%------------------------------------------------------------------------------
% File     : SWW475_10 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Software Verification
% Problem  : Java type soundness line 22, 100 axioms selected
% Version  : SWW475_1 with the conjecture removed
% English  :

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

% Status   : Satisfiable
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    :  368 (  76 unt; 117 typ;   0 def)
%            Number of atoms       :  634 ( 151 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  541 ( 158   ~;   0   |;  16   &)
%                                         (  40 <=>; 327  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :   42 (  41 usr)
%            Number of type conns  :  118 (  66   >;  52   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   75 (  75 usr;  10 con; 0-5 aty)
%            Number of variables   : 1160 (1136   !;  24   ?;1160   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 15:23:13
%------------------------------------------------------------------------------
%----Should-be-implicit typings (41)
tff(ty_ty_tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    exp_list_char: $tType ).

tff(ty_ty_tc__HOL__Obool,type,
    bool: $tType ).

tff(ty_ty_tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_J,type,
    list_exp_list_char: $tType ).

tff(ty_ty_tc__List__Olist_Itc__String__Ochar_J,type,
    list_char: $tType ).

tff(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
    list_P1999446415t_char: $tType ).

tff(ty_ty_tc__Type__Oty,type,
    ty: $tType ).

tff(ty_ty_tc__Value__Oval,type,
    val: $tType ).

tff(ty_ty_tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__fun_I,type,
    fun_ex1201926843l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och,type,
    fun_li1372729616l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_Itc__Ty,type,
    fun_li688206603ion_ty: $tType ).

tff(ty_ty_tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_Itc__Va,type,
    fun_li1432931796on_val: $tType ).

tff(ty_ty_tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc,type,
    fun_na939144002on_val: $tType ).

tff(ty_ty_tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooptio,type,
    fun_fu1693644106l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__,type,
    fun_fu100249073l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    fun_Pr680585871l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__001,type,
    fun_Pr633696065l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    fun_Pr248118298l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_002,type,
    fun_Pr597144499l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
    fun_Pr1696029455l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_003,type,
    fun_Pr598845249l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    fun_Pr691271849l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___004,type,
    fun_Pr220980979l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    fun_Pr859510977l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_005,type,
    fun_Pr1511900787l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
    fun_Pr693020585l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    fun_Pr903661919l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    fun_Pr302334223l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option_,type,
    fun_Pr27327839l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
    fun_Pr111684683l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr,type,
    fun_Pr1329133739l_bool: $tType ).

tff(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
    produc124828825on_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    produc2061676504on_val: $tType ).

tff(ty_ty_tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List_,type,
    produc12694297on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    produc1102272487on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
    produc430140671on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
    produc409205479on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
    produc231486621on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__O,type,
    produc1466422861on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_,type,
    produc1454067869on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_It,type,
    produc1464201097on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_It,type,
    produc319655913on_val: $tType ).

%----Explicit typings (76)
tff(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    hconf_97414254t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > bool ).

tff(sy_c_Expr_Oexp_OCall_000tc__List__Olist_Itc__String__Ochar_J,type,
    call_list_char: ( exp_list_char * list_char * list_exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OCast_000tc__List__Olist_Itc__String__Ochar_J,type,
    cast_list_char: ( list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OFAcc_000tc__List__Olist_Itc__String__Ochar_J,type,
    fAcc_list_char: ( exp_list_char * list_char * list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OTryCatch_000tc__List__Olist_Itc__String__Ochar_J,type,
    tryCatch_list_char: ( exp_list_char * list_char * list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
    val_list_char: val > exp_list_char ).

tff(sy_c_Expr_Oexp_Othrow_000tc__List__Olist_Itc__String__Ochar_J,type,
    throw_list_char: exp_list_char > exp_list_char ).

tff(sy_c_List_Olist_OCons_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    cons_exp_list_char: ( exp_list_char * list_exp_list_char ) > list_exp_list_char ).

tff(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    map_ad325961431ar_val: ( fun_li1432931796on_val * fun_li1432931796on_val ) > fun_li1432931796on_val ).

tff(sy_c_Objects_Ohext,type,
    hext: ( fun_na939144002on_val * fun_na939144002on_val ) > bool ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    produc1259058957on_val: ( exp_list_char * produc12694297on_val ) > produc124828825on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    produc379668296on_val: ( list_exp_list_char * produc12694297on_val ) > produc2061676504on_val ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
    produc899768717on_val: ( fun_na939144002on_val * fun_li1432931796on_val ) > produc12694297on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
    produc1441475159on_val: ( produc124828825on_val * produc124828825on_val ) > produc1102272487on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
    produc1611380469on_val: ( produc2061676504on_val * produc2061676504on_val ) > produc430140671on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooptio,type,
    produc870913623on_val: ( produc12694297on_val * produc12694297on_val ) > produc409205479on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
    produc1564932627on_val: ( produc1102272487on_val * produc1102272487on_val ) > produc231486621on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
    produc1951691075on_val: ( produc430140671on_val * produc430140671on_val ) > produc1466422861on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Opti,type,
    produc935654419on_val: ( produc409205479on_val * produc409205479on_val ) > produc1454067869on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Li,type,
    produc1729053055on_val: ( produc231486621on_val * produc231486621on_val ) > produc1464201097on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__E,type,
    produc722767071on_val: ( produc1466422861on_val * produc1466422861on_val ) > produc319655913on_val ).

tff(sy_c_Product__Type_Ocurry_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_,type,
    produc1911975310l_bool: fun_Pr680585871l_bool > fun_ex1201926843l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_It,type,
    produc1838470831l_bool: fun_Pr248118298l_bool > fun_li1372729616l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr,type,
    produc2062775566l_bool: fun_Pr1696029455l_bool > fun_fu100249073l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
    produc1159035454l_bool: fun_Pr691271849l_bool > fun_Pr633696065l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List,type,
    produc2053127004l_bool: fun_Pr859510977l_bool > fun_Pr597144499l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oopti,type,
    produc1073654846l_bool: fun_Pr693020585l_bool > fun_Pr598845249l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
    produc1497005946l_bool: fun_Pr903661919l_bool > fun_Pr220980979l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp,type,
    produc971707818l_bool: fun_Pr302334223l_bool > fun_Pr1511900787l_bool ).

tff(sy_c_SmallStep_Ored,type,
    red: list_P1999446415t_char > fun_Pr691271849l_bool ).

tff(sy_c_SmallStep_Oreds,type,
    reds: list_P1999446415t_char > fun_Pr859510977l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
    transi2024712006on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_I,type,
    transi374442731on_val: fun_Pr859510977l_bool > fun_Pr859510977l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Optio,type,
    transi921647814on_val: fun_Pr693020585l_bool > fun_Pr693020585l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
    transi910771962on_val: fun_Pr903661919l_bool > fun_Pr903661919l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ex,type,
    transi208336786on_val: fun_Pr302334223l_bool > fun_Pr302334223l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_,type,
    transi594096122on_val: fun_Pr27327839l_bool > fun_Pr27327839l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oex,type,
    transi678815536on_val: fun_Pr111684683l_bool > fun_Pr111684683l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__prod_Itc__List__Oli,type,
    transi1751449568on_val: fun_Pr1329133739l_bool > fun_Pr1329133739l_bool ).

tff(sy_c_Value_Oval_ONull,type,
    null: val ).

tff(sy_c_WellTypeRT_OWTrt,type,
    wTrt: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char * ty ) > bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I,type,
    hAPP_e1833980889l_bool: ( fun_ex1201926843l_bool * exp_list_char ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar,type,
    hAPP_l146377954l_bool: ( fun_li1372729616l_bool * list_exp_list_char ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
    hAPP_f1033709212l_bool: ( fun_fu1693644106l_bool * fun_li1432931796on_val ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
    hAPP_f1175813647l_bool: ( fun_fu100249073l_bool * fun_na939144002on_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    hAPP_P1708370145l_bool: ( fun_Pr680585871l_bool * produc124828825on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_006,type,
    hAPP_P1116729363l_bool: ( fun_Pr633696065l_bool * produc124828825on_val ) > fun_Pr680585871l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
    hAPP_P71593144l_bool: ( fun_Pr248118298l_bool * produc2061676504on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_007,type,
    hAPP_P1183008383l_bool: ( fun_Pr597144499l_bool * produc2061676504on_val ) > fun_Pr248118298l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
    hAPP_P159683425l_bool: ( fun_Pr1696029455l_bool * produc12694297on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_008,type,
    hAPP_P1988153107l_bool: ( fun_Pr598845249l_bool * produc12694297on_val ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_P282169671l_bool: ( fun_Pr691271849l_bool * produc1102272487on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_009,type,
    hAPP_P2062527807l_bool: ( fun_Pr220980979l_bool * produc1102272487on_val ) > fun_Pr691271849l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis,type,
    hAPP_P1333315679l_bool: ( fun_Pr859510977l_bool * produc430140671on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_010,type,
    hAPP_P220718911l_bool: ( fun_Pr1511900787l_bool * produc430140671on_val ) > fun_Pr859510977l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc,type,
    hAPP_P1221872711l_bool: ( fun_Pr693020585l_bool * produc409205479on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
    hAPP_P378063101l_bool: ( fun_Pr903661919l_bool * produc231486621on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,type,
    hAPP_P2028072621l_bool: ( fun_Pr302334223l_bool * produc1466422861on_val ) > bool ).

