) ) )).

thf(fact_402_snoc__listrel1__snoc__iff,axiom,(
    ! [Xs_77: list_l1475218533le_alt,X_38: list_A2115238852le_alt,Ys_29: list_l1475218533le_alt,Y_16: list_A2115238852le_alt,R_27: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( append1166001599le_alt @ Xs_77 @ ( cons_l635097956le_alt @ X_38 @ nil_li1907286804le_alt ) ) @ ( append1166001599le_alt @ Ys_29 @ ( cons_l635097956le_alt @ Y_16 @ nil_li1907286804le_alt ) ) ) @ ( listre620555643le_alt @ R_27 ) )
    <=> ( ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_77 @ Ys_29 ) @ ( listre620555643le_alt @ R_27 ) )
          & ( X_38 = Y_16 ) )
        | ( ( Xs_77 = Ys_29 )
          & ( member28618436le_alt @ ( produc776457805le_alt @ X_38 @ Y_16 ) @ R_27 ) ) ) ) )).

thf(fact_403_snoc__listrel1__snoc__iff,axiom,(
    ! [Xs_77: list_A2115238852le_alt,X_38: arrow_475358991le_alt,Ys_29: list_A2115238852le_alt,Y_16: arrow_475358991le_alt,R_27: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( append179082452le_alt @ Xs_77 @ ( cons_A228743023le_alt @ X_38 @ nil_Ar1286194111le_alt ) ) @ ( append179082452le_alt @ Ys_29 @ ( cons_A228743023le_alt @ Y_16 @ nil_Ar1286194111le_alt ) ) ) @ ( listre2064003096le_alt @ R_27 ) )
    <=> ( ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_77 @ Ys_29 ) @ ( listre2064003096le_alt @ R_27 ) )
          & ( X_38 = Y_16 ) )
        | ( ( Xs_77 = Ys_29 )
          & ( member214075476le_alt @ ( produc1347929815le_alt @ X_38 @ Y_16 ) @ R_27 ) ) ) ) )).

thf(fact_404_rotate1__def,axiom,(
    ! [Xs_76: list_A2115238852le_alt] :
      ( ( rotate335349260le_alt @ Xs_76 )
      = ( list_c1623890103le_alt @ nil_Ar1286194111le_alt
        @ ^ [X_2: arrow_475358991le_alt,Xs_21: list_A2115238852le_alt] :
            ( append179082452le_alt @ Xs_21 @ ( cons_A228743023le_alt @ X_2 @ nil_Ar1286194111le_alt ) )
        @ Xs_76 ) ) )).

thf(fact_405_rotate1__is__Nil__conv,axiom,(
    ! [Xs_75: list_A2115238852le_alt] :
      ( ( ( rotate335349260le_alt @ Xs_75 )
        = nil_Ar1286194111le_alt )
    <=> ( Xs_75 = nil_Ar1286194111le_alt ) ) )).

thf(fact_406_distinct1__rotate,axiom,(
    ! [Xs_74: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( rotate335349260le_alt @ Xs_74 ) )
    <=> ( distin236324274le_alt @ Xs_74 ) ) )).

thf(fact_407_listrel1I2,axiom,(
    ! [X_37: arrow_475358991le_alt,Xs_73: list_A2115238852le_alt,Ys_28: list_A2115238852le_alt,R_26: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_73 @ Ys_28 ) @ ( listre2064003096le_alt @ R_26 ) )
     => ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_37 @ Xs_73 ) @ ( cons_A228743023le_alt @ X_37 @ Ys_28 ) ) @ ( listre2064003096le_alt @ R_26 ) ) ) )).

thf(fact_408_not__listrel1__Nil,axiom,(
    ! [Xs_72: list_A2115238852le_alt,R_25: produc1501160679le_alt > $o] :
      ~ ( member28618436le_alt @ ( produc776457805le_alt @ Xs_72 @ nil_Ar1286194111le_alt ) @ ( listre2064003096le_alt @ R_25 ) ) )).

thf(fact_409_not__Nil__listrel1,axiom,(
    ! [Xs_71: list_A2115238852le_alt,R_24: produc1501160679le_alt > $o] :
      ~ ( member28618436le_alt @ ( produc776457805le_alt @ nil_Ar1286194111le_alt @ Xs_71 ) @ ( listre2064003096le_alt @ R_24 ) ) )).

thf(fact_410_append__listrel1I,axiom,(
    ! [Us_2: list_A2115238852le_alt,Vs_2: list_A2115238852le_alt,Xs_70: list_A2115238852le_alt,Ys_27: list_A2115238852le_alt,R_23: produc1501160679le_alt > $o] :
      ( ( ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_70 @ Ys_27 ) @ ( listre2064003096le_alt @ R_23 ) )
          & ( Us_2 = Vs_2 ) )
        | ( ( Xs_70 = Ys_27 )
          & ( member28618436le_alt @ ( produc776457805le_alt @ Us_2 @ Vs_2 ) @ ( listre2064003096le_alt @ R_23 ) ) ) )
     => ( member28618436le_alt @ ( produc776457805le_alt @ ( append179082452le_alt @ Xs_70 @ Us_2 ) @ ( append179082452le_alt @ Ys_27 @ Vs_2 ) ) @ ( listre2064003096le_alt @ R_23 ) ) ) )).

thf(fact_411_Cons__listrel1__Cons,axiom,(
    ! [X_36: list_A2115238852le_alt,Xs_69: list_l1475218533le_alt,Y_15: list_A2115238852le_alt,Ys_26: list_l1475218533le_alt,R_22: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ X_36 @ Xs_69 ) @ ( cons_l635097956le_alt @ Y_15 @ Ys_26 ) ) @ ( listre620555643le_alt @ R_22 ) )
    <=> ( ( ( member28618436le_alt @ ( produc776457805le_alt @ X_36 @ Y_15 ) @ R_22 )
          & ( Xs_69 = Ys_26 ) )
        | ( ( X_36 = Y_15 )
          & ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_69 @ Ys_26 ) @ ( listre620555643le_alt @ R_22 ) ) ) ) ) )).

thf(fact_412_Cons__listrel1__Cons,axiom,(
    ! [X_36: arrow_475358991le_alt,Xs_69: list_A2115238852le_alt,Y_15: arrow_475358991le_alt,Ys_26: list_A2115238852le_alt,R_22: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_36 @ Xs_69 ) @ ( cons_A228743023le_alt @ Y_15 @ Ys_26 ) ) @ ( listre2064003096le_alt @ R_22 ) )
    <=> ( ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_36 @ Y_15 ) @ R_22 )
          & ( Xs_69 = Ys_26 ) )
        | ( ( X_36 = Y_15 )
          & ( member28618436le_alt @ ( produc776457805le_alt @ Xs_69 @ Ys_26 ) @ ( listre2064003096le_alt @ R_22 ) ) ) ) ) )).

thf(fact_413_listrel1I1,axiom,(
    ! [Xs_68: list_A2115238852le_alt,X_35: arrow_475358991le_alt,Y_14: arrow_475358991le_alt,R_21: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_35 @ Y_14 ) @ R_21 )
     => ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_35 @ Xs_68 ) @ ( cons_A228743023le_alt @ Y_14 @ Xs_68 ) ) @ ( listre2064003096le_alt @ R_21 ) ) ) )).

thf(fact_414_listrel1I1,axiom,(
    ! [Xs_68: list_l1475218533le_alt,X_35: list_A2115238852le_alt,Y_14: list_A2115238852le_alt,R_21: produc1362454231le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ X_35 @ Y_14 ) @ R_21 )
     => ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ X_35 @ Xs_68 ) @ ( cons_l635097956le_alt @ Y_14 @ Xs_68 ) ) @ ( listre620555643le_alt @ R_21 ) ) ) )).

thf(fact_415_listrel1I,axiom,(
    ! [Ys_25: list_A2115238852le_alt,Xs_67: list_A2115238852le_alt,Us_1: list_A2115238852le_alt,Vs_1: list_A2115238852le_alt,X_34: arrow_475358991le_alt,Y_13: arrow_475358991le_alt,R_20: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_34 @ Y_13 ) @ R_20 )
     => ( ( Xs_67
          = ( append179082452le_alt @ Us_1 @ ( cons_A228743023le_alt @ X_34 @ Vs_1 ) ) )
       => ( ( Ys_25
            = ( append179082452le_alt @ Us_1 @ ( cons_A228743023le_alt @ Y_13 @ Vs_1 ) ) )
         => ( member28618436le_alt @ ( produc776457805le_alt @ Xs_67 @ Ys_25 ) @ ( listre2064003096le_alt @ R_20 ) ) ) ) ) )).

thf(fact_416_listrel1I,axiom,(
    ! [Ys_25: list_l1475218533le_alt,Xs_67: list_l1475218533le_alt,Us_1: list_l1475218533le_alt,Vs_1: list_l1475218533le_alt,X_34: list_A2115238852le_alt,Y_13: list_A2115238852le_alt,R_20: produc1362454231le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ X_34 @ Y_13 ) @ R_20 )
     => ( ( Xs_67
          = ( append1166001599le_alt @ Us_1 @ ( cons_l635097956le_alt @ X_34 @ Vs_1 ) ) )
       => ( ( Ys_25
            = ( append1166001599le_alt @ Us_1 @ ( cons_l635097956le_alt @ Y_13 @ Vs_1 ) ) )
         => ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_67 @ Ys_25 ) @ ( listre620555643le_alt @ R_20 ) ) ) ) ) )).

thf(fact_417_listrel1E,axiom,(
    ! [Xs_66: list_l1475218533le_alt,Ys_24: list_l1475218533le_alt,R_19: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_66 @ Ys_24 ) @ ( listre620555643le_alt @ R_19 ) )
     => ~ ! [X_2: list_A2115238852le_alt,Y_1: list_A2115238852le_alt] :
            ( ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Y_1 ) @ R_19 )
           => ! [Us: list_l1475218533le_alt,Vs: list_l1475218533le_alt] :
                ( ( Xs_66
                  = ( append1166001599le_alt @ Us @ ( cons_l635097956le_alt @ X_2 @ Vs ) ) )
               => ( Ys_24
                 != ( append1166001599le_alt @ Us @ ( cons_l635097956le_alt @ Y_1 @ Vs ) ) ) ) ) ) )).

thf(fact_418_listrel1E,axiom,(
    ! [Xs_66: list_A2115238852le_alt,Ys_24: list_A2115238852le_alt,R_19: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_66 @ Ys_24 ) @ ( listre2064003096le_alt @ R_19 ) )
     => ~ ! [X_2: arrow_475358991le_alt,Y_1: arrow_475358991le_alt] :
            ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Y_1 ) @ R_19 )
           => ! [Us: list_A2115238852le_alt,Vs: list_A2115238852le_alt] :
                ( ( Xs_66
                  = ( append179082452le_alt @ Us @ ( cons_A228743023le_alt @ X_2 @ Vs ) ) )
               => ( Ys_24
                 != ( append179082452le_alt @ Us @ ( cons_A228743023le_alt @ Y_1 @ Vs ) ) ) ) ) ) )).

thf(fact_419_Cons__listrel1E1,axiom,(
    ! [X_33: list_A2115238852le_alt,Xs_65: list_l1475218533le_alt,Ys_23: list_l1475218533le_alt,R_18: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ X_33 @ Xs_65 ) @ Ys_23 ) @ ( listre620555643le_alt @ R_18 ) )
     => ( ! [Y_1: list_A2115238852le_alt] :
            ( ( Ys_23
              = ( cons_l635097956le_alt @ Y_1 @ Xs_65 ) )
           => ~ ( member28618436le_alt @ ( produc776457805le_alt @ X_33 @ Y_1 ) @ R_18 ) )
       => ~ ! [Zs: list_l1475218533le_alt] :
              ( ( Ys_23
                = ( cons_l635097956le_alt @ X_33 @ Zs ) )
             => ~ ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_65 @ Zs ) @ ( listre620555643le_alt @ R_18 ) ) ) ) ) )).

thf(fact_420_Cons__listrel1E1,axiom,(
    ! [X_33: arrow_475358991le_alt,Xs_65: list_A2115238852le_alt,Ys_23: list_A2115238852le_alt,R_18: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_33 @ Xs_65 ) @ Ys_23 ) @ ( listre2064003096le_alt @ R_18 ) )
     => ( ! [Y_1: arrow_475358991le_alt] :
            ( ( Ys_23
              = ( cons_A228743023le_alt @ Y_1 @ Xs_65 ) )
           => ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X_33 @ Y_1 ) @ R_18 ) )
       => ~ ! [Zs: list_A2115238852le_alt] :
              ( ( Ys_23
                = ( cons_A228743023le_alt @ X_33 @ Zs ) )
             => ~ ( member28618436le_alt @ ( produc776457805le_alt @ Xs_65 @ Zs ) @ ( listre2064003096le_alt @ R_18 ) ) ) ) ) )).

thf(fact_421_Cons__listrel1E2,axiom,(
    ! [Xs_64: list_l1475218533le_alt,Y_12: list_A2115238852le_alt,Ys_22: list_l1475218533le_alt,R_17: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_64 @ ( cons_l635097956le_alt @ Y_12 @ Ys_22 ) ) @ ( listre620555643le_alt @ R_17 ) )
     => ( ! [X_2: list_A2115238852le_alt] :
            ( ( Xs_64
              = ( cons_l635097956le_alt @ X_2 @ Ys_22 ) )
           => ~ ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Y_12 ) @ R_17 ) )
       => ~ ! [Zs: list_l1475218533le_alt] :
              ( ( Xs_64
                = ( cons_l635097956le_alt @ Y_12 @ Zs ) )
             => ~ ( member1732936276le_alt @ ( produc1317709143le_alt @ Zs @ Ys_22 ) @ ( listre620555643le_alt @ R_17 ) ) ) ) ) )).

thf(fact_422_Cons__listrel1E2,axiom,(
    ! [Xs_64: list_A2115238852le_alt,Y_12: arrow_475358991le_alt,Ys_22: list_A2115238852le_alt,R_17: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_64 @ ( cons_A228743023le_alt @ Y_12 @ Ys_22 ) ) @ ( listre2064003096le_alt @ R_17 ) )
     => ( ! [X_2: arrow_475358991le_alt] :
            ( ( Xs_64
              = ( cons_A228743023le_alt @ X_2 @ Ys_22 ) )
           => ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Y_12 ) @ R_17 ) )
       => ~ ! [Zs: list_A2115238852le_alt] :
              ( ( Xs_64
                = ( cons_A228743023le_alt @ Y_12 @ Zs ) )
             => ~ ( member28618436le_alt @ ( produc776457805le_alt @ Zs @ Ys_22 ) @ ( listre2064003096le_alt @ R_17 ) ) ) ) ) )).

thf(fact_423_Cons__in__lex,axiom,(
    ! [X_32: list_A2115238852le_alt,Xs_63: list_l1475218533le_alt,Y_11: list_A2115238852le_alt,Ys_21: list_l1475218533le_alt,R_16: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ X_32 @ Xs_63 ) @ ( cons_l635097956le_alt @ Y_11 @ Ys_21 ) ) @ ( lex_li663137712le_alt @ R_16 ) )
    <=> ( ( ( member28618436le_alt @ ( produc776457805le_alt @ X_32 @ Y_11 ) @ R_16 )
          & ( ( size_s1911906171le_alt @ Xs_63 )
            = ( size_s1911906171le_alt @ Ys_21 ) ) )
        | ( ( X_32 = Y_11 )
          & ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_63 @ Ys_21 ) @ ( lex_li663137712le_alt @ R_16 ) ) ) ) ) )).

thf(fact_424_Cons__in__lex,axiom,(
    ! [X_32: arrow_475358991le_alt,Xs_63: list_A2115238852le_alt,Y_11: arrow_475358991le_alt,Ys_21: list_A2115238852le_alt,R_16: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_32 @ Xs_63 ) @ ( cons_A228743023le_alt @ Y_11 @ Ys_21 ) ) @ ( lex_Ar1415517219le_alt @ R_16 ) )
    <=> ( ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_32 @ Y_11 ) @ R_16 )
          & ( ( size_s1858781230le_alt @ Xs_63 )
            = ( size_s1858781230le_alt @ Ys_21 ) ) )
        | ( ( X_32 = Y_11 )
          & ( member28618436le_alt @ ( produc776457805le_alt @ Xs_63 @ Ys_21 ) @ ( lex_Ar1415517219le_alt @ R_16 ) ) ) ) ) )).