tff(sy_c_hBOOL,type,
    hBOOL: bool > $o ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    member773094996on_val: ( produc1102272487on_val * fun_Pr691271849l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    member875476972on_val: ( produc430140671on_val * fun_Pr859510977l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
    member563141460on_val: ( produc409205479on_val * fun_Pr693020585l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    member808015754on_val: ( produc231486621on_val * fun_Pr903661919l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    member88670778on_val: ( produc1466422861on_val * fun_Pr302334223l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option_,type,
    member2032527242on_val: ( produc1454067869on_val * fun_Pr27327839l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
    member712690550on_val: ( produc1464201097on_val * fun_Pr111684683l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr,type,
    member1837727190on_val: ( produc319655913on_val * fun_Pr1329133739l_bool ) > bool ).

tff(sy_v_E,type,
    e_1: fun_li688206603ion_ty ).

tff(sy_v_P,type,
    p: list_P1999446415t_char ).

tff(sy_v_T,type,
    t: ty ).

tff(sy_v_e,type,
    e: exp_list_char ).

tff(sy_v_e_H,type,
    e_2: exp_list_char ).

tff(sy_v_h,type,
    h_1: fun_na939144002on_val ).

tff(sy_v_h_H,type,
    h: fun_na939144002on_val ).

tff(sy_v_l,type,
    l_1: fun_li1432931796on_val ).

tff(sy_v_l_H,type,
    l: fun_li1432931796on_val ).

%----Relevant facts (248)
tff(fact_0_prod__induct5,axiom,
    ! [X: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_8: produc430140671on_val,B_1: produc2061676504on_val,C_2: list_exp_list_char,D_1: fun_na939144002on_val,E_1: fun_li1432931796on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_8,produc1611380469on_val(B_1,produc379668296on_val(C_2,produc899768717on_val(D_1,E_1))))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X)) ) ).

tff(fact_1_prod__induct5,axiom,
    ! [X: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_8: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D_1: fun_na939144002on_val,E_1: fun_li1432931796on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_8,produc1441475159on_val(B_1,produc1259058957on_val(C_2,produc899768717on_val(D_1,E_1))))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).

tff(fact_2_prod__cases5,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_8: produc430140671on_val,B_1: produc2061676504on_val,C_2: list_exp_list_char,D_1: fun_na939144002on_val,E_1: fun_li1432931796on_val] : ( Y_1 != produc1951691075on_val(A_8,produc1611380469on_val(B_1,produc379668296on_val(C_2,produc899768717on_val(D_1,E_1)))) ) ).

tff(fact_3_prod__cases5,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_8: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D_1: fun_na939144002on_val,E_1: fun_li1432931796on_val] : ( Y_1 != produc1564932627on_val(A_8,produc1441475159on_val(B_1,produc1259058957on_val(C_2,produc899768717on_val(D_1,E_1)))) ) ).

tff(fact_4_prod__induct4,axiom,
    ! [X: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_8: produc2061676504on_val,B_1: list_exp_list_char,C_2: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_8,produc379668296on_val(B_1,produc899768717on_val(C_2,D_1)))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X)) ) ).

tff(fact_5_prod__induct4,axiom,
    ! [X: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_8: produc124828825on_val,B_1: exp_list_char,C_2: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_8,produc1259058957on_val(B_1,produc899768717on_val(C_2,D_1)))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X)) ) ).

tff(fact_6_prod__induct4,axiom,
    ! [X: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_8: produc430140671on_val,B_1: produc2061676504on_val,C_2: list_exp_list_char,D_1: produc12694297on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_8,produc1611380469on_val(B_1,produc379668296on_val(C_2,D_1)))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X)) ) ).

tff(fact_7_prod__induct4,axiom,
    ! [X: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_8: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D_1: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_8,produc1441475159on_val(B_1,produc1259058957on_val(C_2,D_1)))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).

tff(fact_8_prod__cases4,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_8: produc2061676504on_val,B_1: list_exp_list_char,C_2: fun_na939144002on_val,D_1: fun_li1432931796on_val] : ( Y_1 != produc1611380469on_val(A_8,produc379668296on_val(B_1,produc899768717on_val(C_2,D_1))) ) ).

tff(fact_9_prod__cases4,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_8: produc124828825on_val,B_1: exp_list_char,C_2: fun_na939144002on_val,D_1: fun_li1432931796on_val] : ( Y_1 != produc1441475159on_val(A_8,produc1259058957on_val(B_1,produc899768717on_val(C_2,D_1))) ) ).

tff(fact_10_prod__cases4,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_8: produc430140671on_val,B_1: produc2061676504on_val,C_2: list_exp_list_char,D_1: produc12694297on_val] : ( Y_1 != produc1951691075on_val(A_8,produc1611380469on_val(B_1,produc379668296on_val(C_2,D_1))) ) ).

tff(fact_11_prod__cases4,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_8: produc1102272487on_val,B_1: produc124828825on_val,C_2: exp_list_char,D_1: produc12694297on_val] : ( Y_1 != produc1564932627on_val(A_8,produc1441475159on_val(B_1,produc1259058957on_val(C_2,D_1))) ) ).

tff(fact_12_red__hext__incr,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_13_prod__induct3,axiom,
    ! [X: produc2061676504on_val,Pa: fun_Pr248118298l_bool] :
      ( ! [A_8: list_exp_list_char,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : hBOOL(hAPP_P71593144l_bool(Pa,produc379668296on_val(A_8,produc899768717on_val(B_1,C_2))))
     => hBOOL(hAPP_P71593144l_bool(Pa,X)) ) ).

tff(fact_14_prod__induct3,axiom,
    ! [X: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_8: produc2061676504on_val,B_1: list_exp_list_char,C_2: produc12694297on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_8,produc379668296on_val(B_1,C_2))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X)) ) ).

tff(fact_15_prod__induct3,axiom,
    ! [X: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
      ( ! [A_8: exp_list_char,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_8,produc899768717on_val(B_1,C_2))))
     => hBOOL(hAPP_P1708370145l_bool(Pa,X)) ) ).

tff(fact_16_prod__induct3,axiom,
    ! [X: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_8: produc124828825on_val,B_1: exp_list_char,C_2: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_8,produc1259058957on_val(B_1,C_2))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X)) ) ).

tff(fact_17_prod__induct3,axiom,
    ! [X: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_8: produc430140671on_val,B_1: produc2061676504on_val,C_2: produc2061676504on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_8,produc1611380469on_val(B_1,C_2))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X)) ) ).

tff(fact_18_prod__induct3,axiom,
    ! [X: produc409205479on_val,Pa: fun_Pr693020585l_bool] :
      ( ! [A_8: produc12694297on_val,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_8,produc899768717on_val(B_1,C_2))))
     => hBOOL(hAPP_P1221872711l_bool(Pa,X)) ) ).

tff(fact_19_prod__induct3,axiom,
    ! [X: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_8: produc1102272487on_val,B_1: produc124828825on_val,C_2: produc124828825on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_8,produc1441475159on_val(B_1,C_2))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).

tff(fact_20_prod__cases3,axiom,
    ! [Y_1: produc2061676504on_val] :
      ~ ! [A_8: list_exp_list_char,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : ( Y_1 != produc379668296on_val(A_8,produc899768717on_val(B_1,C_2)) ) ).

tff(fact_21_prod__cases3,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_8: produc2061676504on_val,B_1: list_exp_list_char,C_2: produc12694297on_val] : ( Y_1 != produc1611380469on_val(A_8,produc379668296on_val(B_1,C_2)) ) ).

tff(fact_22_prod__cases3,axiom,
    ! [Y_1: produc124828825on_val] :
      ~ ! [A_8: exp_list_char,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : ( Y_1 != produc1259058957on_val(A_8,produc899768717on_val(B_1,C_2)) ) ).

tff(fact_23_prod__cases3,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_8: produc124828825on_val,B_1: exp_list_char,C_2: produc12694297on_val] : ( Y_1 != produc1441475159on_val(A_8,produc1259058957on_val(B_1,C_2)) ) ).

tff(fact_24_prod__cases3,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_8: produc430140671on_val,B_1: produc2061676504on_val,C_2: produc2061676504on_val] : ( Y_1 != produc1951691075on_val(A_8,produc1611380469on_val(B_1,C_2)) ) ).

tff(fact_25_prod__cases3,axiom,
    ! [Y_1: produc409205479on_val] :
      ~ ! [A_8: produc12694297on_val,B_1: fun_na939144002on_val,C_2: fun_li1432931796on_val] : ( Y_1 != produc870913623on_val(A_8,produc899768717on_val(B_1,C_2)) ) ).

tff(fact_26_prod__cases3,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_8: produc1102272487on_val,B_1: produc124828825on_val,C_2: produc124828825on_val] : ( Y_1 != produc1564932627on_val(A_8,produc1441475159on_val(B_1,C_2)) ) ).

tff(fact_27_split__paired__All,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ! [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ! [A_8: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,produc379668296on_val(A_8,B_1))) ) ).

tff(fact_28_split__paired__All,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ! [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ! [A_8: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_8,B_1))) ) ).

tff(fact_29_split__paired__All,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ! [A_8: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_8,B_1))) ) ).

tff(fact_30_split__paired__All,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ! [A_8: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_8,B_1))) ) ).

tff(fact_31_split__paired__All,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ! [A_8: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_8,B_1))) ) ).

tff(fact_32_split__paired__All,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ! [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ! [A_8: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_8,B_1))) ) ).

tff(fact_33_split__paired__All,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ! [A_8: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_8,B_1))) ) ).

tff(fact_34_split__paired__All,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ! [A_8: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_8,B_1))) ) ).

tff(fact_35_Pair__eq,axiom,
    ! [A_2: list_exp_list_char,B: produc12694297on_val,A_12: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( produc379668296on_val(A_2,B) = produc379668296on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_36_Pair__eq,axiom,
    ! [A_2: produc2061676504on_val,B: produc2061676504on_val,A_12: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( produc1611380469on_val(A_2,B) = produc1611380469on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_37_Pair__eq,axiom,
    ! [A_2: fun_na939144002on_val,B: fun_li1432931796on_val,A_12: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( produc899768717on_val(A_2,B) = produc899768717on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_38_Pair__eq,axiom,
    ! [A_2: exp_list_char,B: produc12694297on_val,A_12: exp_list_char,B_2: produc12694297on_val] :
      ( ( produc1259058957on_val(A_2,B) = produc1259058957on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_39_Pair__eq,axiom,
    ! [A_2: produc124828825on_val,B: produc124828825on_val,A_12: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( produc1441475159on_val(A_2,B) = produc1441475159on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_40_Pair__eq,axiom,
    ! [A_2: produc430140671on_val,B: produc430140671on_val,A_12: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( produc1951691075on_val(A_2,B) = produc1951691075on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_41_Pair__eq,axiom,
    ! [A_2: produc12694297on_val,B: produc12694297on_val,A_12: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( produc870913623on_val(A_2,B) = produc870913623on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_42_Pair__eq,axiom,
    ! [A_2: produc1102272487on_val,B: produc1102272487on_val,A_12: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( produc1564932627on_val(A_2,B) = produc1564932627on_val(A_12,B_2) )
    <=> ( ( A_2 = A_12 )
        & ( B = B_2 ) ) ) ).

tff(fact_43_Pair__inject,axiom,
    ! [A_2: list_exp_list_char,B: produc12694297on_val,A_12: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( produc379668296on_val(A_2,B) = produc379668296on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_44_Pair__inject,axiom,
    ! [A_2: produc2061676504on_val,B: produc2061676504on_val,A_12: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( produc1611380469on_val(A_2,B) = produc1611380469on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_45_Pair__inject,axiom,
    ! [A_2: fun_na939144002on_val,B: fun_li1432931796on_val,A_12: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( produc899768717on_val(A_2,B) = produc899768717on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_46_Pair__inject,axiom,
    ! [A_2: exp_list_char,B: produc12694297on_val,A_12: exp_list_char,B_2: produc12694297on_val] :
      ( ( produc1259058957on_val(A_2,B) = produc1259058957on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_47_Pair__inject,axiom,
    ! [A_2: produc124828825on_val,B: produc124828825on_val,A_12: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( produc1441475159on_val(A_2,B) = produc1441475159on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_48_Pair__inject,axiom,
    ! [A_2: produc430140671on_val,B: produc430140671on_val,A_12: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( produc1951691075on_val(A_2,B) = produc1951691075on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_49_Pair__inject,axiom,
    ! [A_2: produc12694297on_val,B: produc12694297on_val,A_12: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( produc870913623on_val(A_2,B) = produc870913623on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_50_Pair__inject,axiom,
    ! [A_2: produc1102272487on_val,B: produc1102272487on_val,A_12: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( produc1564932627on_val(A_2,B) = produc1564932627on_val(A_12,B_2) )
     => ~ ( ( A_2 = A_12 )
         => ( B != B_2 ) ) ) ).

tff(fact_51_hext__refl,axiom,
    ! [Ha: fun_na939144002on_val] : hBOOL(hext(Ha,Ha)) ).

tff(fact_52_WTrt__hext__mono,axiom,
    ! [H_a: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,T: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,T))
     => ( hBOOL(hext(Ha,H_a))
       => hBOOL(wTrt(Pa,H_a,E,Ea,T)) ) ) ).

tff(fact_53_red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,La))),produc1259058957on_val(E_a,produc899768717on_val(H_a,map_ad325961431ar_val(L_0,L_a)))),red(Pa))) ) ).

tff(fact_54_prod_Oexhaust,axiom,
    ! [Y_1: produc2061676504on_val] :
      ~ ! [A_8: list_exp_list_char,B_1: produc12694297on_val] : ( Y_1 != produc379668296on_val(A_8,B_1) ) ).

tff(fact_55_prod_Oexhaust,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_8: produc2061676504on_val,B_1: produc2061676504on_val] : ( Y_1 != produc1611380469on_val(A_8,B_1) ) ).

tff(fact_56_prod_Oexhaust,axiom,
    ! [Y_1: produc12694297on_val] :
      ~ ! [A_8: fun_na939144002on_val,B_1: fun_li1432931796on_val] : ( Y_1 != produc899768717on_val(A_8,B_1) ) ).

tff(fact_57_prod_Oexhaust,axiom,
    ! [Y_1: produc124828825on_val] :
      ~ ! [A_8: exp_list_char,B_1: produc12694297on_val] : ( Y_1 != produc1259058957on_val(A_8,B_1) ) ).

tff(fact_58_prod_Oexhaust,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_8: produc124828825on_val,B_1: produc124828825on_val] : ( Y_1 != produc1441475159on_val(A_8,B_1) ) ).

tff(fact_59_prod_Oexhaust,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_8: produc430140671on_val,B_1: produc430140671on_val] : ( Y_1 != produc1951691075on_val(A_8,B_1) ) ).

tff(fact_60_prod_Oexhaust,axiom,
    ! [Y_1: produc409205479on_val] :
      ~ ! [A_8: produc12694297on_val,B_1: produc12694297on_val] : ( Y_1 != produc870913623on_val(A_8,B_1) ) ).

tff(fact_61_prod_Oexhaust,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_8: produc1102272487on_val,B_1: produc1102272487on_val] : ( Y_1 != produc1564932627on_val(A_8,B_1) ) ).

tff(fact_62_PairE,axiom,
    ! [P: produc2061676504on_val] :
      ~ ! [X_1: list_exp_list_char,Y: produc12694297on_val] : ( P != produc379668296on_val(X_1,Y) ) ).

tff(fact_63_PairE,axiom,
    ! [P: produc430140671on_val] :
      ~ ! [X_1: produc2061676504on_val,Y: produc2061676504on_val] : ( P != produc1611380469on_val(X_1,Y) ) ).

tff(fact_64_PairE,axiom,
    ! [P: produc12694297on_val] :
      ~ ! [X_1: fun_na939144002on_val,Y: fun_li1432931796on_val] : ( P != produc899768717on_val(X_1,Y) ) ).

tff(fact_65_PairE,axiom,
    ! [P: produc124828825on_val] :
      ~ ! [X_1: exp_list_char,Y: produc12694297on_val] : ( P != produc1259058957on_val(X_1,Y) ) ).

tff(fact_66_PairE,axiom,
    ! [P: produc1102272487on_val] :
      ~ ! [X_1: produc124828825on_val,Y: produc124828825on_val] : ( P != produc1441475159on_val(X_1,Y) ) ).

tff(fact_67_PairE,axiom,
    ! [P: produc1466422861on_val] :
      ~ ! [X_1: produc430140671on_val,Y: produc430140671on_val] : ( P != produc1951691075on_val(X_1,Y) ) ).

tff(fact_68_PairE,axiom,
    ! [P: produc409205479on_val] :
      ~ ! [X_1: produc12694297on_val,Y: produc12694297on_val] : ( P != produc870913623on_val(X_1,Y) ) ).

tff(fact_69_PairE,axiom,
    ! [P: produc231486621on_val] :
      ~ ! [X_1: produc1102272487on_val,Y: produc1102272487on_val] : ( P != produc1564932627on_val(X_1,Y) ) ).

tff(fact_70_split__paired__Ex,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ? [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ? [A_8: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,produc379668296on_val(A_8,B_1))) ) ).

tff(fact_71_split__paired__Ex,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ? [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ? [A_8: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_8,B_1))) ) ).

tff(fact_72_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ? [A_8: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_8,B_1))) ) ).

tff(fact_73_split__paired__Ex,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ? [A_8: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_8,B_1))) ) ).

tff(fact_74_split__paired__Ex,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ? [A_8: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_8,B_1))) ) ).

tff(fact_75_split__paired__Ex,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ? [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ? [A_8: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_8,B_1))) ) ).

tff(fact_76_split__paired__Ex,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ? [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ? [A_8: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_8,B_1))) ) ).

tff(fact_77_split__paired__Ex,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ? [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ? [A_8: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_8,B_1))) ) ).

tff(fact_78_hext__trans,axiom,
    ! [H: fun_na939144002on_val,Ha: fun_na939144002on_val,H_a: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_a))
     => ( hBOOL(hext(H_a,H))
       => hBOOL(hext(Ha,H)) ) ) ).