thf(fact_425_dropWhile__eq__Cons__conv,axiom,(
    ! [P_19: arrow_475358991le_alt > $o,Xs_62: list_A2115238852le_alt,Y_10: arrow_475358991le_alt,Ys_20: list_A2115238852le_alt] :
      ( ( ( dropWh1316781920le_alt @ P_19 @ Xs_62 )
        = ( cons_A228743023le_alt @ Y_10 @ Ys_20 ) )
    <=> ( ( Xs_62
          = ( append179082452le_alt @ ( takeWh1696291512le_alt @ P_19 @ Xs_62 ) @ ( cons_A228743023le_alt @ Y_10 @ Ys_20 ) ) )
        & ~ ( P_19 @ Y_10 ) ) ) )).

thf(fact_426_partition_Osimps_I2_J,axiom,(
    ! [P_18: arrow_475358991le_alt > $o,X_31: arrow_475358991le_alt,Xs_61: list_A2115238852le_alt] :
      ( ( partit1487577784le_alt @ P_18 @ ( cons_A228743023le_alt @ X_31 @ Xs_61 ) )
      = ( produc677212559le_alt
        @ ^ [Yes_1: list_A2115238852le_alt,No_1: list_A2115238852le_alt] :
            ( if_Pro314693991le_alt @ ( P_18 @ X_31 ) @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_31 @ Yes_1 ) @ No_1 ) @ ( produc776457805le_alt @ Yes_1 @ ( cons_A228743023le_alt @ X_31 @ No_1 ) ) )
        @ ( partit1487577784le_alt @ P_18 @ Xs_61 ) ) ) )).

thf(fact_427_dropWhile_Osimps_I2_J,axiom,(
    ! [Xs_60: list_A2115238852le_alt,P_17: arrow_475358991le_alt > $o,X_30: arrow_475358991le_alt] :
      ( ( ( P_17 @ X_30 )
       => ( ( dropWh1316781920le_alt @ P_17 @ ( cons_A228743023le_alt @ X_30 @ Xs_60 ) )
          = ( dropWh1316781920le_alt @ P_17 @ Xs_60 ) ) )
      & ( ~ ( P_17 @ X_30 )
       => ( ( dropWh1316781920le_alt @ P_17 @ ( cons_A228743023le_alt @ X_30 @ Xs_60 ) )
          = ( cons_A228743023le_alt @ X_30 @ Xs_60 ) ) ) ) )).

thf(fact_428_dropWhile_Osimps_I1_J,axiom,(
    ! [P_16: arrow_475358991le_alt > $o] :
      ( ( dropWh1316781920le_alt @ P_16 @ nil_Ar1286194111le_alt )
      = nil_Ar1286194111le_alt ) )).

thf(fact_429_distinct__dropWhile,axiom,(
    ! [P_15: arrow_475358991le_alt > $o,Xs_59: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_59 )
     => ( distin236324274le_alt @ ( dropWh1316781920le_alt @ P_15 @ Xs_59 ) ) ) )).

thf(fact_430_split__curry,axiom,(
    ! [F_3: produc1501160679le_alt > $o] :
      ( ( produc362454893_alt_o @ ( produc910278158_alt_o @ F_3 ) )
      = F_3 ) )).

thf(fact_431_curry__split,axiom,(
    ! [F_2: arrow_475358991le_alt > arrow_475358991le_alt > $o] :
      ( ( produc910278158_alt_o @ ( produc362454893_alt_o @ F_2 ) )
      = F_2 ) )).

thf(fact_432_listrel1__eq__len,axiom,(
    ! [Xs_58: list_A2115238852le_alt,Ys_19: list_A2115238852le_alt,R_15: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_58 @ Ys_19 ) @ ( listre2064003096le_alt @ R_15 ) )
     => ( ( size_s1858781230le_alt @ Xs_58 )
        = ( size_s1858781230le_alt @ Ys_19 ) ) ) )).

thf(fact_433_takeWhile__dropWhile__id,axiom,(
    ! [P_14: arrow_475358991le_alt > $o,Xs_57: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( takeWh1696291512le_alt @ P_14 @ Xs_57 ) @ ( dropWh1316781920le_alt @ P_14 @ Xs_57 ) )
      = Xs_57 ) )).

thf(fact_434_lexord__lex,axiom,(
    ! [X_29: list_A2115238852le_alt,Y_9: list_A2115238852le_alt,R_14: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ X_29 @ Y_9 ) @ ( lex_Ar1415517219le_alt @ R_14 ) )
    <=> ( ( member28618436le_alt @ ( produc776457805le_alt @ X_29 @ Y_9 ) @ ( lexord958095404le_alt @ R_14 ) )
        & ( ( size_s1858781230le_alt @ X_29 )
          = ( size_s1858781230le_alt @ Y_9 ) ) ) ) )).

thf(fact_435_lexn__length,axiom,(
    ! [Xs_56: list_A2115238852le_alt,Ys_18: list_A2115238852le_alt,R_13: produc1501160679le_alt > $o,N_8: nat] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_56 @ Ys_18 ) @ ( lexn_A170361439le_alt @ R_13 @ N_8 ) )
     => ( ( ( size_s1858781230le_alt @ Xs_56 )
          = N_8 )
        & ( ( size_s1858781230le_alt @ Ys_18 )
          = N_8 ) ) ) )).

thf(fact_436_splitI,axiom,(
    ! [F_1: list_A2115238852le_alt > list_A2115238852le_alt > $o,A_3: list_A2115238852le_alt,B_3: list_A2115238852le_alt] :
      ( ( F_1 @ A_3 @ B_3 )
     => ( produc1948161143_alt_o @ F_1 @ ( produc776457805le_alt @ A_3 @ B_3 ) ) ) )).

thf(fact_437_splitI,axiom,(
    ! [F_1: arrow_475358991le_alt > arrow_475358991le_alt > $o,A_3: arrow_475358991le_alt,B_3: arrow_475358991le_alt] :
      ( ( F_1 @ A_3 @ B_3 )
     => ( produc362454893_alt_o @ F_1 @ ( produc1347929815le_alt @ A_3 @ B_3 ) ) ) )).

thf(fact_438_prod__caseI,axiom,(
    ! [F1: list_A2115238852le_alt > list_A2115238852le_alt > $o,A_2: list_A2115238852le_alt,B_2: list_A2115238852le_alt] :
      ( ( F1 @ A_2 @ B_2 )
     => ( produc1948161143_alt_o @ F1 @ ( produc776457805le_alt @ A_2 @ B_2 ) ) ) )).

thf(fact_439_prod__caseI,axiom,(
    ! [F1: arrow_475358991le_alt > arrow_475358991le_alt > $o,A_2: arrow_475358991le_alt,B_2: arrow_475358991le_alt] :
      ( ( F1 @ A_2 @ B_2 )
     => ( produc362454893_alt_o @ F1 @ ( produc1347929815le_alt @ A_2 @ B_2 ) ) ) )).

thf(fact_440_splitD,axiom,(
    ! [F: list_A2115238852le_alt > list_A2115238852le_alt > $o,A_1: list_A2115238852le_alt,B_1: list_A2115238852le_alt] :
      ( ( produc1948161143_alt_o @ F @ ( produc776457805le_alt @ A_1 @ B_1 ) )
     => ( F @ A_1 @ B_1 ) ) )).

thf(fact_441_splitD,axiom,(
    ! [F: arrow_475358991le_alt > arrow_475358991le_alt > $o,A_1: arrow_475358991le_alt,B_1: arrow_475358991le_alt] :
      ( ( produc362454893_alt_o @ F @ ( produc1347929815le_alt @ A_1 @ B_1 ) )
     => ( F @ A_1 @ B_1 ) ) )).

thf(fact_442_splitI2,axiom,(
    ! [C_1: list_A2115238852le_alt > list_A2115238852le_alt > $o,P_13: produc1362454231le_alt] :
      ( ! [A: list_A2115238852le_alt,B: list_A2115238852le_alt] :
          ( ( P_13
            = ( produc776457805le_alt @ A @ B ) )
         => ( C_1 @ A @ B ) )
     => ( produc1948161143_alt_o @ C_1 @ P_13 ) ) )).

thf(fact_443_splitI2,axiom,(
    ! [C_1: arrow_475358991le_alt > arrow_475358991le_alt > $o,P_13: produc1501160679le_alt] :
      ( ! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
          ( ( P_13
            = ( produc1347929815le_alt @ A @ B ) )
         => ( C_1 @ A @ B ) )
     => ( produc362454893_alt_o @ C_1 @ P_13 ) ) )).

thf(fact_444_splitE,axiom,(
    ! [C: list_A2115238852le_alt > list_A2115238852le_alt > $o,P_12: produc1362454231le_alt] :
      ( ( produc1948161143_alt_o @ C @ P_12 )
     => ~ ! [X_2: list_A2115238852le_alt,Y_1: list_A2115238852le_alt] :
            ( ( P_12
              = ( produc776457805le_alt @ X_2 @ Y_1 ) )
           => ~ ( C @ X_2 @ Y_1 ) ) ) )).

thf(fact_445_splitE,axiom,(
    ! [C: arrow_475358991le_alt > arrow_475358991le_alt > $o,P_12: produc1501160679le_alt] :
      ( ( produc362454893_alt_o @ C @ P_12 )
     => ~ ! [X_2: arrow_475358991le_alt,Y_1: arrow_475358991le_alt] :
            ( ( P_12
              = ( produc1347929815le_alt @ X_2 @ Y_1 ) )
           => ~ ( C @ X_2 @ Y_1 ) ) ) )).

thf(fact_446_not__distinct__decomp,axiom,(
    ! [Ws: list_A2115238852le_alt] :
      ( ~ ( distin236324274le_alt @ Ws )
     => ? [Xs_21: list_A2115238852le_alt,Ys: list_A2115238852le_alt,Zs: list_A2115238852le_alt,Y_1: arrow_475358991le_alt] :
          ( Ws
          = ( append179082452le_alt @ Xs_21 @ ( append179082452le_alt @ ( cons_A228743023le_alt @ Y_1 @ nil_Ar1286194111le_alt ) @ ( append179082452le_alt @ Ys @ ( append179082452le_alt @ ( cons_A228743023le_alt @ Y_1 @ nil_Ar1286194111le_alt ) @ Zs ) ) ) ) ) ) )).

thf(fact_447_listrel_OCons,axiom,(
    ! [Xs_55: list_A2115238852le_alt,Ys_17: list_A2115238852le_alt,X_28: arrow_475358991le_alt,Y_8: arrow_475358991le_alt,R_12: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_28 @ Y_8 ) @ R_12 )
     => ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_55 @ Ys_17 ) @ ( listre1920655591le_alt @ R_12 ) )
       => ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ X_28 @ Xs_55 ) @ ( cons_A228743023le_alt @ Y_8 @ Ys_17 ) ) @ ( listre1920655591le_alt @ R_12 ) ) ) ) )).

thf(fact_448_listrel_OCons,axiom,(
    ! [Xs_55: list_l1475218533le_alt,Ys_17: list_l1475218533le_alt,X_28: list_A2115238852le_alt,Y_8: list_A2115238852le_alt,R_12: produc1362454231le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ X_28 @ Y_8 ) @ R_12 )
     => ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_55 @ Ys_17 ) @ ( listre623166444le_alt @ R_12 ) )
       => ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ X_28 @ Xs_55 ) @ ( cons_l635097956le_alt @ Y_8 @ Ys_17 ) ) @ ( listre623166444le_alt @ R_12 ) ) ) ) )).

thf(fact_449_tl__append,axiom,(
    ! [Xs_54: list_A2115238852le_alt,Ys_16: list_A2115238852le_alt] :
      ( ( tl_Arr465451158le_alt @ ( append179082452le_alt @ Xs_54 @ Ys_16 ) )
      = ( list_c1623890103le_alt @ ( tl_Arr465451158le_alt @ Ys_16 )
        @ ^ [Z: arrow_475358991le_alt,Zs: list_A2115238852le_alt] :
            ( append179082452le_alt @ Zs @ Ys_16 )
        @ Xs_54 ) ) )).

thf(fact_450_listrel__Nil2,axiom,(
    ! [Xs_53: list_A2115238852le_alt,R_11: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_53 @ nil_Ar1286194111le_alt ) @ ( listre1920655591le_alt @ R_11 ) )
     => ( Xs_53 = nil_Ar1286194111le_alt ) ) )).

thf(fact_451_listrel__Nil1,axiom,(
    ! [Xs_52: list_A2115238852le_alt,R_10: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ nil_Ar1286194111le_alt @ Xs_52 ) @ ( listre1920655591le_alt @ R_10 ) )
     => ( Xs_52 = nil_Ar1286194111le_alt ) ) )).

thf(fact_452_tl_Osimps_I2_J,axiom,(
    ! [X_27: arrow_475358991le_alt,Xs_51: list_A2115238852le_alt] :
      ( ( tl_Arr465451158le_alt @ ( cons_A228743023le_alt @ X_27 @ Xs_51 ) )
      = Xs_51 ) )).

thf(fact_453_tl_Osimps_I1_J,axiom,
    ( ( tl_Arr465451158le_alt @ nil_Ar1286194111le_alt )
    = nil_Ar1286194111le_alt )).

thf(fact_454_distinct__tl,axiom,(
    ! [Xs_50: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_50 )
     => ( distin236324274le_alt @ ( tl_Arr465451158le_alt @ Xs_50 ) ) ) )).

thf(fact_455_listrel_ONil,axiom,(
    ! [R_9: produc1501160679le_alt > $o] :
      ( member28618436le_alt @ ( produc776457805le_alt @ nil_Ar1286194111le_alt @ nil_Ar1286194111le_alt ) @ ( listre1920655591le_alt @ R_9 ) ) )).

thf(fact_456_listrel__eq__len,axiom,(
    ! [Xs_49: list_A2115238852le_alt,Ys_15: list_A2115238852le_alt,R_8: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_49 @ Ys_15 ) @ ( listre1920655591le_alt @ R_8 ) )
     => ( ( size_s1858781230le_alt @ Xs_49 )
        = ( size_s1858781230le_alt @ Ys_15 ) ) ) )).

thf(fact_457_tl__append2,axiom,(
    ! [Ys_14: list_A2115238852le_alt,Xs_48: list_A2115238852le_alt] :
      ( ( Xs_48 != nil_Ar1286194111le_alt )
     => ( ( tl_Arr465451158le_alt @ ( append179082452le_alt @ Xs_48 @ Ys_14 ) )
        = ( append179082452le_alt @ ( tl_Arr465451158le_alt @ Xs_48 ) @ Ys_14 ) ) ) )).

thf(fact_458_listrel__Cons2,axiom,(
    ! [Xs_47: list_l1475218533le_alt,Y_7: list_A2115238852le_alt,Ys_13: list_l1475218533le_alt,R_7: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_47 @ ( cons_l635097956le_alt @ Y_7 @ Ys_13 ) ) @ ( listre623166444le_alt @ R_7 ) )
     => ~ ! [X_2: list_A2115238852le_alt,Xs_21: list_l1475218533le_alt] :
            ( ( Xs_47
              = ( cons_l635097956le_alt @ X_2 @ Xs_21 ) )
           => ( ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Y_7 ) @ R_7 )
             => ~ ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_21 @ Ys_13 ) @ ( listre623166444le_alt @ R_7 ) ) ) ) ) )).

thf(fact_459_listrel__Cons2,axiom,(
    ! [Xs_47: list_A2115238852le_alt,Y_7: arrow_475358991le_alt,Ys_13: list_A2115238852le_alt,R_7: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_47 @ ( cons_A228743023le_alt @ Y_7 @ Ys_13 ) ) @ ( listre1920655591le_alt @ R_7 ) )
     => ~ ! [X_2: arrow_475358991le_alt,Xs_21: list_A2115238852le_alt] :
            ( ( Xs_47
              = ( cons_A228743023le_alt @ X_2 @ Xs_21 ) )
           => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Y_7 ) @ R_7 )
             => ~ ( member28618436le_alt @ ( produc776457805le_alt @ Xs_21 @ Ys_13 ) @ ( listre1920655591le_alt @ R_7 ) ) ) ) ) )).

thf(fact_460_listrel__Cons1,axiom,(
    ! [Y_6: list_A2115238852le_alt,Ys_12: list_l1475218533le_alt,Xs_46: list_l1475218533le_alt,R_6: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ ( cons_l635097956le_alt @ Y_6 @ Ys_12 ) @ Xs_46 ) @ ( listre623166444le_alt @ R_6 ) )
     => ~ ! [Y_1: list_A2115238852le_alt,Ys: list_l1475218533le_alt] :
            ( ( Xs_46
              = ( cons_l635097956le_alt @ Y_1 @ Ys ) )
           => ( ( member28618436le_alt @ ( produc776457805le_alt @ Y_6 @ Y_1 ) @ R_6 )
             => ~ ( member1732936276le_alt @ ( produc1317709143le_alt @ Ys_12 @ Ys ) @ ( listre623166444le_alt @ R_6 ) ) ) ) ) )).