tff(fact_79_Red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,La))),produc1259058957on_val(E_a,produc899768717on_val(H_a,map_ad325961431ar_val(L_0,L_a)))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_80_map__add__assoc,axiom,
    ! [M1: fun_li1432931796on_val,M2: fun_li1432931796on_val,M3: fun_li1432931796on_val] : ( map_ad325961431ar_val(M1,map_ad325961431ar_val(M2,M3)) = map_ad325961431ar_val(map_ad325961431ar_val(M1,M2),M3) ) ).

tff(fact_81_curryI,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_2: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(F_1,produc379668296on_val(A_2,B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_2),B)) ) ).

tff(fact_82_curryI,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_2: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(F_1,produc1611380469on_val(A_2,B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_2),B)) ) ).

tff(fact_83_curryI,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_2: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(F_1,produc899768717on_val(A_2,B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_2),B)) ) ).

tff(fact_84_curryI,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_2: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(F_1,produc1259058957on_val(A_2,B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_2),B)) ) ).

tff(fact_85_curryI,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_2: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(F_1,produc1441475159on_val(A_2,B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_2),B)) ) ).

tff(fact_86_curryI,axiom,
    ! [F_1: fun_Pr302334223l_bool,A_2: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P2028072621l_bool(F_1,produc1951691075on_val(A_2,B)))
     => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A_2),B)) ) ).

tff(fact_87_curryI,axiom,
    ! [F_1: fun_Pr693020585l_bool,A_2: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1221872711l_bool(F_1,produc870913623on_val(A_2,B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A_2),B)) ) ).

tff(fact_88_curryI,axiom,
    ! [F_1: fun_Pr903661919l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P378063101l_bool(F_1,produc1564932627on_val(A_2,B)))
     => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A_2),B)) ) ).

tff(fact_89_reds__hext__incr,axiom,
    ! [Esa: list_exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,Es_a: list_exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,produc899768717on_val(Ha,La)),produc379668296on_val(Es_a,produc899768717on_val(H_a,L_a))),reds(Pa)))
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_90_red__reds_OTryRed,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V_1,E_2),S_1),produc1259058957on_val(tryCatch_list_char(E_a,C,V_1,E_2),S)),red(Pa))) ) ).

tff(fact_91_red__reds_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(fAcc_list_char(E_a,F,D),S)),red(Pa))) ) ).

tff(fact_92_red__reds_OCastRed,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(cast_list_char(C,E_a),S)),red(Pa))) ) ).

tff(fact_93_curryE,axiom,
    ! [F_1: fun_Pr302334223l_bool,A_2: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P2028072621l_bool(F_1,produc1951691075on_val(A_2,B))) ) ).

tff(fact_94_curryE,axiom,
    ! [F_1: fun_Pr693020585l_bool,A_2: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P1221872711l_bool(F_1,produc870913623on_val(A_2,B))) ) ).

tff(fact_95_curryE,axiom,
    ! [F_1: fun_Pr903661919l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P378063101l_bool(F_1,produc1564932627on_val(A_2,B))) ) ).

tff(fact_96_curryE,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_2: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,produc1441475159on_val(A_2,B))) ) ).

tff(fact_97_curryE,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_2: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,produc1259058957on_val(A_2,B))) ) ).

tff(fact_98_curryE,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_2: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,produc899768717on_val(A_2,B))) ) ).

tff(fact_99_curryE,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_2: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,produc1611380469on_val(A_2,B))) ) ).

tff(fact_100_curryE,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_2: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,produc379668296on_val(A_2,B))) ) ).

tff(fact_101_curryD,axiom,
    ! [F_1: fun_Pr302334223l_bool,A_2: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P2028072621l_bool(F_1,produc1951691075on_val(A_2,B))) ) ).

tff(fact_102_curryD,axiom,
    ! [F_1: fun_Pr693020585l_bool,A_2: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P1221872711l_bool(F_1,produc870913623on_val(A_2,B))) ) ).

tff(fact_103_curryD,axiom,
    ! [F_1: fun_Pr903661919l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P378063101l_bool(F_1,produc1564932627on_val(A_2,B))) ) ).

tff(fact_104_curryD,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_2: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,produc1441475159on_val(A_2,B))) ) ).

tff(fact_105_curryD,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_2: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,produc1259058957on_val(A_2,B))) ) ).

tff(fact_106_curryD,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_2: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,produc899768717on_val(A_2,B))) ) ).

tff(fact_107_curryD,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_2: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,produc1611380469on_val(A_2,B))) ) ).

tff(fact_108_curryD,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_2: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_2),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,produc379668296on_val(A_2,B))) ) ).

tff(fact_109_curry__conv,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_2: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_2),B))
    <=> hBOOL(hAPP_P282169671l_bool(F_1,produc1441475159on_val(A_2,B))) ) ).

tff(fact_110_curry__conv,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_2: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_2),B))
    <=> hBOOL(hAPP_P1708370145l_bool(F_1,produc1259058957on_val(A_2,B))) ) ).

tff(fact_111_curry__conv,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_2: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_2),B))
    <=> hBOOL(hAPP_P159683425l_bool(F_1,produc899768717on_val(A_2,B))) ) ).

tff(fact_112_curry__conv,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_2: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_2),B))
    <=> hBOOL(hAPP_P1333315679l_bool(F_1,produc1611380469on_val(A_2,B))) ) ).

tff(fact_113_curry__conv,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_2: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_2),B))
    <=> hBOOL(hAPP_P71593144l_bool(F_1,produc379668296on_val(A_2,B))) ) ).

tff(fact_114_TryReds,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V_1,E_2),S_1),produc1259058957on_val(tryCatch_list_char(E_a,C,V_1,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_115_FAccReds,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(fAcc_list_char(E_a,F,D),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_116_CastReds,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(cast_list_char(C,E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_117_rtrancl_Ortrancl__refl,axiom,
    ! [A_2: produc430140671on_val,R: fun_Pr302334223l_bool] : hBOOL(member88670778on_val(produc1951691075on_val(A_2,A_2),transi208336786on_val(R))) ).

tff(fact_118_rtrancl_Ortrancl__refl,axiom,
    ! [A_2: produc12694297on_val,R: fun_Pr693020585l_bool] : hBOOL(member563141460on_val(produc870913623on_val(A_2,A_2),transi921647814on_val(R))) ).

tff(fact_119_rtrancl_Ortrancl__refl,axiom,
    ! [A_2: produc1102272487on_val,R: fun_Pr903661919l_bool] : hBOOL(member808015754on_val(produc1564932627on_val(A_2,A_2),transi910771962on_val(R))) ).

tff(fact_120_rtrancl_Ortrancl__refl,axiom,
    ! [A_2: produc124828825on_val,R: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(produc1441475159on_val(A_2,A_2),transi2024712006on_val(R))) ).

tff(fact_121_rtrancl_Ortrancl__refl,axiom,
    ! [A_2: produc2061676504on_val,R: fun_Pr859510977l_bool] : hBOOL(member875476972on_val(produc1611380469on_val(A_2,A_2),transi374442731on_val(R))) ).

tff(fact_122_r__into__rtrancl,axiom,
    ! [P: produc1466422861on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(P,R))
     => hBOOL(member88670778on_val(P,transi208336786on_val(R))) ) ).

tff(fact_123_r__into__rtrancl,axiom,
    ! [P: produc409205479on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(P,R))
     => hBOOL(member563141460on_val(P,transi921647814on_val(R))) ) ).

tff(fact_124_r__into__rtrancl,axiom,
    ! [P: produc231486621on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(P,R))
     => hBOOL(member808015754on_val(P,transi910771962on_val(R))) ) ).

tff(fact_125_r__into__rtrancl,axiom,
    ! [P: produc1102272487on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(P,R))
     => hBOOL(member773094996on_val(P,transi2024712006on_val(R))) ) ).

tff(fact_126_r__into__rtrancl,axiom,
    ! [P: produc430140671on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(P,R))
     => hBOOL(member875476972on_val(P,transi374442731on_val(R))) ) ).

tff(fact_127_exp_Osimps_I168_J,axiom,
    ! [Exp_41: exp_list_char,List1_21: list_char,List2_21: list_char,Exp1_11: exp_list_char,List_21: list_char,A_13: list_char,Exp2_11: exp_list_char] : ( fAcc_list_char(Exp_41,List1_21,List2_21) != tryCatch_list_char(Exp1_11,List_21,A_13,Exp2_11) ) ).

tff(fact_128_rtrancl__idemp,axiom,
    ! [R: fun_Pr302334223l_bool] : ( transi208336786on_val(transi208336786on_val(R)) = transi208336786on_val(R) ) ).

tff(fact_129_rtrancl__idemp,axiom,
    ! [R: fun_Pr693020585l_bool] : ( transi921647814on_val(transi921647814on_val(R)) = transi921647814on_val(R) ) ).

tff(fact_130_rtrancl__idemp,axiom,
    ! [R: fun_Pr903661919l_bool] : ( transi910771962on_val(transi910771962on_val(R)) = transi910771962on_val(R) ) ).

tff(fact_131_rtrancl__idemp,axiom,
    ! [R: fun_Pr691271849l_bool] : ( transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R) ) ).

tff(fact_132_rtrancl__idemp,axiom,
    ! [R: fun_Pr859510977l_bool] : ( transi374442731on_val(transi374442731on_val(R)) = transi374442731on_val(R) ) ).

tff(fact_133_exp_Osimps_I2_J,axiom,
    ! [List_20: list_char,Exp_11: exp_list_char,List_19: list_char,Exp_10: exp_list_char] :
      ( ( cast_list_char(List_20,Exp_11) = cast_list_char(List_19,Exp_10) )
    <=> ( ( List_20 = List_19 )
        & ( Exp_11 = Exp_10 ) ) ) ).

tff(fact_134_exp_Osimps_I7_J,axiom,
    ! [Exp_11: exp_list_char,List1_5: list_char,List2_5: list_char,Exp_10: exp_list_char,List1_4: list_char,List2_4: list_char] :
      ( ( fAcc_list_char(Exp_11,List1_5,List2_5) = fAcc_list_char(Exp_10,List1_4,List2_4) )
    <=> ( ( Exp_11 = Exp_10 )
        & ( List1_5 = List1_4 )
        & ( List2_5 = List2_4 ) ) ) ).

tff(fact_135_exp_Osimps_I15_J,axiom,
    ! [Exp1_10: exp_list_char,List_20: list_char,A_2: list_char,Exp2_10: exp_list_char,Exp1_9: exp_list_char,List_19: list_char,A_12: list_char,Exp2_9: exp_list_char] :
      ( ( tryCatch_list_char(Exp1_10,List_20,A_2,Exp2_10) = tryCatch_list_char(Exp1_9,List_19,A_12,Exp2_9) )
    <=> ( ( Exp1_10 = Exp1_9 )
        & ( List_20 = List_19 )
        & ( A_2 = A_12 )
        & ( Exp2_10 = Exp2_9 ) ) ) ).

tff(fact_136_rtrancl__trans,axiom,
    ! [C_1: produc430140671on_val,A_2: produc430140671on_val,B: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,B),transi208336786on_val(R)))
     => ( hBOOL(member88670778on_val(produc1951691075on_val(B,C_1),transi208336786on_val(R)))
       => hBOOL(member88670778on_val(produc1951691075on_val(A_2,C_1),transi208336786on_val(R))) ) ) ).

tff(fact_137_rtrancl__trans,axiom,
    ! [C_1: produc12694297on_val,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
     => ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R)))
       => hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).

tff(fact_138_rtrancl__trans,axiom,
    ! [C_1: produc1102272487on_val,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
     => ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R)))
       => hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).

tff(fact_139_rtrancl__trans,axiom,
    ! [C_1: produc124828825on_val,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R)))
       => hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).

tff(fact_140_rtrancl__trans,axiom,
    ! [C_1: produc2061676504on_val,A_2: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,B),transi374442731on_val(R)))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(B,C_1),transi374442731on_val(R)))
       => hBOOL(member875476972on_val(produc1611380469on_val(A_2,C_1),transi374442731on_val(R))) ) ) ).

tff(fact_141_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc430140671on_val,A_2: produc430140671on_val,B: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,B),transi208336786on_val(R)))
     => ( hBOOL(member88670778on_val(produc1951691075on_val(B,C_1),R))
       => hBOOL(member88670778on_val(produc1951691075on_val(A_2,C_1),transi208336786on_val(R))) ) ) ).

tff(fact_142_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc12694297on_val,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
     => ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),R))
       => hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).

tff(fact_143_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc1102272487on_val,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
     => ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),R))
       => hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).

tff(fact_144_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc124828825on_val,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),R))
       => hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).

tff(fact_145_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc2061676504on_val,A_2: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,B),transi374442731on_val(R)))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(B,C_1),R))
       => hBOOL(member875476972on_val(produc1611380469on_val(A_2,C_1),transi374442731on_val(R))) ) ) ).

tff(fact_146_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc430140671on_val,A_2: produc430140671on_val,B: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,B),R))
     => ( hBOOL(member88670778on_val(produc1951691075on_val(B,C_1),transi208336786on_val(R)))
       => hBOOL(member88670778on_val(produc1951691075on_val(A_2,C_1),transi208336786on_val(R))) ) ) ).

tff(fact_147_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc12694297on_val,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),R))
     => ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R)))
       => hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).

tff(fact_148_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc1102272487on_val,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),R))
     => ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R)))
       => hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).

tff(fact_149_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc124828825on_val,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),R))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R)))
       => hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).

tff(fact_150_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc2061676504on_val,A_2: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,B),R))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(B,C_1),transi374442731on_val(R)))
       => hBOOL(member875476972on_val(produc1611380469on_val(A_2,C_1),transi374442731on_val(R))) ) ) ).

tff(fact_151_exp_Osimps_I53_J,axiom,
    ! [Exp_40: exp_list_char,List1_20: list_char,List2_20: list_char,List_18: list_char,Exp_39: exp_list_char] : ( fAcc_list_char(Exp_40,List1_20,List2_20) != cast_list_char(List_18,Exp_39) ) ).

tff(fact_152_exp_Osimps_I52_J,axiom,
    ! [List_17: list_char,Exp_38: exp_list_char,Exp_37: exp_list_char,List1_19: list_char,List2_19: list_char] : ( cast_list_char(List_17,Exp_38) != fAcc_list_char(Exp_37,List1_19,List2_19) ) ).

tff(fact_153_exp_Osimps_I69_J,axiom,
    ! [Exp1_8: exp_list_char,List_16: list_char,A_11: list_char,Exp2_8: exp_list_char,List_15: list_char,Exp_36: exp_list_char] : ( tryCatch_list_char(Exp1_8,List_16,A_11,Exp2_8) != cast_list_char(List_15,Exp_36) ) ).

tff(fact_154_exp_Osimps_I68_J,axiom,
    ! [List_14: list_char,Exp_35: exp_list_char,Exp1_7: exp_list_char,List_13: list_char,A_10: list_char,Exp2_7: exp_list_char] : ( cast_list_char(List_14,Exp_35) != tryCatch_list_char(Exp1_7,List_13,A_10,Exp2_7) ) ).

tff(fact_155_exp_Osimps_I169_J,axiom,
    ! [Exp1_6: exp_list_char,List_12: list_char,A_9: list_char,Exp2_6: exp_list_char,Exp_34: exp_list_char,List1_18: list_char,List2_18: list_char] : ( tryCatch_list_char(Exp1_6,List_12,A_9,Exp2_6) != fAcc_list_char(Exp_34,List1_18,List2_18) ) ).