thf(fact_461_listrel__Cons1,axiom,(
    ! [Y_6: arrow_475358991le_alt,Ys_12: list_A2115238852le_alt,Xs_46: list_A2115238852le_alt,R_6: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ ( cons_A228743023le_alt @ Y_6 @ Ys_12 ) @ Xs_46 ) @ ( listre1920655591le_alt @ R_6 ) )
     => ~ ! [Y_1: arrow_475358991le_alt,Ys: list_A2115238852le_alt] :
            ( ( Xs_46
              = ( cons_A228743023le_alt @ Y_1 @ Ys ) )
           => ( ( member214075476le_alt @ ( produc1347929815le_alt @ Y_6 @ Y_1 ) @ R_6 )
             => ~ ( member28618436le_alt @ ( produc776457805le_alt @ Ys_12 @ Ys ) @ ( listre1920655591le_alt @ R_6 ) ) ) ) ) )).

thf(fact_462_listrelp__listrel__eq,axiom,(
    ! [R_5: produc1501160679le_alt > $o,X_2: list_A2115238852le_alt,Xa: list_A2115238852le_alt] :
      ( ( listre1213162009le_alt
        @ ^ [Y_1: arrow_475358991le_alt,Z: arrow_475358991le_alt] :
            ( member214075476le_alt @ ( produc1347929815le_alt @ Y_1 @ Z ) @ R_5 )
        @ X_2
        @ Xa )
    <=> ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Xa ) @ ( listre1920655591le_alt @ R_5 ) ) ) )).

thf(fact_463_listrelp__listrel__eq,axiom,(
    ! [R_5: produc1362454231le_alt > $o,X_2: list_l1475218533le_alt,Xa: list_l1475218533le_alt] :
      ( ( listre816681018le_alt
        @ ^ [Y_1: list_A2115238852le_alt,Z: list_A2115238852le_alt] :
            ( member28618436le_alt @ ( produc776457805le_alt @ Y_1 @ Z ) @ R_5 )
        @ X_2
        @ Xa )
    <=> ( member1732936276le_alt @ ( produc1317709143le_alt @ X_2 @ Xa ) @ ( listre623166444le_alt @ R_5 ) ) ) )).

thf(fact_464_rotate1__hd__tl,axiom,(
    ! [Xs_45: list_A2115238852le_alt] :
      ( ( Xs_45 != nil_Ar1286194111le_alt )
     => ( ( rotate335349260le_alt @ Xs_45 )
        = ( append179082452le_alt @ ( tl_Arr465451158le_alt @ Xs_45 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ Xs_45 ) @ nil_Ar1286194111le_alt ) ) ) ) )).

thf(fact_465_listrel_Osimps,axiom,(
    ! [A1_1: list_l1475218533le_alt,A2_1: list_l1475218533le_alt,R_4: produc1362454231le_alt > $o] :
      ( ( member1732936276le_alt @ ( produc1317709143le_alt @ A1_1 @ A2_1 ) @ ( listre623166444le_alt @ R_4 ) )
    <=> ( ( ( A1_1 = nil_li1907286804le_alt )
          & ( A2_1 = nil_li1907286804le_alt ) )
        | ? [X_2: list_A2115238852le_alt,Y_1: list_A2115238852le_alt,Xs_21: list_l1475218533le_alt,Ys: list_l1475218533le_alt] :
            ( ( A1_1
              = ( cons_l635097956le_alt @ X_2 @ Xs_21 ) )
            & ( A2_1
              = ( cons_l635097956le_alt @ Y_1 @ Ys ) )
            & ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Y_1 ) @ R_4 )
            & ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_21 @ Ys ) @ ( listre623166444le_alt @ R_4 ) ) ) ) ) )).

thf(fact_466_listrel_Osimps,axiom,(
    ! [A1_1: list_A2115238852le_alt,A2_1: list_A2115238852le_alt,R_4: produc1501160679le_alt > $o] :
      ( ( member28618436le_alt @ ( produc776457805le_alt @ A1_1 @ A2_1 ) @ ( listre1920655591le_alt @ R_4 ) )
    <=> ( ( ( A1_1 = nil_Ar1286194111le_alt )
          & ( A2_1 = nil_Ar1286194111le_alt ) )
        | ? [X_2: arrow_475358991le_alt,Y_1: arrow_475358991le_alt,Xs_21: list_A2115238852le_alt,Ys: list_A2115238852le_alt] :
            ( ( A1_1
              = ( cons_A228743023le_alt @ X_2 @ Xs_21 ) )
            & ( A2_1
              = ( cons_A228743023le_alt @ Y_1 @ Ys ) )
            & ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Y_1 ) @ R_4 )
            & ( member28618436le_alt @ ( produc776457805le_alt @ Xs_21 @ Ys ) @ ( listre1920655591le_alt @ R_4 ) ) ) ) ) )).

thf(fact_467_hd_Osimps,axiom,(
    ! [X_26: arrow_475358991le_alt,Xs_44: list_A2115238852le_alt] :
      ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X_26 @ Xs_44 ) )
      = X_26 ) )).

thf(fact_468_listrelp_OCons,axiom,(
    ! [Xs_43: list_A2115238852le_alt,Ys_11: list_A2115238852le_alt,R_3: arrow_475358991le_alt > arrow_475358991le_alt > $o,X_25: arrow_475358991le_alt,Y_5: arrow_475358991le_alt] :
      ( ( R_3 @ X_25 @ Y_5 )
     => ( ( listre1213162009le_alt @ R_3 @ Xs_43 @ Ys_11 )
       => ( listre1213162009le_alt @ R_3 @ ( cons_A228743023le_alt @ X_25 @ Xs_43 ) @ ( cons_A228743023le_alt @ Y_5 @ Ys_11 ) ) ) ) )).

thf(fact_469_listrelp_ONil,axiom,(
    ! [R_2: arrow_475358991le_alt > arrow_475358991le_alt > $o] :
      ( listre1213162009le_alt @ R_2 @ nil_Ar1286194111le_alt @ nil_Ar1286194111le_alt ) )).

thf(fact_470_hd__append,axiom,(
    ! [Ys_10: list_A2115238852le_alt,Xs_42: list_A2115238852le_alt] :
      ( ( ( Xs_42 = nil_Ar1286194111le_alt )
       => ( ( hd_Arr1965683346le_alt @ ( append179082452le_alt @ Xs_42 @ Ys_10 ) )
          = ( hd_Arr1965683346le_alt @ Ys_10 ) ) )
      & ( ( Xs_42 != nil_Ar1286194111le_alt )
       => ( ( hd_Arr1965683346le_alt @ ( append179082452le_alt @ Xs_42 @ Ys_10 ) )
          = ( hd_Arr1965683346le_alt @ Xs_42 ) ) ) ) )).

thf(fact_471_hd__append2,axiom,(
    ! [Ys_9: list_A2115238852le_alt,Xs_41: list_A2115238852le_alt] :
      ( ( Xs_41 != nil_Ar1286194111le_alt )
     => ( ( hd_Arr1965683346le_alt @ ( append179082452le_alt @ Xs_41 @ Ys_9 ) )
        = ( hd_Arr1965683346le_alt @ Xs_41 ) ) ) )).

thf(fact_472_hd__dropWhile,axiom,(
    ! [P_11: arrow_475358991le_alt > $o,Xs_40: list_A2115238852le_alt] :
      ( ( ( dropWh1316781920le_alt @ P_11 @ Xs_40 )
       != nil_Ar1286194111le_alt )
     => ~ ( P_11 @ ( hd_Arr1965683346le_alt @ ( dropWh1316781920le_alt @ P_11 @ Xs_40 ) ) ) ) )).

thf(fact_473_listrelp_Osimps,axiom,(
    ! [R_1: arrow_475358991le_alt > arrow_475358991le_alt > $o,A1: list_A2115238852le_alt,A2: list_A2115238852le_alt] :
      ( ( listre1213162009le_alt @ R_1 @ A1 @ A2 )
    <=> ( ( ( A1 = nil_Ar1286194111le_alt )
          & ( A2 = nil_Ar1286194111le_alt ) )
        | ? [X_2: arrow_475358991le_alt,Y_1: arrow_475358991le_alt,Xs_21: list_A2115238852le_alt,Ys: list_A2115238852le_alt] :
            ( ( A1
              = ( cons_A228743023le_alt @ X_2 @ Xs_21 ) )
            & ( A2
              = ( cons_A228743023le_alt @ Y_1 @ Ys ) )
            & ( R_1 @ X_2 @ Y_1 )
            & ( listre1213162009le_alt @ R_1 @ Xs_21 @ Ys ) ) ) ) )).

thf(fact_474_equal,axiom,(
    equal_484611810le_alt = fequal781288069le_alt )).

thf(fact_475_equal__refl,axiom,(
    ! [X_24: list_A2115238852le_alt] :
      ( equal_484611810le_alt @ X_24 @ X_24 ) )).

thf(fact_476_equal__eq,axiom,(
    ! [X_23: list_A2115238852le_alt,Y_4: list_A2115238852le_alt] :
      ( ( equal_484611810le_alt @ X_23 @ Y_4 )
    <=> ( X_23 = Y_4 ) ) )).

thf(fact_477_eq__equal,axiom,(
    fequal781288069le_alt = equal_484611810le_alt )).

thf(fact_478_last__rev,axiom,(
    ! [Xs_39: list_A2115238852le_alt] :
      ( ( Xs_39 != nil_Ar1286194111le_alt )
     => ( ( last_A1217315288le_alt @ ( rev_Ar1106406943le_alt @ Xs_39 ) )
        = ( hd_Arr1965683346le_alt @ Xs_39 ) ) ) )).

thf(fact_479_hd__rev,axiom,(
    ! [Xs_38: list_A2115238852le_alt] :
      ( ( Xs_38 != nil_Ar1286194111le_alt )
     => ( ( hd_Arr1965683346le_alt @ ( rev_Ar1106406943le_alt @ Xs_38 ) )
        = ( last_A1217315288le_alt @ Xs_38 ) ) ) )).

thf(fact_480_replicate__append__same,axiom,(
    ! [I_3: nat,X_22: arrow_475358991le_alt] :
      ( ( append179082452le_alt @ ( replic1511538809le_alt @ I_3 @ X_22 ) @ ( cons_A228743023le_alt @ X_22 @ nil_Ar1286194111le_alt ) )
      = ( cons_A228743023le_alt @ X_22 @ ( replic1511538809le_alt @ I_3 @ X_22 ) ) ) )).

thf(fact_481_dropWhile__eq__drop,axiom,(
    ! [P_10: arrow_475358991le_alt > $o,Xs_37: list_A2115238852le_alt] :
      ( ( dropWh1316781920le_alt @ P_10 @ Xs_37 )
      = ( drop_A1346709759le_alt @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_10 @ Xs_37 ) ) @ Xs_37 ) ) )).

thf(fact_482_butlast__drop,axiom,(
    ! [N_7: nat,Xs_36: list_A2115238852le_alt] :
      ( ( butlas274947851le_alt @ ( drop_A1346709759le_alt @ N_7 @ Xs_36 ) )
      = ( drop_A1346709759le_alt @ N_7 @ ( butlas274947851le_alt @ Xs_36 ) ) ) )).

thf(fact_483_drop__butlast,axiom,(
    ! [N_6: nat,Xs_35: list_A2115238852le_alt] :
      ( ( drop_A1346709759le_alt @ N_6 @ ( butlas274947851le_alt @ Xs_35 ) )
      = ( butlas274947851le_alt @ ( drop_A1346709759le_alt @ N_6 @ Xs_35 ) ) ) )).

thf(fact_484_drop__Nil,axiom,(
    ! [N_5: nat] :
      ( ( drop_A1346709759le_alt @ N_5 @ nil_Ar1286194111le_alt )
      = nil_Ar1286194111le_alt ) )).

thf(fact_485_distinct__drop,axiom,(
    ! [I_2: nat,Xs_34: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_34 )
     => ( distin236324274le_alt @ ( drop_A1346709759le_alt @ I_2 @ Xs_34 ) ) ) )).

thf(fact_486_rev__append,axiom,(
    ! [Xs_33: list_A2115238852le_alt,Ys_8: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ ( append179082452le_alt @ Xs_33 @ Ys_8 ) )
      = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Ys_8 ) @ ( rev_Ar1106406943le_alt @ Xs_33 ) ) ) )).

thf(fact_487_rev__is__Nil__conv,axiom,(
    ! [Xs_32: list_A2115238852le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ Xs_32 )
        = nil_Ar1286194111le_alt )
    <=> ( Xs_32 = nil_Ar1286194111le_alt ) ) )).

thf(fact_488_Nil__is__rev__conv,axiom,(
    ! [Xs_31: list_A2115238852le_alt] :
      ( ( nil_Ar1286194111le_alt
        = ( rev_Ar1106406943le_alt @ Xs_31 ) )
    <=> ( Xs_31 = nil_Ar1286194111le_alt ) ) )).

thf(fact_489_rev_Osimps_I1_J,axiom,
    ( ( rev_Ar1106406943le_alt @ nil_Ar1286194111le_alt )
    = nil_Ar1286194111le_alt )).

thf(fact_490_append__replicate__commute,axiom,(
    ! [N_4: nat,X_21: arrow_475358991le_alt,K_1: nat] :
      ( ( append179082452le_alt @ ( replic1511538809le_alt @ N_4 @ X_21 ) @ ( replic1511538809le_alt @ K_1 @ X_21 ) )
      = ( append179082452le_alt @ ( replic1511538809le_alt @ K_1 @ X_21 ) @ ( replic1511538809le_alt @ N_4 @ X_21 ) ) ) )).

thf(fact_491_distinct__rev,axiom,(
    ! [Xs_30: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( rev_Ar1106406943le_alt @ Xs_30 ) )
    <=> ( distin236324274le_alt @ Xs_30 ) ) )).

thf(fact_492_rev__singleton__conv,axiom,(
    ! [Xs_29: list_A2115238852le_alt,X_20: arrow_475358991le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ Xs_29 )
        = ( cons_A228743023le_alt @ X_20 @ nil_Ar1286194111le_alt ) )
    <=> ( Xs_29
        = ( cons_A228743023le_alt @ X_20 @ nil_Ar1286194111le_alt ) ) ) )).

thf(fact_493_singleton__rev__conv,axiom,(
    ! [X_19: arrow_475358991le_alt,Xs_28: list_A2115238852le_alt] :
      ( ( ( cons_A228743023le_alt @ X_19 @ nil_Ar1286194111le_alt )
        = ( rev_Ar1106406943le_alt @ Xs_28 ) )
    <=> ( Xs_28
        = ( cons_A228743023le_alt @ X_19 @ nil_Ar1286194111le_alt ) ) ) )).

thf(fact_494_replicate__app__Cons__same,axiom,(
    ! [N_3: nat,X_18: arrow_475358991le_alt,Xs_27: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( replic1511538809le_alt @ N_3 @ X_18 ) @ ( cons_A228743023le_alt @ X_18 @ Xs_27 ) )
      = ( cons_A228743023le_alt @ X_18 @ ( append179082452le_alt @ ( replic1511538809le_alt @ N_3 @ X_18 ) @ Xs_27 ) ) ) )).

thf(fact_495_rev_Osimps_I2_J,axiom,(
    ! [X_17: arrow_475358991le_alt,Xs_26: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X_17 @ Xs_26 ) )
      = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Xs_26 ) @ ( cons_A228743023le_alt @ X_17 @ nil_Ar1286194111le_alt ) ) ) )).

thf(fact_496_rev__eq__Cons__iff,axiom,(
    ! [Xs_25: list_A2115238852le_alt,Y_3: arrow_475358991le_alt,Ys_7: list_A2115238852le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ Xs_25 )
        = ( cons_A228743023le_alt @ Y_3 @ Ys_7 ) )
    <=> ( Xs_25
        = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Ys_7 ) @ ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) ) ) ) )).