tff(fact_156_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1511900787l_bool,Ax: produc430140671on_val,Ay: produc430140671on_val,Bx: produc430140671on_val,By: produc430140671on_val,R: fun_Pr1329133739l_bool] :
      ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Ax,Ay),produc1951691075on_val(Bx,By)),transi1751449568on_val(R)))
     => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Ax),Ay))
       => ( ! [A_8: produc430140671on_val,B_1: produc430140671on_val,Aa: produc430140671on_val,Ba: produc430140671on_val] :
              ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Ax,Ay),produc1951691075on_val(A_8,B_1)),transi1751449568on_val(R)))
             => ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(A_8,B_1),produc1951691075on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_157_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr598845249l_bool,Ax: produc12694297on_val,Ay: produc12694297on_val,Bx: produc12694297on_val,By: produc12694297on_val,R: fun_Pr27327839l_bool] :
      ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay))
       => ( ! [A_8: produc12694297on_val,B_1: produc12694297on_val,Aa: produc12694297on_val,Ba: produc12694297on_val] :
              ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(A_8,B_1)),transi594096122on_val(R)))
             => ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_8,B_1),produc870913623on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_158_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr220980979l_bool,Ax: produc1102272487on_val,Ay: produc1102272487on_val,Bx: produc1102272487on_val,By: produc1102272487on_val,R: fun_Pr111684683l_bool] :
      ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
     => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay))
       => ( ! [A_8: produc1102272487on_val,B_1: produc1102272487on_val,Aa: produc1102272487on_val,Ba: produc1102272487on_val] :
              ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(A_8,B_1)),transi678815536on_val(R)))
             => ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_8,B_1),produc1564932627on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_159_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
       => ( ! [A_8: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A_8,B_1)),transi910771962on_val(R)))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_8,B_1),produc1441475159on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_160_rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
       => ( ! [A_8: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A_8,B_1)),transi921647814on_val(R)))
             => ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_8,B_1),produc899768717on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_161_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Ax,Ay),produc1611380469on_val(Bx,By)),transi208336786on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay))
       => ( ! [A_8: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Ax,Ay),produc1611380469on_val(A_8,B_1)),transi208336786on_val(R)))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(A_8,B_1),produc1611380469on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_162_rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
       => ( ! [A_8: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A_8,B_1)),transi2024712006on_val(R)))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_8,B_1),produc1259058957on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_163_rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Ax,Ay),produc379668296on_val(Bx,By)),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay))
       => ( ! [A_8: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Ax,Ay),produc379668296on_val(A_8,B_1)),transi374442731on_val(R)))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(A_8,B_1),produc379668296on_val(Aa,Ba)),R))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_8),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_164_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1511900787l_bool,Ax: produc430140671on_val,Ay: produc430140671on_val,Bx: produc430140671on_val,By: produc430140671on_val,R: fun_Pr1329133739l_bool] :
      ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Ax,Ay),produc1951691075on_val(Bx,By)),transi1751449568on_val(R)))
     => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Bx),By))
       => ( ! [A_8: produc430140671on_val,B_1: produc430140671on_val,Aa: produc430140671on_val,Ba: produc430140671on_val] :
              ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(A_8,B_1),produc1951691075on_val(Aa,Ba)),R))
             => ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Aa,Ba),produc1951691075on_val(Bx,By)),transi1751449568on_val(R)))
               => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_165_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr598845249l_bool,Ax: produc12694297on_val,Ay: produc12694297on_val,Bx: produc12694297on_val,By: produc12694297on_val,R: fun_Pr27327839l_bool] :
      ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By))
       => ( ! [A_8: produc12694297on_val,B_1: produc12694297on_val,Aa: produc12694297on_val,Ba: produc12694297on_val] :
              ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_8,B_1),produc870913623on_val(Aa,Ba)),R))
             => ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Aa,Ba),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_166_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr220980979l_bool,Ax: produc1102272487on_val,Ay: produc1102272487on_val,Bx: produc1102272487on_val,By: produc1102272487on_val,R: fun_Pr111684683l_bool] :
      ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
     => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By))
       => ( ! [A_8: produc1102272487on_val,B_1: produc1102272487on_val,Aa: produc1102272487on_val,Ba: produc1102272487on_val] :
              ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_8,B_1),produc1564932627on_val(Aa,Ba)),R))
             => ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Aa,Ba),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
               => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_167_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
       => ( ! [A_8: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_8,B_1),produc1441475159on_val(Aa,Ba)),R))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Aa,Ba),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_168_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
       => ( ! [A_8: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_8,B_1),produc899768717on_val(Aa,Ba)),R))
             => ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Aa,Ba),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_169_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Ax,Ay),produc1611380469on_val(Bx,By)),transi208336786on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By))
       => ( ! [A_8: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(A_8,B_1),produc1611380469on_val(Aa,Ba)),R))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Aa,Ba),produc1611380469on_val(Bx,By)),transi208336786on_val(R)))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_170_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
       => ( ! [A_8: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_8,B_1),produc1259058957on_val(Aa,Ba)),R))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Aa,Ba),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_171_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Ax,Ay),produc379668296on_val(Bx,By)),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By))
       => ( ! [A_8: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(A_8,B_1),produc379668296on_val(Aa,Ba)),R))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Aa,Ba),produc379668296on_val(Bx,By)),transi374442731on_val(R)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_8),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_172_converse__rtranclE2,axiom,
    ! [Xa: produc430140671on_val,Xb: produc430140671on_val,Za: produc430140671on_val,Zb: produc430140671on_val,R: fun_Pr1329133739l_bool] :
      ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Xa,Xb),produc1951691075on_val(Za,Zb)),transi1751449568on_val(R)))
     => ( ( produc1951691075on_val(Xa,Xb) != produc1951691075on_val(Za,Zb) )
       => ~ ! [A_8: produc430140671on_val,B_1: produc430140671on_val] :
              ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Xa,Xb),produc1951691075on_val(A_8,B_1)),R))
             => ~ hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(A_8,B_1),produc1951691075on_val(Za,Zb)),transi1751449568on_val(R))) ) ) ) ).

tff(fact_173_converse__rtranclE2,axiom,
    ! [Xa: produc12694297on_val,Xb: produc12694297on_val,Za: produc12694297on_val,Zb: produc12694297on_val,R: fun_Pr27327839l_bool] :
      ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa,Xb),produc870913623on_val(Za,Zb)),transi594096122on_val(R)))
     => ( ( produc870913623on_val(Xa,Xb) != produc870913623on_val(Za,Zb) )
       => ~ ! [A_8: produc12694297on_val,B_1: produc12694297on_val] :
              ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa,Xb),produc870913623on_val(A_8,B_1)),R))
             => ~ hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_8,B_1),produc870913623on_val(Za,Zb)),transi594096122on_val(R))) ) ) ) ).

tff(fact_174_converse__rtranclE2,axiom,
    ! [Xa: produc1102272487on_val,Xb: produc1102272487on_val,Za: produc1102272487on_val,Zb: produc1102272487on_val,R: fun_Pr111684683l_bool] :
      ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa,Xb),produc1564932627on_val(Za,Zb)),transi678815536on_val(R)))
     => ( ( produc1564932627on_val(Xa,Xb) != produc1564932627on_val(Za,Zb) )
       => ~ ! [A_8: produc1102272487on_val,B_1: produc1102272487on_val] :
              ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa,Xb),produc1564932627on_val(A_8,B_1)),R))
             => ~ hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_8,B_1),produc1564932627on_val(Za,Zb)),transi678815536on_val(R))) ) ) ) ).

tff(fact_175_converse__rtranclE2,axiom,
    ! [Xa: produc124828825on_val,Xb: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa,Xb),produc1441475159on_val(Za,Zb)),transi910771962on_val(R)))
     => ( ( produc1441475159on_val(Xa,Xb) != produc1441475159on_val(Za,Zb) )
       => ~ ! [A_8: produc124828825on_val,B_1: produc124828825on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa,Xb),produc1441475159on_val(A_8,B_1)),R))
             => ~ hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_8,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R))) ) ) ) ).

tff(fact_176_converse__rtranclE2,axiom,
    ! [Xa: fun_na939144002on_val,Xb: fun_li1432931796on_val,Za: fun_na939144002on_val,Zb: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa,Xb),produc899768717on_val(Za,Zb)),transi921647814on_val(R)))
     => ( ( produc899768717on_val(Xa,Xb) != produc899768717on_val(Za,Zb) )
       => ~ ! [A_8: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa,Xb),produc899768717on_val(A_8,B_1)),R))
             => ~ hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_8,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R))) ) ) ) ).

tff(fact_177_converse__rtranclE2,axiom,
    ! [Xa: produc2061676504on_val,Xb: produc2061676504on_val,Za: produc2061676504on_val,Zb: produc2061676504on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Xa,Xb),produc1611380469on_val(Za,Zb)),transi208336786on_val(R)))
     => ( ( produc1611380469on_val(Xa,Xb) != produc1611380469on_val(Za,Zb) )
       => ~ ! [A_8: produc2061676504on_val,B_1: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Xa,Xb),produc1611380469on_val(A_8,B_1)),R))
             => ~ hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(A_8,B_1),produc1611380469on_val(Za,Zb)),transi208336786on_val(R))) ) ) ) ).

tff(fact_178_converse__rtranclE2,axiom,
    ! [Xa: exp_list_char,Xb: produc12694297on_val,Za: exp_list_char,Zb: produc12694297on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa,Xb),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R)))
     => ( ( produc1259058957on_val(Xa,Xb) != produc1259058957on_val(Za,Zb) )
       => ~ ! [A_8: exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa,Xb),produc1259058957on_val(A_8,B_1)),R))
             => ~ hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_8,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R))) ) ) ) ).

tff(fact_179_converse__rtranclE2,axiom,
    ! [Xa: list_exp_list_char,Xb: produc12694297on_val,Za: list_exp_list_char,Zb: produc12694297on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Xa,Xb),produc379668296on_val(Za,Zb)),transi374442731on_val(R)))
     => ( ( produc379668296on_val(Xa,Xb) != produc379668296on_val(Za,Zb) )
       => ~ ! [A_8: list_exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Xa,Xb),produc379668296on_val(A_8,B_1)),R))
             => ~ hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(A_8,B_1),produc379668296on_val(Za,Zb)),transi374442731on_val(R))) ) ) ) ).

tff(fact_180_rtranclE,axiom,
    ! [A_2: produc430140671on_val,B: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,B),transi208336786on_val(R)))
     => ( ( A_2 != B )
       => ~ ! [Y: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,Y),transi208336786on_val(R)))
             => ~ hBOOL(member88670778on_val(produc1951691075on_val(Y,B),R)) ) ) ) ).

tff(fact_181_rtranclE,axiom,
    ! [A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
     => ( ( A_2 != B )
       => ~ ! [Y: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(A_2,Y),transi921647814on_val(R)))
             => ~ hBOOL(member563141460on_val(produc870913623on_val(Y,B),R)) ) ) ) ).

tff(fact_182_rtranclE,axiom,
    ! [A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
     => ( ( A_2 != B )
       => ~ ! [Y: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,Y),transi910771962on_val(R)))
             => ~ hBOOL(member808015754on_val(produc1564932627on_val(Y,B),R)) ) ) ) ).

tff(fact_183_rtranclE,axiom,
    ! [A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
     => ( ( A_2 != B )
       => ~ ! [Y: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,Y),transi2024712006on_val(R)))
             => ~ hBOOL(member773094996on_val(produc1441475159on_val(Y,B),R)) ) ) ) ).

tff(fact_184_rtranclE,axiom,
    ! [A_2: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,B),transi374442731on_val(R)))
     => ( ( A_2 != B )
       => ~ ! [Y: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,Y),transi374442731on_val(R)))
             => ~ hBOOL(member875476972on_val(produc1611380469on_val(Y,B),R)) ) ) ) ).

tff(fact_185_converse__rtranclE,axiom,
    ! [X: produc430140671on_val,Z_1: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(X,Z_1),transi208336786on_val(R)))
     => ( ( X != Z_1 )
       => ~ ! [Y: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(X,Y),R))
             => ~ hBOOL(member88670778on_val(produc1951691075on_val(Y,Z_1),transi208336786on_val(R))) ) ) ) ).

tff(fact_186_converse__rtranclE,axiom,
    ! [X: produc12694297on_val,Z_1: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(X,Z_1),transi921647814on_val(R)))
     => ( ( X != Z_1 )
       => ~ ! [Y: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(X,Y),R))
             => ~ hBOOL(member563141460on_val(produc870913623on_val(Y,Z_1),transi921647814on_val(R))) ) ) ) ).

tff(fact_187_converse__rtranclE,axiom,
    ! [X: produc1102272487on_val,Z_1: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(X,Z_1),transi910771962on_val(R)))
     => ( ( X != Z_1 )
       => ~ ! [Y: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(X,Y),R))
             => ~ hBOOL(member808015754on_val(produc1564932627on_val(Y,Z_1),transi910771962on_val(R))) ) ) ) ).

tff(fact_188_converse__rtranclE,axiom,
    ! [X: produc124828825on_val,Z_1: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(X,Z_1),transi2024712006on_val(R)))
     => ( ( X != Z_1 )
       => ~ ! [Y: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(X,Y),R))
             => ~ hBOOL(member773094996on_val(produc1441475159on_val(Y,Z_1),transi2024712006on_val(R))) ) ) ) ).

tff(fact_189_converse__rtranclE,axiom,
    ! [X: produc2061676504on_val,Z_1: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(X,Z_1),transi374442731on_val(R)))
     => ( ( X != Z_1 )
       => ~ ! [Y: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(X,Y),R))
             => ~ hBOOL(member875476972on_val(produc1611380469on_val(Y,Z_1),transi374442731on_val(R))) ) ) ) ).

tff(fact_190_rtrancl__induct,axiom,
    ! [Pa: fun_Pr859510977l_bool,A_2: produc430140671on_val,B: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,B),transi208336786on_val(R)))
     => ( hBOOL(hAPP_P1333315679l_bool(Pa,A_2))
       => ( ! [Y: produc430140671on_val,Z: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,Y),transi208336786on_val(R)))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(Y,Z),R))
               => ( hBOOL(hAPP_P1333315679l_bool(Pa,Y))
                 => hBOOL(hAPP_P1333315679l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(Pa,B)) ) ) ) ).

tff(fact_191_rtrancl__induct,axiom,
    ! [Pa: fun_Pr1696029455l_bool,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(Pa,A_2))
       => ( ! [Y: produc12694297on_val,Z: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(A_2,Y),transi921647814on_val(R)))
             => ( hBOOL(member563141460on_val(produc870913623on_val(Y,Z),R))
               => ( hBOOL(hAPP_P159683425l_bool(Pa,Y))
                 => hBOOL(hAPP_P159683425l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(Pa,B)) ) ) ) ).

tff(fact_192_rtrancl__induct,axiom,
    ! [Pa: fun_Pr691271849l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
     => ( hBOOL(hAPP_P282169671l_bool(Pa,A_2))
       => ( ! [Y: produc1102272487on_val,Z: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,Y),transi910771962on_val(R)))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(Y,Z),R))
               => ( hBOOL(hAPP_P282169671l_bool(Pa,Y))
                 => hBOOL(hAPP_P282169671l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(Pa,B)) ) ) ) ).

tff(fact_193_rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,A_2))
       => ( ! [Y: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,Y),transi2024712006on_val(R)))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(Y,Z),R))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Y))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).

tff(fact_194_rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A_2: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,B),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,A_2))
       => ( ! [Y: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,Y),transi374442731on_val(R)))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(Y,Z),R))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Y))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,B)) ) ) ) ).

tff(fact_195_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr859510977l_bool,A_2: produc430140671on_val,B: produc430140671on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A_2,B),transi208336786on_val(R)))
     => ( hBOOL(hAPP_P1333315679l_bool(Pa,B))
       => ( ! [Y: produc430140671on_val,Z: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(Y,Z),R))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(Z,B),transi208336786on_val(R)))
               => ( hBOOL(hAPP_P1333315679l_bool(Pa,Z))
                 => hBOOL(hAPP_P1333315679l_bool(Pa,Y)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(Pa,A_2)) ) ) ) ).

tff(fact_196_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr1696029455l_bool,A_2: produc12694297on_val,B: produc12694297on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(Pa,B))
       => ( ! [Y: produc12694297on_val,Z: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(Y,Z),R))
             => ( hBOOL(member563141460on_val(produc870913623on_val(Z,B),transi921647814on_val(R)))
               => ( hBOOL(hAPP_P159683425l_bool(Pa,Z))
                 => hBOOL(hAPP_P159683425l_bool(Pa,Y)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(Pa,A_2)) ) ) ) ).

tff(fact_197_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr691271849l_bool,A_2: produc1102272487on_val,B: produc1102272487on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
     => ( hBOOL(hAPP_P282169671l_bool(Pa,B))
       => ( ! [Y: produc1102272487on_val,Z: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(Y,Z),R))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(Z,B),transi910771962on_val(R)))
               => ( hBOOL(hAPP_P282169671l_bool(Pa,Z))
                 => hBOOL(hAPP_P282169671l_bool(Pa,Y)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(Pa,A_2)) ) ) ) ).

tff(fact_198_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A_2: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
       => ( ! [Y: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(Y,Z),R))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R)))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Y)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,A_2)) ) ) ) ).

tff(fact_199_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A_2: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A_2,B),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,B))
       => ( ! [Y: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(Y,Z),R))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(Z,B),transi374442731on_val(R)))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Z))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Y)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,A_2)) ) ) ) ).

tff(fact_200_ListReds1,axiom,
    ! [Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(Ea,Esa),S_1),produc379668296on_val(cons_exp_list_char(E_a,Esa),S)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_201_red__reds_OListRed1,axiom,
    ! [Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(Ea,Esa),S_1),produc379668296on_val(cons_exp_list_char(E_a,Esa),S)),reds(Pa))) ) ).

tff(fact_202_ListRedsVal,axiom,
    ! [Esa: list_exp_list_char,Es_a: list_exp_list_char,S_2: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,V: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_0),produc1259058957on_val(val_list_char(V),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1_1),produc379668296on_val(Es_a,S_2)),transi374442731on_val(reds(Pa))))
       => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(Ea,Esa),S_0),produc379668296on_val(cons_exp_list_char(val_list_char(V),Es_a),S_2)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_203_ListReds2,axiom,
    ! [V: val,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),transi374442731on_val(reds(Pa))))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(val_list_char(V),Esa),S_1),produc379668296on_val(cons_exp_list_char(val_list_char(V),Es_a),S)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_204_TryRedsVal,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,V: val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(val_list_char(V),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V_1,E_2),S_1),produc1259058957on_val(val_list_char(V),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_205_exp_Osimps_I3_J,axiom,
    ! [Val_11: val,Val_10: val] :
      ( ( val_list_char(Val_11) = val_list_char(Val_10) )
    <=> ( Val_11 = Val_10 ) ) ).

tff(fact_206_exp_Osimps_I92_J,axiom,
    ! [Val_9: val,Exp1_5: exp_list_char,List_11: list_char,A_7: list_char,Exp2_5: exp_list_char] : ( val_list_char(Val_9) != tryCatch_list_char(Exp1_5,List_11,A_7,Exp2_5) ) ).

tff(fact_207_exp_Osimps_I93_J,axiom,
    ! [Exp1_4: exp_list_char,List_10: list_char,A_6: list_char,Exp2_4: exp_list_char,Val_8: val] : ( tryCatch_list_char(Exp1_4,List_10,A_6,Exp2_4) != val_list_char(Val_8) ) ).

tff(fact_208_exp_Osimps_I76_J,axiom,
    ! [Val_7: val,Exp_33: exp_list_char,List1_17: list_char,List2_17: list_char] : ( val_list_char(Val_7) != fAcc_list_char(Exp_33,List1_17,List2_17) ) ).

tff(fact_209_exp_Osimps_I77_J,axiom,
    ! [Exp_32: exp_list_char,List1_16: list_char,List2_16: list_char,Val_6: val] : ( fAcc_list_char(Exp_32,List1_16,List2_16) != val_list_char(Val_6) ) ).

tff(fact_210_exp_Osimps_I45_J,axiom,
    ! [Val_5: val,List_9: list_char,Exp_31: exp_list_char] : ( val_list_char(Val_5) != cast_list_char(List_9,Exp_31) ) ).

tff(fact_211_exp_Osimps_I44_J,axiom,
    ! [List_8: list_char,Exp_30: exp_list_char,Val_4: val] : ( cast_list_char(List_8,Exp_30) != val_list_char(Val_4) ) ).

tff(fact_212_red__reds_ORedTry,axiom,
    ! [V: val,C: list_char,V_1: list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(val_list_char(V),C,V_1,E_2),S_1),produc1259058957on_val(val_list_char(V),S_1)),red(Pa))) ).

tff(fact_213_red__reds_OListRed2,axiom,
    ! [V: val,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),reds(Pa)))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(val_list_char(V),Esa),S_1),produc379668296on_val(cons_exp_list_char(val_list_char(V),Es_a),S)),reds(Pa))) ) ).