thf(fact_497_takeWhile__neq__rev,axiom,(
    ! [X_16: arrow_475358991le_alt,Xs_24: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_24 )
     => ( ( member84363362le_alt @ X_16 @ ( set_Ar577454304le_alt @ Xs_24 ) )
       => ( ( takeWh1696291512le_alt
            @ ^ [Y_1: arrow_475358991le_alt] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Ar1106406943le_alt @ Xs_24 ) )
          = ( rev_Ar1106406943le_alt
            @ ( tl_Arr465451158le_alt
              @ ( dropWh1316781920le_alt
                @ ^ [Y_1: arrow_475358991le_alt] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_498_takeWhile__neq__rev,axiom,(
    ! [X_16: produc1362454231le_alt,Xs_24: list_P1295265784le_alt] :
      ( ( distin561495412le_alt @ Xs_24 )
     => ( ( member28618436le_alt @ X_16 @ ( set_Pr412222150le_alt @ Xs_24 ) )
       => ( ( takeWh1571807982le_alt
            @ ^ [Y_1: produc1362454231le_alt] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Pr1619606471le_alt @ Xs_24 ) )
          = ( rev_Pr1619606471le_alt
            @ ( tl_Pro1448262032le_alt
              @ ( dropWh612508742le_alt
                @ ^ [Y_1: produc1362454231le_alt] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_499_takeWhile__neq__rev,axiom,(
    ! [X_16: arrow_1429601828e_indi,Xs_24: list_A1484739013e_indi] :
      ( ( distin1916799041e_indi @ Xs_24 )
     => ( ( member2052026769e_indi @ X_16 @ ( set_Ar778541203e_indi @ Xs_24 ) )
       => ( ( takeWh831911099e_indi
            @ ^ [Y_1: arrow_1429601828e_indi] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Ar501922580e_indi @ Xs_24 ) )
          = ( rev_Ar501922580e_indi
            @ ( tl_Arr25726557e_indi
              @ ( dropWh1160116755e_indi
                @ ^ [Y_1: arrow_1429601828e_indi] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_500_takeWhile__neq__rev,axiom,(
    ! [X_16: $o,Xs_24: list_o] :
      ( ( distinct_o @ Xs_24 )
     => ( ( member_o @ X_16 @ ( set_o @ Xs_24 ) )
       => ( ( takeWhile_o
            @ ^ [Y_1: $o] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_o @ Xs_24 ) )
          = ( rev_o
            @ ( tl_o
              @ ( dropWhile_o
                @ ^ [Y_1: $o] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_501_takeWhile__neq__rev,axiom,(
    ! [X_16: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_24: list_A518015091_alt_o] :
      ( ( distin1908010863_alt_o @ Xs_24 )
     => ( ( member616898751_alt_o @ X_16 @ ( set_Ar1356274881_alt_o @ Xs_24 ) )
       => ( ( takeWh877796585_alt_o
            @ ^ [Y_1: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Ar5548482_alt_o @ Xs_24 ) )
          = ( rev_Ar5548482_alt_o
            @ ( tl_Arr2017860491_alt_o
              @ ( dropWh583351873_alt_o
                @ ^ [Y_1: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_502_takeWhile__neq__rev,axiom,(
    ! [X_16: produc1501160679le_alt > $o,Xs_24: list_P1178103901_alt_o] :
      ( ( distin1582710603_alt_o @ Xs_24 )
     => ( ( member377231867_alt_o @ X_16 @ ( set_Pr592386425_alt_o @ Xs_24 ) )
       => ( ( takeWh1715715921_alt_o
            @ ^ [Y_1: produc1501160679le_alt > $o] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Pr1006783032_alt_o @ Xs_24 ) )
          = ( rev_Pr1006783032_alt_o
            @ ( tl_Pro1735316527_alt_o
              @ ( dropWh1049991161_alt_o
                @ ^ [Y_1: produc1501160679le_alt > $o] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_503_takeWhile__neq__rev,axiom,(
    ! [X_16: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_24: list_A524553945_alt_o] :
      ( ( distin1869760583_alt_o @ Xs_24 )
     => ( ( member526088951_alt_o @ X_16 @ ( set_Ar571341173_alt_o @ Xs_24 ) )
       => ( ( takeWh1825606477_alt_o
            @ ^ [Y_1: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Ar413755828_alt_o @ Xs_24 ) )
          = ( rev_Ar413755828_alt_o
            @ ( tl_Arr1704054571_alt_o
              @ ( dropWh73644021_alt_o
                @ ^ [Y_1: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_504_takeWhile__neq__rev,axiom,(
    ! [X_16: produc1501160679le_alt,Xs_24: list_P736798472le_alt] :
      ( ( distin1776819972le_alt @ Xs_24 )
     => ( ( member214075476le_alt @ X_16 @ ( set_Pr1525059414le_alt @ Xs_24 ) )
       => ( ( takeWh302148478le_alt
            @ ^ [Y_1: produc1501160679le_alt] :
                ( (~) @ ( Y_1 = X_16 ) )
            @ ( rev_Pr1216324055le_alt @ Xs_24 ) )
          = ( rev_Pr1216324055le_alt
            @ ( tl_Pro932635936le_alt
              @ ( dropWh680325334le_alt
                @ ^ [Y_1: produc1501160679le_alt] :
                    ( (~) @ ( Y_1 = X_16 ) )
                @ Xs_24 ) ) ) ) ) ) )).

thf(fact_505_dropWhile__neq__rev,axiom,(
    ! [X_15: arrow_475358991le_alt,Xs_23: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ Xs_23 )
     => ( ( member84363362le_alt @ X_15 @ ( set_Ar577454304le_alt @ Xs_23 ) )
       => ( ( dropWh1316781920le_alt
            @ ^ [Y_1: arrow_475358991le_alt] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Ar1106406943le_alt @ Xs_23 ) )
          = ( cons_A228743023le_alt @ X_15
            @ ( rev_Ar1106406943le_alt
              @ ( takeWh1696291512le_alt
                @ ^ [Y_1: arrow_475358991le_alt] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_506_dropWhile__neq__rev,axiom,(
    ! [X_15: produc1362454231le_alt,Xs_23: list_P1295265784le_alt] :
      ( ( distin561495412le_alt @ Xs_23 )
     => ( ( member28618436le_alt @ X_15 @ ( set_Pr412222150le_alt @ Xs_23 ) )
       => ( ( dropWh612508742le_alt
            @ ^ [Y_1: produc1362454231le_alt] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Pr1619606471le_alt @ Xs_23 ) )
          = ( cons_P2048401015le_alt @ X_15
            @ ( rev_Pr1619606471le_alt
              @ ( takeWh1571807982le_alt
                @ ^ [Y_1: produc1362454231le_alt] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_507_dropWhile__neq__rev,axiom,(
    ! [X_15: arrow_1429601828e_indi,Xs_23: list_A1484739013e_indi] :
      ( ( distin1916799041e_indi @ Xs_23 )
     => ( ( member2052026769e_indi @ X_15 @ ( set_Ar778541203e_indi @ Xs_23 ) )
       => ( ( dropWh1160116755e_indi
            @ ^ [Y_1: arrow_1429601828e_indi] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Ar501922580e_indi @ Xs_23 ) )
          = ( cons_A663037380e_indi @ X_15
            @ ( rev_Ar501922580e_indi
              @ ( takeWh831911099e_indi
                @ ^ [Y_1: arrow_1429601828e_indi] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_508_dropWhile__neq__rev,axiom,(
    ! [X_15: $o,Xs_23: list_o] :
      ( ( distinct_o @ Xs_23 )
     => ( ( member_o @ X_15 @ ( set_o @ Xs_23 ) )
       => ( ( dropWhile_o
            @ ^ [Y_1: $o] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_o @ Xs_23 ) )
          = ( cons_o @ X_15
            @ ( rev_o
              @ ( takeWhile_o
                @ ^ [Y_1: $o] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_509_dropWhile__neq__rev,axiom,(
    ! [X_15: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_23: list_A518015091_alt_o] :
      ( ( distin1908010863_alt_o @ Xs_23 )
     => ( ( member616898751_alt_o @ X_15 @ ( set_Ar1356274881_alt_o @ Xs_23 ) )
       => ( ( dropWh583351873_alt_o
            @ ^ [Y_1: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Ar5548482_alt_o @ Xs_23 ) )
          = ( cons_A279268466_alt_o @ X_15
            @ ( rev_Ar5548482_alt_o
              @ ( takeWh877796585_alt_o
                @ ^ [Y_1: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_510_dropWhile__neq__rev,axiom,(
    ! [X_15: produc1501160679le_alt > $o,Xs_23: list_P1178103901_alt_o] :
      ( ( distin1582710603_alt_o @ Xs_23 )
     => ( ( member377231867_alt_o @ X_15 @ ( set_Pr592386425_alt_o @ Xs_23 ) )
       => ( ( dropWh1049991161_alt_o
            @ ^ [Y_1: produc1501160679le_alt > $o] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Pr1006783032_alt_o @ Xs_23 ) )
          = ( cons_P1239653256_alt_o @ X_15
            @ ( rev_Pr1006783032_alt_o
              @ ( takeWh1715715921_alt_o
                @ ^ [Y_1: produc1501160679le_alt > $o] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_511_dropWhile__neq__rev,axiom,(
    ! [X_15: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_23: list_A524553945_alt_o] :
      ( ( distin1869760583_alt_o @ Xs_23 )
     => ( ( member526088951_alt_o @ X_15 @ ( set_Ar571341173_alt_o @ Xs_23 ) )
       => ( ( dropWh73644021_alt_o
            @ ^ [Y_1: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Ar413755828_alt_o @ Xs_23 ) )
          = ( cons_A2010997508_alt_o @ X_15
            @ ( rev_Ar413755828_alt_o
              @ ( takeWh1825606477_alt_o
                @ ^ [Y_1: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_512_dropWhile__neq__rev,axiom,(
    ! [X_15: produc1501160679le_alt,Xs_23: list_P736798472le_alt] :
      ( ( distin1776819972le_alt @ Xs_23 )
     => ( ( member214075476le_alt @ X_15 @ ( set_Pr1525059414le_alt @ Xs_23 ) )
       => ( ( dropWh680325334le_alt
            @ ^ [Y_1: produc1501160679le_alt] :
                ( (~) @ ( Y_1 = X_15 ) )
            @ ( rev_Pr1216324055le_alt @ Xs_23 ) )
          = ( cons_P1913588871le_alt @ X_15
            @ ( rev_Pr1216324055le_alt
              @ ( takeWh302148478le_alt
                @ ^ [Y_1: produc1501160679le_alt] :
                    ( (~) @ ( Y_1 = X_15 ) )
                @ Xs_23 ) ) ) ) ) ) )).

thf(fact_513_drop__Cons,axiom,(
    ! [N_2: nat,X_14: arrow_475358991le_alt,Xs_22: list_A2115238852le_alt] :
      ( ( drop_A1346709759le_alt @ N_2 @ ( cons_A228743023le_alt @ X_14 @ Xs_22 ) )
      = ( nat_ca2147365008le_alt @ ( cons_A228743023le_alt @ X_14 @ Xs_22 )
        @ ^ [M_1: nat] :
            ( drop_A1346709759le_alt @ M_1 @ Xs_22 )
        @ N_2 ) ) )).

thf(fact_514_rev__foldl__cons,axiom,(
    ! [Xs_20: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ Xs_20 )
      = ( foldl_296410428le_alt
        @ ^ [Xs_21: list_A2115238852le_alt,X_2: arrow_475358991le_alt] :
            ( cons_A228743023le_alt @ X_2 @ Xs_21 )
        @ nil_Ar1286194111le_alt
        @ Xs_20 ) ) )).

thf(fact_515_in__set__dropD,axiom,(
    ! [X_13: arrow_475358991le_alt,N_1: nat,Xs_19: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ X_13 @ ( set_Ar577454304le_alt @ ( drop_A1346709759le_alt @ N_1 @ Xs_19 ) ) )
     => ( member84363362le_alt @ X_13 @ ( set_Ar577454304le_alt @ Xs_19 ) ) ) )).

thf(fact_516_in__set__dropD,axiom,(
    ! [X_13: produc1362454231le_alt,N_1: nat,Xs_19: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ X_13 @ ( set_Pr412222150le_alt @ ( drop_P1438419175le_alt @ N_1 @ Xs_19 ) ) )
     => ( member28618436le_alt @ X_13 @ ( set_Pr412222150le_alt @ Xs_19 ) ) ) )).

thf(fact_517_in__set__dropD,axiom,(
    ! [X_13: arrow_1429601828e_indi,N_1: nat,Xs_19: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ X_13 @ ( set_Ar778541203e_indi @ ( drop_A1596373044e_indi @ N_1 @ Xs_19 ) ) )
     => ( member2052026769e_indi @ X_13 @ ( set_Ar778541203e_indi @ Xs_19 ) ) ) )).

thf(fact_518_in__set__dropD,axiom,(
    ! [X_13: $o,N_1: nat,Xs_19: list_o] :
      ( ( member_o @ X_13 @ ( set_o @ ( drop_o @ N_1 @ Xs_19 ) ) )
     => ( member_o @ X_13 @ ( set_o @ Xs_19 ) ) ) )).

thf(fact_519_in__set__dropD,axiom,(
    ! [X_13: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,N_1: nat,Xs_19: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ X_13 @ ( set_Ar1356274881_alt_o @ ( drop_A1326872290_alt_o @ N_1 @ Xs_19 ) ) )
     => ( member616898751_alt_o @ X_13 @ ( set_Ar1356274881_alt_o @ Xs_19 ) ) ) )).

thf(fact_520_in__set__dropD,axiom,(
    ! [X_13: produc1501160679le_alt > $o,N_1: nat,Xs_19: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_13 @ ( set_Pr592386425_alt_o @ ( drop_P619902232_alt_o @ N_1 @ Xs_19 ) ) )
     => ( member377231867_alt_o @ X_13 @ ( set_Pr592386425_alt_o @ Xs_19 ) ) ) )).

thf(fact_521_in__set__dropD,axiom,(
    ! [X_13: arrow_1429601828e_indi > produc1501160679le_alt > $o,N_1: nat,Xs_19: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_13 @ ( set_Ar571341173_alt_o @ ( drop_A776701076_alt_o @ N_1 @ Xs_19 ) ) )
     => ( member526088951_alt_o @ X_13 @ ( set_Ar571341173_alt_o @ Xs_19 ) ) ) )).

thf(fact_522_in__set__dropD,axiom,(
    ! [X_13: produc1501160679le_alt,N_1: nat,Xs_19: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_13 @ ( set_Pr1525059414le_alt @ ( drop_P933863159le_alt @ N_1 @ Xs_19 ) ) )
     => ( member214075476le_alt @ X_13 @ ( set_Pr1525059414le_alt @ Xs_19 ) ) ) )).

thf(fact_523_set__takeWhileD,axiom,(
    ! [X_12: arrow_475358991le_alt,P_9: arrow_475358991le_alt > $o,Xs_18: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ X_12 @ ( set_Ar577454304le_alt @ ( takeWh1696291512le_alt @ P_9 @ Xs_18 ) ) )
     => ( ( member84363362le_alt @ X_12 @ ( set_Ar577454304le_alt @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_524_set__takeWhileD,axiom,(
    ! [X_12: produc1362454231le_alt,P_9: produc1362454231le_alt > $o,Xs_18: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ X_12 @ ( set_Pr412222150le_alt @ ( takeWh1571807982le_alt @ P_9 @ Xs_18 ) ) )
     => ( ( member28618436le_alt @ X_12 @ ( set_Pr412222150le_alt @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_525_set__takeWhileD,axiom,(
    ! [X_12: arrow_1429601828e_indi,P_9: arrow_1429601828e_indi > $o,Xs_18: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ X_12 @ ( set_Ar778541203e_indi @ ( takeWh831911099e_indi @ P_9 @ Xs_18 ) ) )
     => ( ( member2052026769e_indi @ X_12 @ ( set_Ar778541203e_indi @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_526_set__takeWhileD,axiom,(
    ! [X_12: $o,P_9: $o > $o,Xs_18: list_o] :
      ( ( member_o @ X_12 @ ( set_o @ ( takeWhile_o @ P_9 @ Xs_18 ) ) )
     => ( ( member_o @ X_12 @ ( set_o @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_527_set__takeWhileD,axiom,(
    ! [X_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,P_9: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,Xs_18: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ X_12 @ ( set_Ar1356274881_alt_o @ ( takeWh877796585_alt_o @ P_9 @ Xs_18 ) ) )
     => ( ( member616898751_alt_o @ X_12 @ ( set_Ar1356274881_alt_o @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_528_set__takeWhileD,axiom,(
    ! [X_12: produc1501160679le_alt > $o,P_9: ( produc1501160679le_alt > $o ) > $o,Xs_18: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_12 @ ( set_Pr592386425_alt_o @ ( takeWh1715715921_alt_o @ P_9 @ Xs_18 ) ) )
     => ( ( member377231867_alt_o @ X_12 @ ( set_Pr592386425_alt_o @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_529_set__takeWhileD,axiom,(
    ! [X_12: arrow_1429601828e_indi > produc1501160679le_alt > $o,P_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,Xs_18: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_12 @ ( set_Ar571341173_alt_o @ ( takeWh1825606477_alt_o @ P_9 @ Xs_18 ) ) )
     => ( ( member526088951_alt_o @ X_12 @ ( set_Ar571341173_alt_o @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_530_set__takeWhileD,axiom,(
    ! [X_12: produc1501160679le_alt,P_9: produc1501160679le_alt > $o,Xs_18: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_12 @ ( set_Pr1525059414le_alt @ ( takeWh302148478le_alt @ P_9 @ Xs_18 ) ) )
     => ( ( member214075476le_alt @ X_12 @ ( set_Pr1525059414le_alt @ Xs_18 ) )
        & ( P_9 @ X_12 ) ) ) )).