tff(fact_214_CallRedsParams,axiom,
    ! [V: val,M: list_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),transi374442731on_val(reds(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(val_list_char(V),M,Esa),S_1),produc1259058957on_val(call_list_char(val_list_char(V),M,Es_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_215_red__reds_OCallParams,axiom,
    ! [V: val,M: list_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),reds(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(val_list_char(V),M,Esa),S_1),produc1259058957on_val(call_list_char(val_list_char(V),M,Es_a),S)),red(Pa))) ) ).

tff(fact_216_CastRedsNull,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(val_list_char(null),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(val_list_char(null),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_217_exp_Osimps_I81_J,axiom,
    ! [Exp_29: exp_list_char,List1_15: list_char,List2_15: list_exp_list_char,Val_3: val] : ( call_list_char(Exp_29,List1_15,List2_15) != val_list_char(Val_3) ) ).

tff(fact_218_exp_Osimps_I80_J,axiom,
    ! [Val_2: val,Exp_28: exp_list_char,List1_14: list_char,List2_14: list_exp_list_char] : ( val_list_char(Val_2) != call_list_char(Exp_28,List1_14,List2_14) ) ).

tff(fact_219_mem__def,axiom,
    ! [X: produc1466422861on_val,A_5: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(X,A_5))
    <=> hBOOL(hAPP_P2028072621l_bool(A_5,X)) ) ).

tff(fact_220_mem__def,axiom,
    ! [X: produc409205479on_val,A_5: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(X,A_5))
    <=> hBOOL(hAPP_P1221872711l_bool(A_5,X)) ) ).

tff(fact_221_mem__def,axiom,
    ! [X: produc231486621on_val,A_5: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(X,A_5))
    <=> hBOOL(hAPP_P378063101l_bool(A_5,X)) ) ).

tff(fact_222_mem__def,axiom,
    ! [X: produc1102272487on_val,A_5: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(X,A_5))
    <=> hBOOL(hAPP_P282169671l_bool(A_5,X)) ) ).

tff(fact_223_mem__def,axiom,
    ! [X: produc430140671on_val,A_5: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(X,A_5))
    <=> hBOOL(hAPP_P1333315679l_bool(A_5,X)) ) ).

tff(fact_224_exp_Osimps_I57_J,axiom,
    ! [Exp_27: exp_list_char,List1_13: list_char,List2_13: list_exp_list_char,List_7: list_char,Exp_26: exp_list_char] : ( call_list_char(Exp_27,List1_13,List2_13) != cast_list_char(List_7,Exp_26) ) ).

tff(fact_225_exp_Osimps_I56_J,axiom,
    ! [List_6: list_char,Exp_25: exp_list_char,Exp_24: exp_list_char,List1_12: list_char,List2_12: list_exp_list_char] : ( cast_list_char(List_6,Exp_25) != call_list_char(Exp_24,List1_12,List2_12) ) ).

tff(fact_226_exp_Osimps_I156_J,axiom,
    ! [Exp_23: exp_list_char,List1_11: list_char,List2_11: list_char,Exp_22: exp_list_char,List1_10: list_char,List2_10: list_exp_list_char] : ( fAcc_list_char(Exp_23,List1_11,List2_11) != call_list_char(Exp_22,List1_10,List2_10) ) ).

tff(fact_227_exp_Osimps_I157_J,axiom,
    ! [Exp_21: exp_list_char,List1_9: list_char,List2_9: list_exp_list_char,Exp_20: exp_list_char,List1_8: list_char,List2_8: list_char] : ( call_list_char(Exp_21,List1_9,List2_9) != fAcc_list_char(Exp_20,List1_8,List2_8) ) ).

tff(fact_228_exp_Osimps_I195_J,axiom,
    ! [Exp1_3: exp_list_char,List_5: list_char,A_4: list_char,Exp2_3: exp_list_char,Exp_19: exp_list_char,List1_7: list_char,List2_7: list_exp_list_char] : ( tryCatch_list_char(Exp1_3,List_5,A_4,Exp2_3) != call_list_char(Exp_19,List1_7,List2_7) ) ).

tff(fact_229_exp_Osimps_I194_J,axiom,
    ! [Exp_18: exp_list_char,List1_6: list_char,List2_6: list_exp_list_char,Exp1_2: exp_list_char,List_4: list_char,A_3: list_char,Exp2_2: exp_list_char] : ( call_list_char(Exp_18,List1_6,List2_6) != tryCatch_list_char(Exp1_2,List_4,A_3,Exp2_2) ) ).

tff(fact_230_exp_Osimps_I9_J,axiom,
    ! [Exp_11: exp_list_char,List1_5: list_char,List2_5: list_exp_list_char,Exp_10: exp_list_char,List1_4: list_char,List2_4: list_exp_list_char] :
      ( ( call_list_char(Exp_11,List1_5,List2_5) = call_list_char(Exp_10,List1_4,List2_4) )
    <=> ( ( Exp_11 = Exp_10 )
        & ( List1_5 = List1_4 )
        & ( List2_5 = List2_4 ) ) ) ).

tff(fact_231_red__reds_OCallObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S_1),produc1259058957on_val(call_list_char(E_a,M,Esa),S)),red(Pa))) ) ).

tff(fact_232_CallRedsObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S_1),produc1259058957on_val(call_list_char(E_a,M,Esa),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_233_red__reds_ORedCastNull,axiom,
    ! [C: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,val_list_char(null)),S_1),produc1259058957on_val(val_list_char(null),S_1)),red(Pa))) ).

tff(fact_234_FAccRedsThrow,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A_2),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(throw_list_char(A_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_235_CastRedsThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A_2),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(throw_list_char(A_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_236_exp_Osimps_I91_J,axiom,
    ! [Exp_17: exp_list_char,Val_1: val] : ( throw_list_char(Exp_17) != val_list_char(Val_1) ) ).

tff(fact_237_exp_Osimps_I90_J,axiom,
    ! [Val: val,Exp_16: exp_list_char] : ( val_list_char(Val) != throw_list_char(Exp_16) ) ).

tff(fact_238_exp_Osimps_I193_J,axiom,
    ! [Exp_15: exp_list_char,Exp_14: exp_list_char,List1_3: list_char,List2_3: list_exp_list_char] : ( throw_list_char(Exp_15) != call_list_char(Exp_14,List1_3,List2_3) ) ).

tff(fact_239_exp_Osimps_I192_J,axiom,
    ! [Exp_13: exp_list_char,List1_2: list_char,List2_2: list_exp_list_char,Exp_12: exp_list_char] : ( call_list_char(Exp_13,List1_2,List2_2) != throw_list_char(Exp_12) ) ).

tff(fact_240_exp_Osimps_I14_J,axiom,
    ! [Exp_11: exp_list_char,Exp_10: exp_list_char] :
      ( ( throw_list_char(Exp_11) = throw_list_char(Exp_10) )
    <=> ( Exp_11 = Exp_10 ) ) ).

tff(fact_241_exp_Osimps_I224_J,axiom,
    ! [Exp_9: exp_list_char,Exp1_1: exp_list_char,List_3: list_char,A_1: list_char,Exp2_1: exp_list_char] : ( throw_list_char(Exp_9) != tryCatch_list_char(Exp1_1,List_3,A_1,Exp2_1) ) ).

tff(fact_242_exp_Osimps_I225_J,axiom,
    ! [Exp1: exp_list_char,List_2: list_char,A: list_char,Exp2: exp_list_char,Exp_8: exp_list_char] : ( tryCatch_list_char(Exp1,List_2,A,Exp2) != throw_list_char(Exp_8) ) ).

tff(fact_243_exp_Osimps_I167_J,axiom,
    ! [Exp_7: exp_list_char,Exp_6: exp_list_char,List1_1: list_char,List2_1: list_char] : ( throw_list_char(Exp_7) != fAcc_list_char(Exp_6,List1_1,List2_1) ) ).

tff(fact_244_exp_Osimps_I166_J,axiom,
    ! [Exp_5: exp_list_char,List1: list_char,List2: list_char,Exp_4: exp_list_char] : ( fAcc_list_char(Exp_5,List1,List2) != throw_list_char(Exp_4) ) ).

tff(fact_245_exp_Osimps_I67_J,axiom,
    ! [Exp_3: exp_list_char,List_1: list_char,Exp_2: exp_list_char] : ( throw_list_char(Exp_3) != cast_list_char(List_1,Exp_2) ) ).

tff(fact_246_exp_Osimps_I66_J,axiom,
    ! [List: list_char,Exp_1: exp_list_char,Exp: exp_list_char] : ( cast_list_char(List,Exp_1) != throw_list_char(Exp) ) ).

tff(fact_247_red__reds_OThrowRed,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(Ea),S_1),produc1259058957on_val(throw_list_char(E_a),S)),red(Pa))) ) ).

%----Conjectures (4)
tff(conj_0,hypothesis,
    hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(e,produc899768717on_val(h_1,l_1)),produc1259058957on_val(e_2,produc899768717on_val(h,l))),red(p))) ).

tff(conj_1,hypothesis,
    hBOOL(wTrt(p,h_1,e_1,e,t)) ).

tff(conj_2,hypothesis,
    hBOOL(hconf_97414254t_char(p,h_1)) ).

% tff(conj_3,conjecture,
%     hBOOL(hconf_97414254t_char(p,h)) ).

%------------------------------------------------------------------------------