thf(fact_531_takeWhile__eq__all__conv,axiom,(
    ! [P_8: arrow_475358991le_alt > $o,Xs_17: list_A2115238852le_alt] :
      ( ( ( takeWh1696291512le_alt @ P_8 @ Xs_17 )
        = Xs_17 )
    <=> ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Xs_17 ) )
         => ( P_8 @ X_2 ) ) ) )).

thf(fact_532_in__set__butlastD,axiom,(
    ! [X_11: arrow_475358991le_alt,Xs_16: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ X_11 @ ( set_Ar577454304le_alt @ ( butlas274947851le_alt @ Xs_16 ) ) )
     => ( member84363362le_alt @ X_11 @ ( set_Ar577454304le_alt @ Xs_16 ) ) ) )).

thf(fact_533_in__set__butlastD,axiom,(
    ! [X_11: produc1362454231le_alt,Xs_16: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ X_11 @ ( set_Pr412222150le_alt @ ( butlas464406491le_alt @ Xs_16 ) ) )
     => ( member28618436le_alt @ X_11 @ ( set_Pr412222150le_alt @ Xs_16 ) ) ) )).

thf(fact_534_in__set__butlastD,axiom,(
    ! [X_11: arrow_1429601828e_indi,Xs_16: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ X_11 @ ( set_Ar778541203e_indi @ ( butlas1554122024e_indi @ Xs_16 ) ) )
     => ( member2052026769e_indi @ X_11 @ ( set_Ar778541203e_indi @ Xs_16 ) ) ) )).

thf(fact_535_in__set__butlastD,axiom,(
    ! [X_11: $o,Xs_16: list_o] :
      ( ( member_o @ X_11 @ ( set_o @ ( butlast_o @ Xs_16 ) ) )
     => ( member_o @ X_11 @ ( set_o @ Xs_16 ) ) ) )).

thf(fact_536_in__set__butlastD,axiom,(
    ! [X_11: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_16: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ X_11 @ ( set_Ar1356274881_alt_o @ ( butlas1138247126_alt_o @ Xs_16 ) ) )
     => ( member616898751_alt_o @ X_11 @ ( set_Ar1356274881_alt_o @ Xs_16 ) ) ) )).

thf(fact_537_in__set__butlastD,axiom,(
    ! [X_11: produc1501160679le_alt > $o,Xs_16: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_11 @ ( set_Pr592386425_alt_o @ ( butlas368541988_alt_o @ Xs_16 ) ) )
     => ( member377231867_alt_o @ X_11 @ ( set_Pr592386425_alt_o @ Xs_16 ) ) ) )).

thf(fact_538_in__set__butlastD,axiom,(
    ! [X_11: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_16: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_11 @ ( set_Ar571341173_alt_o @ ( butlas813143712_alt_o @ Xs_16 ) ) )
     => ( member526088951_alt_o @ X_11 @ ( set_Ar571341173_alt_o @ Xs_16 ) ) ) )).

thf(fact_539_in__set__butlastD,axiom,(
    ! [X_11: produc1501160679le_alt,Xs_16: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_11 @ ( set_Pr1525059414le_alt @ ( butlas661498859le_alt @ Xs_16 ) ) )
     => ( member214075476le_alt @ X_11 @ ( set_Pr1525059414le_alt @ Xs_16 ) ) ) )).

thf(fact_540_set__ConsD,axiom,(
    ! [Y_2: arrow_475358991le_alt,X_10: arrow_475358991le_alt,Xs_15: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ Y_2 @ ( set_Ar577454304le_alt @ ( cons_A228743023le_alt @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member84363362le_alt @ Y_2 @ ( set_Ar577454304le_alt @ Xs_15 ) ) ) ) )).

thf(fact_541_set__ConsD,axiom,(
    ! [Y_2: produc1362454231le_alt,X_10: produc1362454231le_alt,Xs_15: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ Y_2 @ ( set_Pr412222150le_alt @ ( cons_P2048401015le_alt @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member28618436le_alt @ Y_2 @ ( set_Pr412222150le_alt @ Xs_15 ) ) ) ) )).

thf(fact_542_set__ConsD,axiom,(
    ! [Y_2: arrow_1429601828e_indi,X_10: arrow_1429601828e_indi,Xs_15: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ Y_2 @ ( set_Ar778541203e_indi @ ( cons_A663037380e_indi @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member2052026769e_indi @ Y_2 @ ( set_Ar778541203e_indi @ Xs_15 ) ) ) ) )).

thf(fact_543_set__ConsD,axiom,(
    ! [Y_2: $o,X_10: $o,Xs_15: list_o] :
      ( ( member_o @ Y_2 @ ( set_o @ ( cons_o @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2
        <=> X_10 )
        | ( member_o @ Y_2 @ ( set_o @ Xs_15 ) ) ) ) )).

thf(fact_544_set__ConsD,axiom,(
    ! [Y_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,X_10: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_15: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ Y_2 @ ( set_Ar1356274881_alt_o @ ( cons_A279268466_alt_o @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member616898751_alt_o @ Y_2 @ ( set_Ar1356274881_alt_o @ Xs_15 ) ) ) ) )).

thf(fact_545_set__ConsD,axiom,(
    ! [Y_2: produc1501160679le_alt > $o,X_10: produc1501160679le_alt > $o,Xs_15: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ Y_2 @ ( set_Pr592386425_alt_o @ ( cons_P1239653256_alt_o @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member377231867_alt_o @ Y_2 @ ( set_Pr592386425_alt_o @ Xs_15 ) ) ) ) )).

thf(fact_546_set__ConsD,axiom,(
    ! [Y_2: arrow_1429601828e_indi > produc1501160679le_alt > $o,X_10: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_15: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ Y_2 @ ( set_Ar571341173_alt_o @ ( cons_A2010997508_alt_o @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member526088951_alt_o @ Y_2 @ ( set_Ar571341173_alt_o @ Xs_15 ) ) ) ) )).

thf(fact_547_set__ConsD,axiom,(
    ! [Y_2: produc1501160679le_alt,X_10: produc1501160679le_alt,Xs_15: list_P736798472le_alt] :
      ( ( member214075476le_alt @ Y_2 @ ( set_Pr1525059414le_alt @ ( cons_P1913588871le_alt @ X_10 @ Xs_15 ) ) )
     => ( ( Y_2 = X_10 )
        | ( member214075476le_alt @ Y_2 @ ( set_Pr1525059414le_alt @ Xs_15 ) ) ) ) )).

thf(fact_548_in__set__insert,axiom,(
    ! [X_9: arrow_475358991le_alt,Xs_14: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ X_9 @ ( set_Ar577454304le_alt @ Xs_14 ) )
     => ( ( insert2120566741le_alt @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_549_in__set__insert,axiom,(
    ! [X_9: produc1362454231le_alt,Xs_14: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ X_9 @ ( set_Pr412222150le_alt @ Xs_14 ) )
     => ( ( insert1334153361le_alt @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_550_in__set__insert,axiom,(
    ! [X_9: arrow_1429601828e_indi,Xs_14: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ X_9 @ ( set_Ar778541203e_indi @ Xs_14 ) )
     => ( ( insert1474580190e_indi @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_551_in__set__insert,axiom,(
    ! [X_9: $o,Xs_14: list_o] :
      ( ( member_o @ X_9 @ ( set_o @ Xs_14 ) )
     => ( ( insert_o @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_552_in__set__insert,axiom,(
    ! [X_9: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_14: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ X_9 @ ( set_Ar1356274881_alt_o @ Xs_14 ) )
     => ( ( insert81217164_alt_o @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_553_in__set__insert,axiom,(
    ! [X_9: produc1501160679le_alt > $o,Xs_14: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_9 @ ( set_Pr592386425_alt_o @ Xs_14 ) )
     => ( ( insert451602158_alt_o @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_554_in__set__insert,axiom,(
    ! [X_9: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_14: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_9 @ ( set_Ar571341173_alt_o @ Xs_14 ) )
     => ( ( insert128393578_alt_o @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_555_in__set__insert,axiom,(
    ! [X_9: produc1501160679le_alt,Xs_14: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_9 @ ( set_Pr1525059414le_alt @ Xs_14 ) )
     => ( ( insert1177064865le_alt @ X_9 @ Xs_14 )
        = Xs_14 ) ) )).

thf(fact_556_distinct_Osimps_I2_J,axiom,(
    ! [X_8: arrow_475358991le_alt,Xs_13: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member84363362le_alt @ X_8 @ ( set_Ar577454304le_alt @ Xs_13 ) )
        & ( distin236324274le_alt @ Xs_13 ) ) ) )).

thf(fact_557_distinct_Osimps_I2_J,axiom,(
    ! [X_8: produc1362454231le_alt,Xs_13: list_P1295265784le_alt] :
      ( ( distin561495412le_alt @ ( cons_P2048401015le_alt @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member28618436le_alt @ X_8 @ ( set_Pr412222150le_alt @ Xs_13 ) )
        & ( distin561495412le_alt @ Xs_13 ) ) ) )).

thf(fact_558_distinct_Osimps_I2_J,axiom,(
    ! [X_8: arrow_1429601828e_indi,Xs_13: list_A1484739013e_indi] :
      ( ( distin1916799041e_indi @ ( cons_A663037380e_indi @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member2052026769e_indi @ X_8 @ ( set_Ar778541203e_indi @ Xs_13 ) )
        & ( distin1916799041e_indi @ Xs_13 ) ) ) )).

thf(fact_559_distinct_Osimps_I2_J,axiom,(
    ! [X_8: $o,Xs_13: list_o] :
      ( ( distinct_o @ ( cons_o @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member_o @ X_8 @ ( set_o @ Xs_13 ) )
        & ( distinct_o @ Xs_13 ) ) ) )).

thf(fact_560_distinct_Osimps_I2_J,axiom,(
    ! [X_8: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_13: list_A518015091_alt_o] :
      ( ( distin1908010863_alt_o @ ( cons_A279268466_alt_o @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member616898751_alt_o @ X_8 @ ( set_Ar1356274881_alt_o @ Xs_13 ) )
        & ( distin1908010863_alt_o @ Xs_13 ) ) ) )).

thf(fact_561_distinct_Osimps_I2_J,axiom,(
    ! [X_8: produc1501160679le_alt > $o,Xs_13: list_P1178103901_alt_o] :
      ( ( distin1582710603_alt_o @ ( cons_P1239653256_alt_o @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member377231867_alt_o @ X_8 @ ( set_Pr592386425_alt_o @ Xs_13 ) )
        & ( distin1582710603_alt_o @ Xs_13 ) ) ) )).

thf(fact_562_distinct_Osimps_I2_J,axiom,(
    ! [X_8: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_13: list_A524553945_alt_o] :
      ( ( distin1869760583_alt_o @ ( cons_A2010997508_alt_o @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member526088951_alt_o @ X_8 @ ( set_Ar571341173_alt_o @ Xs_13 ) )
        & ( distin1869760583_alt_o @ Xs_13 ) ) ) )).

thf(fact_563_distinct_Osimps_I2_J,axiom,(
    ! [X_8: produc1501160679le_alt,Xs_13: list_P736798472le_alt] :
      ( ( distin1776819972le_alt @ ( cons_P1913588871le_alt @ X_8 @ Xs_13 ) )
    <=> ( ~ ( member214075476le_alt @ X_8 @ ( set_Pr1525059414le_alt @ Xs_13 ) )
        & ( distin1776819972le_alt @ Xs_13 ) ) ) )).

thf(fact_564_takeWhile__append1,axiom,(
    ! [Ys_6: list_A2115238852le_alt,P_7: arrow_475358991le_alt > $o,X_7: arrow_475358991le_alt,Xs_12: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ X_7 @ ( set_Ar577454304le_alt @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh1696291512le_alt @ P_7 @ ( append179082452le_alt @ Xs_12 @ Ys_6 ) )
          = ( takeWh1696291512le_alt @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_565_takeWhile__append1,axiom,(
    ! [Ys_6: list_P1295265784le_alt,P_7: produc1362454231le_alt > $o,X_7: produc1362454231le_alt,Xs_12: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ X_7 @ ( set_Pr412222150le_alt @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh1571807982le_alt @ P_7 @ ( append423770578le_alt @ Xs_12 @ Ys_6 ) )
          = ( takeWh1571807982le_alt @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_566_takeWhile__append1,axiom,(
    ! [Ys_6: list_A1484739013e_indi,P_7: arrow_1429601828e_indi > $o,X_7: arrow_1429601828e_indi,Xs_12: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ X_7 @ ( set_Ar778541203e_indi @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh831911099e_indi @ P_7 @ ( append711934367e_indi @ Xs_12 @ Ys_6 ) )
          = ( takeWh831911099e_indi @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_567_takeWhile__append1,axiom,(
    ! [Ys_6: list_o,P_7: $o > $o,X_7: $o,Xs_12: list_o] :
      ( ( member_o @ X_7 @ ( set_o @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWhile_o @ P_7 @ ( append_o @ Xs_12 @ Ys_6 ) )
          = ( takeWhile_o @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_568_takeWhile__append1,axiom,(
    ! [Ys_6: list_A518015091_alt_o,P_7: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,X_7: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_12: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ X_7 @ ( set_Ar1356274881_alt_o @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh877796585_alt_o @ P_7 @ ( append326058957_alt_o @ Xs_12 @ Ys_6 ) )
          = ( takeWh877796585_alt_o @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_569_takeWhile__append1,axiom,(
    ! [Ys_6: list_P1178103901_alt_o,P_7: ( produc1501160679le_alt > $o ) > $o,X_7: produc1501160679le_alt > $o,Xs_12: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_7 @ ( set_Pr592386425_alt_o @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh1715715921_alt_o @ P_7 @ ( append612833133_alt_o @ Xs_12 @ Ys_6 ) )
          = ( takeWh1715715921_alt_o @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_570_takeWhile__append1,axiom,(
    ! [Ys_6: list_A524553945_alt_o,P_7: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,X_7: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_12: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_7 @ ( set_Ar571341173_alt_o @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh1825606477_alt_o @ P_7 @ ( append295924073_alt_o @ Xs_12 @ Ys_6 ) )
          = ( takeWh1825606477_alt_o @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_571_takeWhile__append1,axiom,(
    ! [Ys_6: list_P736798472le_alt,P_7: produc1501160679le_alt > $o,X_7: produc1501160679le_alt,Xs_12: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_7 @ ( set_Pr1525059414le_alt @ Xs_12 ) )
     => ( ~ ( P_7 @ X_7 )
       => ( ( takeWh302148478le_alt @ P_7 @ ( append1229289570le_alt @ Xs_12 @ Ys_6 ) )
          = ( takeWh302148478le_alt @ P_7 @ Xs_12 ) ) ) ) )).

thf(fact_572_last__in__set,axiom,(
    ! [As: list_A2115238852le_alt] :
      ( ( As != nil_Ar1286194111le_alt )
     => ( member84363362le_alt @ ( last_A1217315288le_alt @ As ) @ ( set_Ar577454304le_alt @ As ) ) ) )).

thf(fact_573_last__in__set,axiom,(
    ! [As: list_P1295265784le_alt] :
      ( ( As != nil_Pr365739559le_alt )
     => ( member28618436le_alt @ ( last_P1879176142le_alt @ As ) @ ( set_Pr412222150le_alt @ As ) ) ) )).

thf(fact_574_last__in__set,axiom,(
    ! [As: list_A1484739013e_indi] :
      ( ( As != nil_Ar380161396e_indi )
     => ( member2052026769e_indi @ ( last_A303846811e_indi @ As ) @ ( set_Ar778541203e_indi @ As ) ) ) )).

thf(fact_575_last__in__set,axiom,(
    ! [As: list_o] :
      ( ( As != nil_o )
     => ( member_o @ ( last_o @ As ) @ ( set_o @ As ) ) ) )).

thf(fact_576_last__in__set,axiom,(
    ! [As: list_A518015091_alt_o] :
      ( ( As != nil_Ar253733922_alt_o )
     => ( member616898751_alt_o @ ( last_A1273867721_alt_o @ As ) @ ( set_Ar1356274881_alt_o @ As ) ) ) )).

thf(fact_577_last__in__set,axiom,(
    ! [As: list_P1178103901_alt_o] :
      ( ( As != nil_Pr28438488_alt_o )
     => ( member377231867_alt_o @ ( last_P685913713_alt_o @ As ) @ ( set_Pr592386425_alt_o @ As ) ) ) )).

thf(fact_578_last__in__set,axiom,(
    ! [As: list_A524553945_alt_o] :
      ( ( As != nil_Ar1876942676_alt_o )
     => ( member526088951_alt_o @ ( last_A1049530989_alt_o @ As ) @ ( set_Ar571341173_alt_o @ As ) ) ) )).

thf(fact_579_last__in__set,axiom,(
    ! [As: list_P736798472le_alt] :
      ( ( As != nil_Pr861385783le_alt )
     => ( member214075476le_alt @ ( last_P1656409182le_alt @ As ) @ ( set_Pr1525059414le_alt @ As ) ) ) )).

thf(fact_580_dropWhile__eq__Nil__conv,axiom,(
    ! [P_6: arrow_475358991le_alt > $o,Xs_11: list_A2115238852le_alt] :
      ( ( ( dropWh1316781920le_alt @ P_6 @ Xs_11 )
        = nil_Ar1286194111le_alt )
    <=> ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Xs_11 ) )
         => ( P_6 @ X_2 ) ) ) )).

thf(fact_581_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_A2115238852le_alt,X_6: arrow_475358991le_alt,Xs_10: list_A2115238852le_alt] :
      ( ( ( member84363362le_alt @ X_6 @ ( set_Ar577454304le_alt @ ( butlas274947851le_alt @ Xs_10 ) ) )
        | ( member84363362le_alt @ X_6 @ ( set_Ar577454304le_alt @ ( butlas274947851le_alt @ Ys_5 ) ) ) )
     => ( member84363362le_alt @ X_6 @ ( set_Ar577454304le_alt @ ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_582_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_P1295265784le_alt,X_6: produc1362454231le_alt,Xs_10: list_P1295265784le_alt] :
      ( ( ( member28618436le_alt @ X_6 @ ( set_Pr412222150le_alt @ ( butlas464406491le_alt @ Xs_10 ) ) )
        | ( member28618436le_alt @ X_6 @ ( set_Pr412222150le_alt @ ( butlas464406491le_alt @ Ys_5 ) ) ) )
     => ( member28618436le_alt @ X_6 @ ( set_Pr412222150le_alt @ ( butlas464406491le_alt @ ( append423770578le_alt @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_583_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_A1484739013e_indi,X_6: arrow_1429601828e_indi,Xs_10: list_A1484739013e_indi] :
      ( ( ( member2052026769e_indi @ X_6 @ ( set_Ar778541203e_indi @ ( butlas1554122024e_indi @ Xs_10 ) ) )
        | ( member2052026769e_indi @ X_6 @ ( set_Ar778541203e_indi @ ( butlas1554122024e_indi @ Ys_5 ) ) ) )
     => ( member2052026769e_indi @ X_6 @ ( set_Ar778541203e_indi @ ( butlas1554122024e_indi @ ( append711934367e_indi @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_584_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_o,X_6: $o,Xs_10: list_o] :
      ( ( ( member_o @ X_6 @ ( set_o @ ( butlast_o @ Xs_10 ) ) )
        | ( member_o @ X_6 @ ( set_o @ ( butlast_o @ Ys_5 ) ) ) )
     => ( member_o @ X_6 @ ( set_o @ ( butlast_o @ ( append_o @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_585_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_A518015091_alt_o,X_6: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_10: list_A518015091_alt_o] :
      ( ( ( member616898751_alt_o @ X_6 @ ( set_Ar1356274881_alt_o @ ( butlas1138247126_alt_o @ Xs_10 ) ) )
        | ( member616898751_alt_o @ X_6 @ ( set_Ar1356274881_alt_o @ ( butlas1138247126_alt_o @ Ys_5 ) ) ) )
     => ( member616898751_alt_o @ X_6 @ ( set_Ar1356274881_alt_o @ ( butlas1138247126_alt_o @ ( append326058957_alt_o @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_586_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_P1178103901_alt_o,X_6: produc1501160679le_alt > $o,Xs_10: list_P1178103901_alt_o] :
      ( ( ( member377231867_alt_o @ X_6 @ ( set_Pr592386425_alt_o @ ( butlas368541988_alt_o @ Xs_10 ) ) )
        | ( member377231867_alt_o @ X_6 @ ( set_Pr592386425_alt_o @ ( butlas368541988_alt_o @ Ys_5 ) ) ) )
     => ( member377231867_alt_o @ X_6 @ ( set_Pr592386425_alt_o @ ( butlas368541988_alt_o @ ( append612833133_alt_o @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_587_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_A524553945_alt_o,X_6: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_10: list_A524553945_alt_o] :
      ( ( ( member526088951_alt_o @ X_6 @ ( set_Ar571341173_alt_o @ ( butlas813143712_alt_o @ Xs_10 ) ) )
        | ( member526088951_alt_o @ X_6 @ ( set_Ar571341173_alt_o @ ( butlas813143712_alt_o @ Ys_5 ) ) ) )
     => ( member526088951_alt_o @ X_6 @ ( set_Ar571341173_alt_o @ ( butlas813143712_alt_o @ ( append295924073_alt_o @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_588_in__set__butlast__appendI,axiom,(
    ! [Ys_5: list_P736798472le_alt,X_6: produc1501160679le_alt,Xs_10: list_P736798472le_alt] :
      ( ( ( member214075476le_alt @ X_6 @ ( set_Pr1525059414le_alt @ ( butlas661498859le_alt @ Xs_10 ) ) )
        | ( member214075476le_alt @ X_6 @ ( set_Pr1525059414le_alt @ ( butlas661498859le_alt @ Ys_5 ) ) ) )
     => ( member214075476le_alt @ X_6 @ ( set_Pr1525059414le_alt @ ( butlas661498859le_alt @ ( append1229289570le_alt @ Xs_10 @ Ys_5 ) ) ) ) ) )).

thf(fact_589_hd__in__set,axiom,(
    ! [Xs_9: list_A2115238852le_alt] :
      ( ( Xs_9 != nil_Ar1286194111le_alt )
     => ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ Xs_9 ) @ ( set_Ar577454304le_alt @ Xs_9 ) ) ) )).

thf(fact_590_hd__in__set,axiom,(
    ! [Xs_9: list_P1295265784le_alt] :
      ( ( Xs_9 != nil_Pr365739559le_alt )
     => ( member28618436le_alt @ ( hd_Pro856774804le_alt @ Xs_9 ) @ ( set_Pr412222150le_alt @ Xs_9 ) ) ) )).

thf(fact_591_hd__in__set,axiom,(
    ! [Xs_9: list_A1484739013e_indi] :
      ( ( Xs_9 != nil_Ar380161396e_indi )
     => ( member2052026769e_indi @ ( hd_Arr1023890273e_indi @ Xs_9 ) @ ( set_Ar778541203e_indi @ Xs_9 ) ) ) )).

thf(fact_592_hd__in__set,axiom,(
    ! [Xs_9: list_o] :
      ( ( Xs_9 != nil_o )
     => ( member_o @ ( hd_o @ Xs_9 ) @ ( set_o @ Xs_9 ) ) ) )).

thf(fact_593_hd__in__set,axiom,(
    ! [Xs_9: list_A518015091_alt_o] :
      ( ( Xs_9 != nil_Ar253733922_alt_o )
     => ( member616898751_alt_o @ ( hd_Arr1786382991_alt_o @ Xs_9 ) @ ( set_Ar1356274881_alt_o @ Xs_9 ) ) ) )).

thf(fact_594_hd__in__set,axiom,(
    ! [Xs_9: list_P1178103901_alt_o] :
      ( ( Xs_9 != nil_Pr28438488_alt_o )
     => ( member377231867_alt_o @ ( hd_Pro622402603_alt_o @ Xs_9 ) @ ( set_Pr592386425_alt_o @ Xs_9 ) ) ) )).

thf(fact_595_hd__in__set,axiom,(
    ! [Xs_9: list_A524553945_alt_o] :
      ( ( Xs_9 != nil_Ar1876942676_alt_o )
     => ( member526088951_alt_o @ ( hd_Arr574592295_alt_o @ Xs_9 ) @ ( set_Ar571341173_alt_o @ Xs_9 ) ) ) )).

thf(fact_596_hd__in__set,axiom,(
    ! [Xs_9: list_P736798472le_alt] :
      ( ( Xs_9 != nil_Pr861385783le_alt )
     => ( member214075476le_alt @ ( hd_Pro297626148le_alt @ Xs_9 ) @ ( set_Pr1525059414le_alt @ Xs_9 ) ) ) )).

thf(fact_597_dropWhile__append1,axiom,(
    ! [Ys_4: list_A2115238852le_alt,P_5: arrow_475358991le_alt > $o,X_5: arrow_475358991le_alt,Xs_8: list_A2115238852le_alt] :
      ( ( member84363362le_alt @ X_5 @ ( set_Ar577454304le_alt @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh1316781920le_alt @ P_5 @ ( append179082452le_alt @ Xs_8 @ Ys_4 ) )
          = ( append179082452le_alt @ ( dropWh1316781920le_alt @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_598_dropWhile__append1,axiom,(
    ! [Ys_4: list_P1295265784le_alt,P_5: produc1362454231le_alt > $o,X_5: produc1362454231le_alt,Xs_8: list_P1295265784le_alt] :
      ( ( member28618436le_alt @ X_5 @ ( set_Pr412222150le_alt @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh612508742le_alt @ P_5 @ ( append423770578le_alt @ Xs_8 @ Ys_4 ) )
          = ( append423770578le_alt @ ( dropWh612508742le_alt @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_599_dropWhile__append1,axiom,(
    ! [Ys_4: list_A1484739013e_indi,P_5: arrow_1429601828e_indi > $o,X_5: arrow_1429601828e_indi,Xs_8: list_A1484739013e_indi] :
      ( ( member2052026769e_indi @ X_5 @ ( set_Ar778541203e_indi @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh1160116755e_indi @ P_5 @ ( append711934367e_indi @ Xs_8 @ Ys_4 ) )
          = ( append711934367e_indi @ ( dropWh1160116755e_indi @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_600_dropWhile__append1,axiom,(
    ! [Ys_4: list_o,P_5: $o > $o,X_5: $o,Xs_8: list_o] :
      ( ( member_o @ X_5 @ ( set_o @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWhile_o @ P_5 @ ( append_o @ Xs_8 @ Ys_4 ) )
          = ( append_o @ ( dropWhile_o @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_601_dropWhile__append1,axiom,(
    ! [Ys_4: list_A518015091_alt_o,P_5: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,X_5: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_8: list_A518015091_alt_o] :
      ( ( member616898751_alt_o @ X_5 @ ( set_Ar1356274881_alt_o @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh583351873_alt_o @ P_5 @ ( append326058957_alt_o @ Xs_8 @ Ys_4 ) )
          = ( append326058957_alt_o @ ( dropWh583351873_alt_o @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_602_dropWhile__append1,axiom,(
    ! [Ys_4: list_P1178103901_alt_o,P_5: ( produc1501160679le_alt > $o ) > $o,X_5: produc1501160679le_alt > $o,Xs_8: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_5 @ ( set_Pr592386425_alt_o @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh1049991161_alt_o @ P_5 @ ( append612833133_alt_o @ Xs_8 @ Ys_4 ) )
          = ( append612833133_alt_o @ ( dropWh1049991161_alt_o @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_603_dropWhile__append1,axiom,(
    ! [Ys_4: list_A524553945_alt_o,P_5: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,X_5: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_8: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_5 @ ( set_Ar571341173_alt_o @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh73644021_alt_o @ P_5 @ ( append295924073_alt_o @ Xs_8 @ Ys_4 ) )
          = ( append295924073_alt_o @ ( dropWh73644021_alt_o @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_604_dropWhile__append1,axiom,(
    ! [Ys_4: list_P736798472le_alt,P_5: produc1501160679le_alt > $o,X_5: produc1501160679le_alt,Xs_8: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_5 @ ( set_Pr1525059414le_alt @ Xs_8 ) )
     => ( ~ ( P_5 @ X_5 )
       => ( ( dropWh680325334le_alt @ P_5 @ ( append1229289570le_alt @ Xs_8 @ Ys_4 ) )
          = ( append1229289570le_alt @ ( dropWh680325334le_alt @ P_5 @ Xs_8 ) @ Ys_4 ) ) ) ) )).

thf(fact_605_List_Oinsert__def,axiom,(
    ! [X_4: arrow_475358991le_alt,Xs_7: list_A2115238852le_alt] :
      ( ( ( member84363362le_alt @ X_4 @ ( set_Ar577454304le_alt @ Xs_7 ) )
       => ( ( insert2120566741le_alt @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member84363362le_alt @ X_4 @ ( set_Ar577454304le_alt @ Xs_7 ) )
       => ( ( insert2120566741le_alt @ X_4 @ Xs_7 )
          = ( cons_A228743023le_alt @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_606_List_Oinsert__def,axiom,(
    ! [X_4: produc1362454231le_alt,Xs_7: list_P1295265784le_alt] :
      ( ( ( member28618436le_alt @ X_4 @ ( set_Pr412222150le_alt @ Xs_7 ) )
       => ( ( insert1334153361le_alt @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member28618436le_alt @ X_4 @ ( set_Pr412222150le_alt @ Xs_7 ) )
       => ( ( insert1334153361le_alt @ X_4 @ Xs_7 )
          = ( cons_P2048401015le_alt @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_607_List_Oinsert__def,axiom,(
    ! [X_4: arrow_1429601828e_indi,Xs_7: list_A1484739013e_indi] :
      ( ( ( member2052026769e_indi @ X_4 @ ( set_Ar778541203e_indi @ Xs_7 ) )
       => ( ( insert1474580190e_indi @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member2052026769e_indi @ X_4 @ ( set_Ar778541203e_indi @ Xs_7 ) )
       => ( ( insert1474580190e_indi @ X_4 @ Xs_7 )
          = ( cons_A663037380e_indi @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_608_List_Oinsert__def,axiom,(
    ! [X_4: $o,Xs_7: list_o] :
      ( ( ( member_o @ X_4 @ ( set_o @ Xs_7 ) )
       => ( ( insert_o @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member_o @ X_4 @ ( set_o @ Xs_7 ) )
       => ( ( insert_o @ X_4 @ Xs_7 )
          = ( cons_o @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_609_List_Oinsert__def,axiom,(
    ! [X_4: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_7: list_A518015091_alt_o] :
      ( ( ( member616898751_alt_o @ X_4 @ ( set_Ar1356274881_alt_o @ Xs_7 ) )
       => ( ( insert81217164_alt_o @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member616898751_alt_o @ X_4 @ ( set_Ar1356274881_alt_o @ Xs_7 ) )
       => ( ( insert81217164_alt_o @ X_4 @ Xs_7 )
          = ( cons_A279268466_alt_o @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_610_List_Oinsert__def,axiom,(
    ! [X_4: produc1501160679le_alt > $o,Xs_7: list_P1178103901_alt_o] :
      ( ( ( member377231867_alt_o @ X_4 @ ( set_Pr592386425_alt_o @ Xs_7 ) )
       => ( ( insert451602158_alt_o @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member377231867_alt_o @ X_4 @ ( set_Pr592386425_alt_o @ Xs_7 ) )
       => ( ( insert451602158_alt_o @ X_4 @ Xs_7 )
          = ( cons_P1239653256_alt_o @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_611_List_Oinsert__def,axiom,(
    ! [X_4: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_7: list_A524553945_alt_o] :
      ( ( ( member526088951_alt_o @ X_4 @ ( set_Ar571341173_alt_o @ Xs_7 ) )
       => ( ( insert128393578_alt_o @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member526088951_alt_o @ X_4 @ ( set_Ar571341173_alt_o @ Xs_7 ) )
       => ( ( insert128393578_alt_o @ X_4 @ Xs_7 )
          = ( cons_A2010997508_alt_o @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_612_List_Oinsert__def,axiom,(
    ! [X_4: produc1501160679le_alt,Xs_7: list_P736798472le_alt] :
      ( ( ( member214075476le_alt @ X_4 @ ( set_Pr1525059414le_alt @ Xs_7 ) )
       => ( ( insert1177064865le_alt @ X_4 @ Xs_7 )
          = Xs_7 ) )
      & ( ~ ( member214075476le_alt @ X_4 @ ( set_Pr1525059414le_alt @ Xs_7 ) )
       => ( ( insert1177064865le_alt @ X_4 @ Xs_7 )
          = ( cons_P1913588871le_alt @ X_4 @ Xs_7 ) ) ) ) )).

thf(fact_613_not__in__set__insert,axiom,(
    ! [X_3: arrow_475358991le_alt,Xs_6: list_A2115238852le_alt] :
      ( ~ ( member84363362le_alt @ X_3 @ ( set_Ar577454304le_alt @ Xs_6 ) )
     => ( ( insert2120566741le_alt @ X_3 @ Xs_6 )
        = ( cons_A228743023le_alt @ X_3 @ Xs_6 ) ) ) )).

thf(fact_614_not__in__set__insert,axiom,(
    ! [X_3: produc1362454231le_alt,Xs_6: list_P1295265784le_alt] :
      ( ~ ( member28618436le_alt @ X_3 @ ( set_Pr412222150le_alt @ Xs_6 ) )
     => ( ( insert1334153361le_alt @ X_3 @ Xs_6 )
        = ( cons_P2048401015le_alt @ X_3 @ Xs_6 ) ) ) )).

thf(fact_615_not__in__set__insert,axiom,(
    ! [X_3: arrow_1429601828e_indi,Xs_6: list_A1484739013e_indi] :
      ( ~ ( member2052026769e_indi @ X_3 @ ( set_Ar778541203e_indi @ Xs_6 ) )
     => ( ( insert1474580190e_indi @ X_3 @ Xs_6 )
        = ( cons_A663037380e_indi @ X_3 @ Xs_6 ) ) ) )).

thf(fact_616_not__in__set__insert,axiom,(
    ! [X_3: $o,Xs_6: list_o] :
      ( ~ ( member_o @ X_3 @ ( set_o @ Xs_6 ) )
     => ( ( insert_o @ X_3 @ Xs_6 )
        = ( cons_o @ X_3 @ Xs_6 ) ) ) )).

thf(fact_617_not__in__set__insert,axiom,(
    ! [X_3: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Xs_6: list_A518015091_alt_o] :
      ( ~ ( member616898751_alt_o @ X_3 @ ( set_Ar1356274881_alt_o @ Xs_6 ) )
     => ( ( insert81217164_alt_o @ X_3 @ Xs_6 )
        = ( cons_A279268466_alt_o @ X_3 @ Xs_6 ) ) ) )).

thf(fact_618_not__in__set__insert,axiom,(
    ! [X_3: produc1501160679le_alt > $o,Xs_6: list_P1178103901_alt_o] :
      ( ~ ( member377231867_alt_o @ X_3 @ ( set_Pr592386425_alt_o @ Xs_6 ) )
     => ( ( insert451602158_alt_o @ X_3 @ Xs_6 )
        = ( cons_P1239653256_alt_o @ X_3 @ Xs_6 ) ) ) )).

thf(fact_619_not__in__set__insert,axiom,(
    ! [X_3: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs_6: list_A524553945_alt_o] :
      ( ~ ( member526088951_alt_o @ X_3 @ ( set_Ar571341173_alt_o @ Xs_6 ) )
     => ( ( insert128393578_alt_o @ X_3 @ Xs_6 )
        = ( cons_A2010997508_alt_o @ X_3 @ Xs_6 ) ) ) )).

thf(fact_620_not__in__set__insert,axiom,(
    ! [X_3: produc1501160679le_alt,Xs_6: list_P736798472le_alt] :
      ( ~ ( member214075476le_alt @ X_3 @ ( set_Pr1525059414le_alt @ Xs_6 ) )
     => ( ( insert1177064865le_alt @ X_3 @ Xs_6 )
        = ( cons_P1913588871le_alt @ X_3 @ Xs_6 ) ) ) )).

thf(fact_621_partition__P,axiom,(
    ! [P_4: arrow_475358991le_alt > $o,Xs_5: list_A2115238852le_alt,Yes: list_A2115238852le_alt,No: list_A2115238852le_alt] :
      ( ( ( partit1487577784le_alt @ P_4 @ Xs_5 )
        = ( produc776457805le_alt @ Yes @ No ) )
     => ( ! [X_2: arrow_475358991le_alt] :
            ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Yes ) )
           => ( P_4 @ X_2 ) )
        & ! [X_2: arrow_475358991le_alt] :
            ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ No ) )
           => ~ ( P_4 @ X_2 ) ) ) ) )).

thf(fact_622_lexord__partial__trans,axiom,(
    ! [Zs_1: list_A2115238852le_alt,Ys_3: list_A2115238852le_alt,R: produc1501160679le_alt > $o,Xs_4: list_A2115238852le_alt] :
      ( ! [X_2: arrow_475358991le_alt,Y_1: arrow_475358991le_alt,Z: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Xs_4 ) )
         => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Y_1 ) @ R )
           => ( ( member214075476le_alt @ ( produc1347929815le_alt @ Y_1 @ Z ) @ R )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member28618436le_alt @ ( produc776457805le_alt @ Xs_4 @ Ys_3 ) @ ( lexord958095404le_alt @ R ) )
       => ( ( member28618436le_alt @ ( produc776457805le_alt @ Ys_3 @ Zs_1 ) @ ( lexord958095404le_alt @ R ) )
         => ( member28618436le_alt @ ( produc776457805le_alt @ Xs_4 @ Zs_1 ) @ ( lexord958095404le_alt @ R ) ) ) ) ) )).

thf(fact_623_lexord__partial__trans,axiom,(
    ! [Zs_1: list_l1475218533le_alt,Ys_3: list_l1475218533le_alt,R: produc1362454231le_alt > $o,Xs_4: list_l1475218533le_alt] :
      ( ! [X_2: list_A2115238852le_alt,Y_1: list_A2115238852le_alt,Z: list_A2115238852le_alt] :
          ( ( member998134961le_alt @ X_2 @ ( set_li1631982259le_alt @ Xs_4 ) )
         => ( ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Y_1 ) @ R )
           => ( ( member28618436le_alt @ ( produc776457805le_alt @ Y_1 @ Z ) @ R )
             => ( member28618436le_alt @ ( produc776457805le_alt @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_4 @ Ys_3 ) @ ( lexord469916775le_alt @ R ) )
       => ( ( member1732936276le_alt @ ( produc1317709143le_alt @ Ys_3 @ Zs_1 ) @ ( lexord469916775le_alt @ R ) )
         => ( member1732936276le_alt @ ( produc1317709143le_alt @ Xs_4 @ Zs_1 ) @ ( lexord469916775le_alt @ R ) ) ) ) ) )).

thf(fact_624_lexord__partial__trans,axiom,(
    ! [Zs_1: list_P1295265784le_alt,Ys_3: list_P1295265784le_alt,R: produc1787997437le_alt > $o,Xs_4: list_P1295265784le_alt] :
      ( ! [X_2: produc1362454231le_alt,Y_1: produc1362454231le_alt,Z: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ ( set_Pr412222150le_alt @ Xs_4 ) )
         => ( ( member902484714le_alt @ ( produc1443807987le_alt @ X_2 @ Y_1 ) @ R )
           => ( ( member902484714le_alt @ ( produc1443807987le_alt @ Y_1 @ Z ) @ R )
             => ( member902484714le_alt @ ( produc1443807987le_alt @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member608607380le_alt @ ( produc1065979415le_alt @ Xs_4 @ Ys_3 ) @ ( lexord973342842le_alt @ R ) )
       => ( ( member608607380le_alt @ ( produc1065979415le_alt @ Ys_3 @ Zs_1 ) @ ( lexord973342842le_alt @ R ) )
         => ( member608607380le_alt @ ( produc1065979415le_alt @ Xs_4 @ Zs_1 ) @ ( lexord973342842le_alt @ R ) ) ) ) ) )).

thf(fact_625_lexord__partial__trans,axiom,(
    ! [Zs_1: list_A1484739013e_indi,Ys_3: list_A1484739013e_indi,R: produc1091721111e_indi > $o,Xs_4: list_A1484739013e_indi] :
      ( ! [X_2: arrow_1429601828e_indi,Y_1: arrow_1429601828e_indi,Z: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ ( set_Ar778541203e_indi @ Xs_4 ) )
         => ( ( member1239815300e_indi @ ( produc1851452045e_indi @ X_2 @ Y_1 ) @ R )
           => ( ( member1239815300e_indi @ ( produc1851452045e_indi @ Y_1 @ Z ) @ R )
             => ( member1239815300e_indi @ ( produc1851452045e_indi @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member1618636500e_indi @ ( produc1195920727e_indi @ Xs_4 @ Ys_3 ) @ ( lexord1661684807e_indi @ R ) )
       => ( ( member1618636500e_indi @ ( produc1195920727e_indi @ Ys_3 @ Zs_1 ) @ ( lexord1661684807e_indi @ R ) )
         => ( member1618636500e_indi @ ( produc1195920727e_indi @ Xs_4 @ Zs_1 ) @ ( lexord1661684807e_indi @ R ) ) ) ) ) )).

thf(fact_626_lexord__partial__trans,axiom,(
    ! [Zs_1: list_o,Ys_3: list_o,R: product_prod_o_o > $o,Xs_4: list_o] :
      ( ! [X_2: $o,Y_1: $o,Z: $o] :
          ( ( member_o @ X_2 @ ( set_o @ Xs_4 ) )
         => ( ( member1392690260od_o_o @ ( product_Pair_o_o @ X_2 @ Y_1 ) @ R )
           => ( ( member1392690260od_o_o @ ( product_Pair_o_o @ Y_1 @ Z ) @ R )
             => ( member1392690260od_o_o @ ( product_Pair_o_o @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member806300420list_o @ ( produc1835210381list_o @ Xs_4 @ Ys_3 ) @ ( lexord_o @ R ) )
       => ( ( member806300420list_o @ ( produc1835210381list_o @ Ys_3 @ Zs_1 ) @ ( lexord_o @ R ) )
         => ( member806300420list_o @ ( produc1835210381list_o @ Xs_4 @ Zs_1 ) @ ( lexord_o @ R ) ) ) ) ) )).

thf(fact_627_lexord__partial__trans,axiom,(
    ! [Zs_1: list_A518015091_alt_o,Ys_3: list_A518015091_alt_o,R: produc344885491_alt_o > $o,Xs_4: list_A518015091_alt_o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Y_1: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,Z: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ ( set_Ar1356274881_alt_o @ Xs_4 ) )
         => ( ( member1909339872_alt_o @ ( produc434968681_alt_o @ X_2 @ Y_1 ) @ R )
           => ( ( member1909339872_alt_o @ ( produc434968681_alt_o @ Y_1 @ Z ) @ R )
             => ( member1909339872_alt_o @ ( produc434968681_alt_o @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member119836116_alt_o @ ( produc385333463_alt_o @ Xs_4 @ Ys_3 ) @ ( lexord1104163445_alt_o @ R ) )
       => ( ( member119836116_alt_o @ ( produc385333463_alt_o @ Ys_3 @ Zs_1 ) @ ( lexord1104163445_alt_o @ R ) )
         => ( member119836116_alt_o @ ( produc385333463_alt_o @ Xs_4 @ Zs_1 ) @ ( lexord1104163445_alt_o @ R ) ) ) ) ) )).

thf(fact_628_lexord__partial__trans,axiom,(
    ! [Zs_1: list_P1178103901_alt_o,Ys_3: list_P1178103901_alt_o,R: produc603869735_alt_o > $o,Xs_4: list_P1178103901_alt_o] :
      ( ! [X_2: produc1501160679le_alt > $o,Y_1: produc1501160679le_alt > $o,Z: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ ( set_Pr592386425_alt_o @ Xs_4 ) )
         => ( ( member1998617236_alt_o @ ( produc548346135_alt_o @ X_2 @ Y_1 ) @ R )
           => ( ( member1998617236_alt_o @ ( produc548346135_alt_o @ Y_1 @ Z ) @ R )
             => ( member1998617236_alt_o @ ( produc548346135_alt_o @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member79660662_alt_o @ ( produc127168767_alt_o @ Xs_4 @ Ys_3 ) @ ( lexord842870469_alt_o @ R ) )
       => ( ( member79660662_alt_o @ ( produc127168767_alt_o @ Ys_3 @ Zs_1 ) @ ( lexord842870469_alt_o @ R ) )
         => ( member79660662_alt_o @ ( produc127168767_alt_o @ Xs_4 @ Zs_1 ) @ ( lexord842870469_alt_o @ R ) ) ) ) ) )).

thf(fact_629_lexord__partial__trans,axiom,(
    ! [Zs_1: list_A524553945_alt_o,Ys_3: list_A524553945_alt_o,R: produc634020647_alt_o > $o,Xs_4: list_A524553945_alt_o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o,Y_1: arrow_1429601828e_indi > produc1501160679le_alt > $o,Z: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ ( set_Ar571341173_alt_o @ Xs_4 ) )
         => ( ( member423327892_alt_o @ ( produc425112727_alt_o @ X_2 @ Y_1 ) @ R )
           => ( ( member423327892_alt_o @ ( produc425112727_alt_o @ Y_1 @ Z ) @ R )
             => ( member423327892_alt_o @ ( produc425112727_alt_o @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member1890873582_alt_o @ ( produc1301429239_alt_o @ Xs_4 @ Ys_3 ) @ ( lexord1645229249_alt_o @ R ) )
       => ( ( member1890873582_alt_o @ ( produc1301429239_alt_o @ Ys_3 @ Zs_1 ) @ ( lexord1645229249_alt_o @ R ) )
         => ( member1890873582_alt_o @ ( produc1301429239_alt_o @ Xs_4 @ Zs_1 ) @ ( lexord1645229249_alt_o @ R ) ) ) ) ) )).

thf(fact_630_lexord__partial__trans,axiom,(
    ! [Zs_1: list_P736798472le_alt,Ys_3: list_P736798472le_alt,R: produc1076844957le_alt > $o,Xs_4: list_P736798472le_alt] :
      ( ! [X_2: produc1501160679le_alt,Y_1: produc1501160679le_alt,Z: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ ( set_Pr1525059414le_alt @ Xs_4 ) )
         => ( ( member1664185994le_alt @ ( produc1348021779le_alt @ X_2 @ Y_1 ) @ R )
           => ( ( member1664185994le_alt @ ( produc1348021779le_alt @ Y_1 @ Z ) @ R )
             => ( member1664185994le_alt @ ( produc1348021779le_alt @ X_2 @ Z ) @ R ) ) ) )
     => ( ( member475755924le_alt @ ( produc1573901719le_alt @ Xs_4 @ Ys_3 ) @ ( lexord501678858le_alt @ R ) )
       => ( ( member475755924le_alt @ ( produc1573901719le_alt @ Ys_3 @ Zs_1 ) @ ( lexord501678858le_alt @ R ) )
         => ( member475755924le_alt @ ( produc1573901719le_alt @ Xs_4 @ Zs_1 ) @ ( lexord501678858le_alt @ R ) ) ) ) ) )).

thf(fact_631_dropWhile__append2,axiom,(
    ! [Ys_2: list_A2115238852le_alt,P_3: arrow_475358991le_alt > $o,Xs_3: list_A2115238852le_alt] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh1316781920le_alt @ P_3 @ ( append179082452le_alt @ Xs_3 @ Ys_2 ) )
        = ( dropWh1316781920le_alt @ P_3 @ Ys_2 ) ) ) )).

thf(fact_632_dropWhile__append2,axiom,(
    ! [Ys_2: list_P1295265784le_alt,P_3: produc1362454231le_alt > $o,Xs_3: list_P1295265784le_alt] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ ( set_Pr412222150le_alt @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh612508742le_alt @ P_3 @ ( append423770578le_alt @ Xs_3 @ Ys_2 ) )
        = ( dropWh612508742le_alt @ P_3 @ Ys_2 ) ) ) )).

thf(fact_633_dropWhile__append2,axiom,(
    ! [Ys_2: list_A1484739013e_indi,P_3: arrow_1429601828e_indi > $o,Xs_3: list_A1484739013e_indi] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ ( set_Ar778541203e_indi @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh1160116755e_indi @ P_3 @ ( append711934367e_indi @ Xs_3 @ Ys_2 ) )
        = ( dropWh1160116755e_indi @ P_3 @ Ys_2 ) ) ) )).

thf(fact_634_dropWhile__append2,axiom,(
    ! [Ys_2: list_o,P_3: $o > $o,Xs_3: list_o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ ( set_o @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWhile_o @ P_3 @ ( append_o @ Xs_3 @ Ys_2 ) )
        = ( dropWhile_o @ P_3 @ Ys_2 ) ) ) )).

thf(fact_635_dropWhile__append2,axiom,(
    ! [Ys_2: list_A518015091_alt_o,P_3: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,Xs_3: list_A518015091_alt_o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ ( set_Ar1356274881_alt_o @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh583351873_alt_o @ P_3 @ ( append326058957_alt_o @ Xs_3 @ Ys_2 ) )
        = ( dropWh583351873_alt_o @ P_3 @ Ys_2 ) ) ) )).

thf(fact_636_dropWhile__append2,axiom,(
    ! [Ys_2: list_P1178103901_alt_o,P_3: ( produc1501160679le_alt > $o ) > $o,Xs_3: list_P1178103901_alt_o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ ( set_Pr592386425_alt_o @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh1049991161_alt_o @ P_3 @ ( append612833133_alt_o @ Xs_3 @ Ys_2 ) )
        = ( dropWh1049991161_alt_o @ P_3 @ Ys_2 ) ) ) )).

thf(fact_637_dropWhile__append2,axiom,(
    ! [Ys_2: list_A524553945_alt_o,P_3: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,Xs_3: list_A524553945_alt_o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ ( set_Ar571341173_alt_o @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh73644021_alt_o @ P_3 @ ( append295924073_alt_o @ Xs_3 @ Ys_2 ) )
        = ( dropWh73644021_alt_o @ P_3 @ Ys_2 ) ) ) )).

thf(fact_638_dropWhile__append2,axiom,(
    ! [Ys_2: list_P736798472le_alt,P_3: produc1501160679le_alt > $o,Xs_3: list_P736798472le_alt] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ ( set_Pr1525059414le_alt @ Xs_3 ) )
         => ( P_3 @ X_2 ) )
     => ( ( dropWh680325334le_alt @ P_3 @ ( append1229289570le_alt @ Xs_3 @ Ys_2 ) )
        = ( dropWh680325334le_alt @ P_3 @ Ys_2 ) ) ) )).

thf(fact_639_takeWhile__append2,axiom,(
    ! [Ys_1: list_A2115238852le_alt,P_2: arrow_475358991le_alt > $o,Xs_2: list_A2115238852le_alt] :
      ( ! [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh1696291512le_alt @ P_2 @ ( append179082452le_alt @ Xs_2 @ Ys_1 ) )
        = ( append179082452le_alt @ Xs_2 @ ( takeWh1696291512le_alt @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_640_takeWhile__append2,axiom,(
    ! [Ys_1: list_P1295265784le_alt,P_2: produc1362454231le_alt > $o,Xs_2: list_P1295265784le_alt] :
      ( ! [X_2: produc1362454231le_alt] :
          ( ( member28618436le_alt @ X_2 @ ( set_Pr412222150le_alt @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh1571807982le_alt @ P_2 @ ( append423770578le_alt @ Xs_2 @ Ys_1 ) )
        = ( append423770578le_alt @ Xs_2 @ ( takeWh1571807982le_alt @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_641_takeWhile__append2,axiom,(
    ! [Ys_1: list_A1484739013e_indi,P_2: arrow_1429601828e_indi > $o,Xs_2: list_A1484739013e_indi] :
      ( ! [X_2: arrow_1429601828e_indi] :
          ( ( member2052026769e_indi @ X_2 @ ( set_Ar778541203e_indi @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh831911099e_indi @ P_2 @ ( append711934367e_indi @ Xs_2 @ Ys_1 ) )
        = ( append711934367e_indi @ Xs_2 @ ( takeWh831911099e_indi @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_642_takeWhile__append2,axiom,(
    ! [Ys_1: list_o,P_2: $o > $o,Xs_2: list_o] :
      ( ! [X_2: $o] :
          ( ( member_o @ X_2 @ ( set_o @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWhile_o @ P_2 @ ( append_o @ Xs_2 @ Ys_1 ) )
        = ( append_o @ Xs_2 @ ( takeWhile_o @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_643_takeWhile__append2,axiom,(
    ! [Ys_1: list_A518015091_alt_o,P_2: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,Xs_2: list_A518015091_alt_o] :
      ( ! [X_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
          ( ( member616898751_alt_o @ X_2 @ ( set_Ar1356274881_alt_o @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh877796585_alt_o @ P_2 @ ( append326058957_alt_o @ Xs_2 @ Ys_1 ) )
        = ( append326058957_alt_o @ Xs_2 @ ( takeWh877796585_alt_o @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_644_takeWhile__append2,axiom,(
    ! [Ys_1: list_P1178103901_alt_o,P_2: ( produc1501160679le_alt > $o ) > $o,Xs_2: list_P1178103901_alt_o] :
      ( ! [X_2: produc1501160679le_alt > $o] :
          ( ( member377231867_alt_o @ X_2 @ ( set_Pr592386425_alt_o @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh1715715921_alt_o @ P_2 @ ( append612833133_alt_o @ Xs_2 @ Ys_1 ) )
        = ( append612833133_alt_o @ Xs_2 @ ( takeWh1715715921_alt_o @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_645_takeWhile__append2,axiom,(
    ! [Ys_1: list_A524553945_alt_o,P_2: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,Xs_2: list_A524553945_alt_o] :
      ( ! [X_2: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
          ( ( member526088951_alt_o @ X_2 @ ( set_Ar571341173_alt_o @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh1825606477_alt_o @ P_2 @ ( append295924073_alt_o @ Xs_2 @ Ys_1 ) )
        = ( append295924073_alt_o @ Xs_2 @ ( takeWh1825606477_alt_o @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_646_takeWhile__append2,axiom,(
    ! [Ys_1: list_P736798472le_alt,P_2: produc1501160679le_alt > $o,Xs_2: list_P736798472le_alt] :
      ( ! [X_2: produc1501160679le_alt] :
          ( ( member214075476le_alt @ X_2 @ ( set_Pr1525059414le_alt @ Xs_2 ) )
         => ( P_2 @ X_2 ) )
     => ( ( takeWh302148478le_alt @ P_2 @ ( append1229289570le_alt @ Xs_2 @ Ys_1 ) )
        = ( append1229289570le_alt @ Xs_2 @ ( takeWh302148478le_alt @ P_2 @ Ys_1 ) ) ) ) )).

thf(fact_647_split__list__propE,axiom,(
    ! [P_1: arrow_475358991le_alt > $o,Xs_1: list_A2115238852le_alt] :
      ( ? [X_2: arrow_475358991le_alt] :
          ( ( member84363362le_alt @ X_2 @ ( set_Ar577454304le_alt @ Xs_1 ) )
          & ( P_1 @ X_2 ) )
     => ~ ! [Ys: list_A2115238852le_alt,X_2: arrow_475358991le_alt] :
            ( ? [Zs: list_A2115238852le_alt] :
                ( Xs_1
                = ( append179082452le_alt @ Ys @ ( cons_A228743023le_alt @ X_2 @ Zs ) ) )
           => ~ ( P_1 @ X_2 ) ) ) )).

thf(fact_648_in__set__conv__decomp,axiom,(
    ! [X_1: produc1501160679le_alt > $o,Xs: list_P1178103901_alt_o] :
      ( ( member377231867_alt_o @ X_1 @ ( set_Pr592386425_alt_o @ Xs ) )
    <=> ? [Ys: list_P1178103901_alt_o,Zs: list_P1178103901_alt_o] :
          ( Xs
          = ( append612833133_alt_o @ Ys @ ( cons_P1239653256_alt_o @ X_1 @ Zs ) ) ) ) )).

thf(fact_649_in__set__conv__decomp,axiom,(
    ! [X_1: arrow_1429601828e_indi > produc1501160679le_alt > $o,Xs: list_A524553945_alt_o] :
      ( ( member526088951_alt_o @ X_1 @ ( set_Ar571341173_alt_o @ Xs ) )
    <=> ? [Ys: list_A524553945_alt_o,Zs: list_A524553945_alt_o] :
          ( Xs
          = ( append295924073_alt_o @ Ys @ ( cons_A2010997508_alt_o @ X_1 @ Zs ) ) ) ) )).

thf(fact_650_in__set__conv__decomp,axiom,(
    ! [X_1: produc1501160679le_alt,Xs: list_P736798472le_alt] :
      ( ( member214075476le_alt @ X_1 @ ( set_Pr1525059414le_alt @ Xs ) )
    <=> ? [Ys: list_P736798472le_alt,Zs: list_P736798472le_alt] :
          ( Xs
          = ( append1229289570le_alt @ Ys @ ( cons_P1913588871le_alt @ X_1 @ Zs ) ) ) ) )).

thf(fact_651_termination__basic__simps_I5_J,axiom,(
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( ord_less_eq_nat @ X @ Y ) ) )).

thf(fact_652_lessI,axiom,(
    ! [N: nat] :
      ( ord_less_nat @ N @ ( suc @ N ) ) )).

thf(fact_653_Suc__mono,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) )).

thf(fact_654_n__not__Suc__n,axiom,(
    ! [N: nat] :
      ( N
     != ( suc @ N ) ) )).

thf(fact_655_Suc__n__not__n,axiom,(
    ! [N: nat] :
      ( ( suc @ N )
     != N ) )).

thf(fact_656_nat_Oinject,axiom,(
    ! [Nat_1: nat,Nat: nat] :
      ( ( ( suc @ Nat_1 )
        = ( suc @ Nat ) )
    <=> ( Nat_1 = Nat ) ) )).

thf(fact_657_Suc__inject,axiom,(
    ! [X: nat,Y: nat] :
      ( ( ( suc @ X )
        = ( suc @ Y ) )
     => ( X = Y ) ) )).

thf(fact_658_less__not__refl,axiom,(
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ N ) )).

thf(fact_659_nat__neq__iff,axiom,(
    ! [M: nat,N: nat] :
      ( ( M != N )
    <=> ( ( ord_less_nat @ M @ N )
        | ( ord_less_nat @ N @ M ) ) ) )).

thf(fact_660_linorder__neqE__nat,axiom,(
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ ( ord_less_nat @ X @ Y )
       => ( ord_less_nat @ Y @ X ) ) ) )).

thf(fact_661_less__irrefl__nat,axiom,(
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ N ) )).

thf(fact_662_less__not__refl2,axiom,(
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ N @ M )
     => ( M != N ) ) )).

thf(fact_663_less__not__refl3,axiom,(
    ! [S: nat,T: nat] :
      ( ( ord_less_nat @ S @ T )
     => ( S != T ) ) )).

thf(fact_664_nat__less__cases,axiom,(
    ! [P: nat > nat > $o,M: nat,N: nat] :
      ( ( ( ord_less_nat @ M @ N )
       => ( P @ N @ M ) )
     => ( ( ( M = N )
         => ( P @ N @ M ) )
       => ( ( ( ord_less_nat @ N @ M )
           => ( P @ N @ M ) )
         => ( P @ N @ M ) ) ) ) )).

thf(fact_665_le__refl,axiom,(
    ! [N: nat] :
      ( ord_less_eq_nat @ N @ N ) )).

thf(fact_666_nat__le__linear,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
      | ( ord_less_eq_nat @ N @ M ) ) )).

thf(fact_667_eq__imp__le,axiom,(
    ! [M: nat,N: nat] :
      ( ( M = N )
     => ( ord_less_eq_nat @ M @ N ) ) )).

thf(fact_668_le__trans,axiom,(
    ! [K: nat,I_1: nat,J: nat] :
      ( ( ord_less_eq_nat @ I_1 @ J )
     => ( ( ord_less_eq_nat @ J @ K )
       => ( ord_less_eq_nat @ I_1 @ K ) ) ) )).

thf(fact_669_le__antisym,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ( ord_less_eq_nat @ N @ M )
       => ( M = N ) ) ) )).

thf(fact_670_Suc__less__SucD,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
     => ( ord_less_nat @ M @ N ) ) )).

thf(fact_671_Suc__lessD,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ ( suc @ M ) @ N )
     => ( ord_less_nat @ M @ N ) ) )).

thf(fact_672_less__SucE,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N ) )
     => ( ~ ( ord_less_nat @ M @ N )
       => ( M = N ) ) ) )).

thf(fact_673_less__trans__Suc,axiom,(
    ! [K: nat,I_1: nat,J: nat] :
      ( ( ord_less_nat @ I_1 @ J )
     => ( ( ord_less_nat @ J @ K )
       => ( ord_less_nat @ ( suc @ I_1 ) @ K ) ) ) )).

thf(fact_674_Suc__lessI,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ( ( suc @ M )
         != N )
       => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) )).

thf(fact_675_less__SucI,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ord_less_nat @ M @ ( suc @ N ) ) ) )).

thf(fact_676_less__antisym,axiom,(
    ! [N: nat,M: nat] :
      ( ~ ( ord_less_nat @ N @ M )
     => ( ( ord_less_nat @ N @ ( suc @ M ) )
       => ( M = N ) ) ) )).

thf(fact_677_not__less__less__Suc__eq,axiom,(
    ! [N: nat,M: nat] :
      ( ~ ( ord_less_nat @ N @ M )
     => ( ( ord_less_nat @ N @ ( suc @ M ) )
      <=> ( N = M ) ) ) )).

thf(fact_678_Suc__less__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
    <=> ( ord_less_nat @ M @ N ) ) )).

thf(fact_679_less__Suc__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N ) )
    <=> ( ( ord_less_nat @ M @ N )
        | ( M = N ) ) ) )).

thf(fact_680_not__less__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ~ ( ord_less_nat @ M @ N )
    <=> ( ord_less_nat @ N @ ( suc @ M ) ) ) )).

thf(fact_681_Suc__n__not__le__n,axiom,(
    ! [N: nat] :
      ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) )).

thf(fact_682_not__less__eq__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ~ ( ord_less_eq_nat @ M @ N )
    <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) )).

thf(fact_683_le__Suc__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
    <=> ( ( ord_less_eq_nat @ M @ N )
        | ( M
          = ( suc @ N ) ) ) ) )).

thf(fact_684_Suc__le__mono,axiom,(
    ! [N: nat,M: nat] :
      ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
    <=> ( ord_less_eq_nat @ N @ M ) ) )).

thf(fact_685_le__SucI,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) )).

thf(fact_686_le__SucE,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
     => ( ~ ( ord_less_eq_nat @ M @ N )
       => ( M
          = ( suc @ N ) ) ) ) )).

thf(fact_687_Suc__leD,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
     => ( ord_less_eq_nat @ M @ N ) ) )).

thf(fact_688_less__or__eq__imp__le,axiom,(
    ! [M: nat,N: nat] :
      ( ( ( ord_less_nat @ M @ N )
        | ( M = N ) )
     => ( ord_less_eq_nat @ M @ N ) ) )).

thf(fact_689_le__neq__implies__less,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ( M != N )
       => ( ord_less_nat @ M @ N ) ) ) )).

thf(fact_690_less__imp__le__nat,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ord_less_eq_nat @ M @ N ) ) )).

thf(fact_691_le__eq__less__or__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
    <=> ( ( ord_less_nat @ M @ N )
        | ( M = N ) ) ) )).

thf(fact_692_nat__less__le,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
    <=> ( ( ord_less_eq_nat @ M @ N )
        & ( M != N ) ) ) )).

thf(fact_693_Suc__le__lessD,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
     => ( ord_less_nat @ M @ N ) ) )).

thf(fact_694_le__less__Suc__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ( ord_less_nat @ N @ ( suc @ M ) )
      <=> ( N = M ) ) ) )).

thf(fact_695_Suc__leI,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) )).

thf(fact_696_le__imp__less__Suc,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ord_less_nat @ M @ ( suc @ N ) ) ) )).

thf(fact_697_Suc__le__eq,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
    <=> ( ord_less_nat @ M @ N ) ) )).

thf(fact_698_less__Suc__eq__le,axiom,(
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N ) )
    <=> ( ord_less_eq_nat @ M @ N ) ) )).

thf(fact_699_less__eq__Suc__le,axiom,(
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ N @ M )
    <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) )).

%----Helper facts (5)
thf(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lc,axiom,(
    ! [X: list_A2115238852le_alt,Y: list_A2115238852le_alt] :
      ( ~ ( fequal781288069le_alt @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lc,axiom,(
    ! [X: list_A2115238852le_alt,Y: list_A2115238852le_alt] :
      ( ( X != Y )
      | ( fequal781288069le_alt @ X @ Y ) ) )).

thf(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,(
    ! [X: produc1362454231le_alt,Y: produc1362454231le_alt] :
      ( ( if_Pro314693991le_alt @ $true @ X @ Y )
      = X ) )).

thf(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,(
    ! [X: produc1362454231le_alt,Y: produc1362454231le_alt] :
      ( ( if_Pro314693991le_alt @ $false @ X @ Y )
      = Y ) )).

thf(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,(
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) )).

%----Conjectures (1)
thf(conj_0,conjecture,(
    ! [I: arrow_1429601828e_indi] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) )
    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ) )).

%------------------------------------------------------------------------------